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id="toc-After_World_War_II" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#After_World_War_II"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>After World War II</span> </div> </a> <ul id="toc-After_World_War_II-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Problems_addressed" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Problems_addressed"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Problems addressed</span> </div> </a> <ul id="toc-Problems_addressed-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Management_science" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Management_science"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Management science</span> </div> </a> <button 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class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Societies_and_journals"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Societies and journals</span> </div> </a> <button aria-controls="toc-Societies_and_journals-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Societies and journals subsection</span> </button> <ul id="toc-Societies_and_journals-sublist" class="vector-toc-list"> <li id="toc-Societies" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Societies"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Societies</span> </div> </a> <ul id="toc-Societies-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Journals_of_INFORMS" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Journals_of_INFORMS"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Journals of INFORMS</span> </div> </a> <ul id="toc-Journals_of_INFORMS-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_journals" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Other_journals"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Other journals</span> </div> </a> <ul id="toc-Other_journals-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Further reading</span> </div> </a> <button aria-controls="toc-Further_reading-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Further reading subsection</span> </button> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> <li id="toc-Classic_books_and_articles" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Classic_books_and_articles"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1</span> <span>Classic books and articles</span> </div> </a> <ul id="toc-Classic_books_and_articles-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Classic_textbooks" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Classic_textbooks"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.2</span> <span>Classic textbooks</span> </div> </a> <ul id="toc-Classic_textbooks-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-History_2" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#History_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.3</span> <span>History</span> </div> </a> <ul id="toc-History_2-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Operations research</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 50 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-50" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">50 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Operasionele_navorsing" title="Operasionele navorsing – Afrikaans" lang="af" hreflang="af" data-title="Operasionele navorsing" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A8%D8%AD%D9%88%D8%AB_%D8%A7%D9%84%D8%B9%D9%85%D9%84%D9%8A%D8%A7%D8%AA" title="بحوث العمليات – Arabic" lang="ar" hreflang="ar" data-title="بحوث العمليات" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Investigaci%C3%B3n_d%27operaciones" title="Investigación d'operaciones – Asturian" lang="ast" hreflang="ast" data-title="Investigación d'operaciones" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/%C6%8Fm%C9%99liyyat_ara%C5%9Fd%C4%B1rmas%C4%B1" title="Əməliyyat araşdırması – Azerbaijani" lang="az" hreflang="az" data-title="Əməliyyat araşdırması" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AA%E0%A6%B0%E0%A6%BF%E0%A6%95%E0%A7%8D%E0%A6%B0%E0%A6%BF%E0%A6%AF%E0%A6%BC%E0%A6%BE%E0%A6%A6%E0%A6%BF_%E0%A6%97%E0%A6%AC%E0%A7%87%E0%A6%B7%E0%A6%A3%E0%A6%BE%E0%A6%AC%E0%A6%BF%E0%A6%A6%E0%A7%8D%E0%A6%AF%E0%A6%BE" title="পরিক্রিয়াদি গবেষণাবিদ্যা – Bangla" lang="bn" hreflang="bn" data-title="পরিক্রিয়াদি গবেষণাবিদ্যা" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9E%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%BE%D0%BD%D0%BD%D0%B8_%D0%B8%D0%B7%D1%81%D0%BB%D0%B5%D0%B4%D0%B2%D0%B0%D0%BD%D0%B8%D1%8F" title="Операционни изследвания – Bulgarian" lang="bg" hreflang="bg" data-title="Операционни изследвания" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Investigaci%C3%B3_operativa" title="Investigació operativa – Catalan" lang="ca" hreflang="ca" data-title="Investigació operativa" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Opera%C4%8Dn%C3%AD_anal%C3%BDza" title="Operační analýza – Czech" lang="cs" hreflang="cs" data-title="Operační analýza" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Operationsanalyse" title="Operationsanalyse – Danish" lang="da" hreflang="da" data-title="Operationsanalyse" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Operations_Research" title="Operations Research – German" lang="de" hreflang="de" data-title="Operations Research" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%95%CF%80%CE%B9%CF%87%CE%B5%CE%B9%CF%81%CE%B7%CF%83%CE%B9%CE%B1%CE%BA%CE%AE_%CE%AD%CF%81%CE%B5%CF%85%CE%BD%CE%B1" title="Επιχειρησιακή έρευνα – Greek" lang="el" hreflang="el" data-title="Επιχειρησιακή έρευνα" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Investigaci%C3%B3n_de_operaciones" title="Investigación de operaciones – Spanish" lang="es" hreflang="es" data-title="Investigación de operaciones" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Ikerkuntza_eragilea" title="Ikerkuntza eragilea – Basque" lang="eu" hreflang="eu" data-title="Ikerkuntza eragilea" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AA%D8%AD%D9%82%DB%8C%D9%82_%D8%AF%D8%B1_%D8%B9%D9%85%D9%84%DB%8C%D8%A7%D8%AA" title="تحقیق در عملیات – Persian" lang="fa" hreflang="fa" data-title="تحقیق در عملیات" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Recherche_op%C3%A9rationnelle" title="Recherche opérationnelle – French" lang="fr" hreflang="fr" data-title="Recherche opérationnelle" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Investigaci%C3%B3n_operativa" title="Investigación operativa – Galician" lang="gl" hreflang="gl" data-title="Investigación operativa" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-glk mw-list-item"><a href="https://glk.wikipedia.org/wiki/%D8%B9%D9%85%D9%84%D9%8A%D8%A7%D8%AA%CB%87_%D8%AA%D8%AD%D9%82%D9%8A%D9%82" title="عملياتˇ تحقيق – Gilaki" lang="glk" hreflang="glk" data-title="عملياتˇ تحقيق" data-language-autonym="گیلکی" data-language-local-name="Gilaki" class="interlanguage-link-target"><span>گیلکی</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9A%B4%EC%9A%A9%EA%B3%BC%ED%95%99" title="운용과학 – Korean" lang="ko" hreflang="ko" data-title="운용과학" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B3%D5%B8%D6%80%D5%AE%D5%B8%D5%B2%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6%D5%B6%D5%A5%D6%80%D5%AB_%D5%B0%D5%A5%D5%BF%D5%A1%D5%A6%D5%B8%D5%BF%D5%B8%D6%82%D5%B4" title="Գործողությունների հետազոտում – Armenian" lang="hy" hreflang="hy" data-title="Գործողությունների հետազոտում" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B8%E0%A4%82%E0%A4%95%E0%A5%8D%E0%A4%B0%E0%A4%BF%E0%A4%AF%E0%A4%BE_%E0%A4%B5%E0%A4%BF%E0%A4%9C%E0%A5%8D%E0%A4%9E%E0%A4%BE%E0%A4%A8" title="संक्रिया विज्ञान – Hindi" lang="hi" hreflang="hi" data-title="संक्रिया विज्ञान" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Riset_operasi" title="Riset operasi – Indonesian" lang="id" hreflang="id" data-title="Riset operasi" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/A%C3%B0ger%C3%B0agreining" title="Aðgerðagreining – Icelandic" lang="is" hreflang="is" data-title="Aðgerðagreining" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Ricerca_operativa" title="Ricerca operativa – Italian" lang="it" hreflang="it" data-title="Ricerca operativa" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%97%D7%A7%D7%A8_%D7%91%D7%99%D7%A6%D7%95%D7%A2%D7%99%D7%9D" title="חקר ביצועים – Hebrew" lang="he" hreflang="he" data-title="חקר ביצועים" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Oper%C3%A1ci%C3%B3kutat%C3%A1s" title="Operációkutatás – Hungarian" lang="hu" hreflang="hu" data-title="Operációkutatás" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%93%E0%B4%AA%E0%B5%8D%E0%B4%AA%E0%B4%B1%E0%B5%87%E0%B4%B7%E0%B5%BB%E0%B4%B8%E0%B5%8D_%E0%B4%97%E0%B4%B5%E0%B5%87%E0%B4%B7%E0%B4%A3%E0%B4%82" title="ഓപ്പറേഷൻസ് ഗവേഷണം – Malayalam" lang="ml" hreflang="ml" data-title="ഓപ്പറേഷൻസ് ഗവേഷണം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Operationeel_onderzoek" title="Operationeel onderzoek – Dutch" lang="nl" hreflang="nl" data-title="Operationeel onderzoek" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%AA%E3%83%9A%E3%83%AC%E3%83%BC%E3%82%B7%E3%83%A7%E3%83%B3%E3%82%BA%E3%83%BB%E3%83%AA%E3%82%B5%E3%83%BC%E3%83%81" title="オペレーションズ・リサーチ – Japanese" lang="ja" hreflang="ja" data-title="オペレーションズ・リサーチ" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Operasjonsanalyse" title="Operasjonsanalyse – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Operasjonsanalyse" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Operasjonsanalyse" title="Operasjonsanalyse – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Operasjonsanalyse" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Badania_operacyjne" title="Badania operacyjne – Polish" lang="pl" hreflang="pl" data-title="Badania operacyjne" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Investiga%C3%A7%C3%A3o_operacional" title="Investigação operacional – Portuguese" lang="pt" hreflang="pt" data-title="Investigação operacional" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%98%D1%81%D1%81%D0%BB%D0%B5%D0%B4%D0%BE%D0%B2%D0%B0%D0%BD%D0%B8%D0%B5_%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%B9" title="Исследование операций – Russian" lang="ru" hreflang="ru" data-title="Исследование операций" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/K%C3%ABrkimet_operacionale" title="Kërkimet operacionale – Albanian" lang="sq" hreflang="sq" data-title="Kërkimet operacionale" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Operations_research" title="Operations research – Simple English" lang="en-simple" hreflang="en-simple" data-title="Operations research" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Opera%C4%8Dn%C3%A1_anal%C3%BDza" title="Operačná analýza – Slovak" lang="sk" hreflang="sk" data-title="Operačná analýza" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%84%DB%8E%DA%A9%DB%86%DA%B5%DB%8C%D9%86%DB%95%D9%88%DB%95%DB%8C_%D8%A6%DB%86%D9%BE%DB%95%D8%B1%D8%A7%D8%B3%DB%8C%DB%86%D9%86%DB%95%DA%A9%D8%A7%D9%86" title="لێکۆڵینەوەی ئۆپەراسیۆنەکان – Central Kurdish" lang="ckb" hreflang="ckb" data-title="لێکۆڵینەوەی ئۆپەراسیۆنەکان" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9E%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D0%BE%D0%BD%D0%B0_%D0%B8%D1%81%D1%82%D1%80%D0%B0%D0%B6%D0%B8%D0%B2%D0%B0%D1%9A%D0%B0" title="Операциона истраживања – Serbian" lang="sr" hreflang="sr" data-title="Операциона истраживања" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Operaciona_istra%C5%BEivanja" title="Operaciona istraživanja – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Operaciona istraživanja" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Operaatioanalyysi" title="Operaatioanalyysi – Finnish" lang="fi" hreflang="fi" data-title="Operaatioanalyysi" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Operationsanalys" title="Operationsanalys – Swedish" lang="sv" hreflang="sv" data-title="Operationsanalys" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%9A%E0%AF%86%E0%AE%AF%E0%AF%8D%E0%AE%AA%E0%AE%A3%E0%AE%BF_%E0%AE%86%E0%AE%AF%E0%AF%8D%E0%AE%B5%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AF%8D" title="செய்பணி ஆய்வியல் – Tamil" lang="ta" hreflang="ta" data-title="செய்பணி ஆய்வியல்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%A7%E0%B8%B4%E0%B8%88%E0%B8%B1%E0%B8%A2%E0%B8%94%E0%B8%B3%E0%B9%80%E0%B8%99%E0%B8%B4%E0%B8%99%E0%B8%81%E0%B8%B2%E0%B8%A3" title="การวิจัยดำเนินการ – Thai" lang="th" hreflang="th" data-title="การวิจัยดำเนินการ" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Y%C3%B6neylem_ara%C5%9Ft%C4%B1rmas%C4%B1" title="Yöneylem araştırması – Turkish" lang="tr" hreflang="tr" data-title="Yöneylem araştırması" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%94%D0%BE%D1%81%D0%BB%D1%96%D0%B4%D0%B6%D0%B5%D0%BD%D0%BD%D1%8F_%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D1%96%D0%B9" title="Дослідження операцій – Ukrainian" lang="uk" hreflang="uk" data-title="Дослідження операцій" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/V%E1%BA%ADn_tr%C3%B9_h%E1%BB%8Dc" title="Vận trù học – Vietnamese" lang="vi" hreflang="vi" data-title="Vận trù học" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Pamiling_kasayoran_ha_operasyon" title="Pamiling kasayoran ha operasyon – Waray" lang="war" hreflang="war" data-title="Pamiling kasayoran ha operasyon" data-language-autonym="Winaray" data-language-local-name="Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E8%BF%90%E7%AD%B9%E5%AD%A6" title="运筹学 – Wu" lang="wuu" hreflang="wuu" data-title="运筹学" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%81%8B%E7%B1%8C%E5%AD%B8" title="運籌學 – Cantonese" lang="yue" hreflang="yue" data-title="運籌學" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E9%81%8B%E7%B1%8C%E5%AD%B8" title="運籌學 – Chinese" lang="zh" hreflang="zh" data-title="運籌學" data-language-autonym="中文" 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<div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Discipline concerning the application of advanced analytical methods</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For the academic journal, see <a href="/wiki/Operations_Research_(journal)" title="Operations Research (journal)">Operations Research (journal)</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Globalize plainlinks metadata ambox ambox-content ambox-globalize" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="Globe icon." src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bd/Ambox_globe_content.svg/48px-Ambox_globe_content.svg.png" decoding="async" width="48" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bd/Ambox_globe_content.svg/73px-Ambox_globe_content.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bd/Ambox_globe_content.svg/97px-Ambox_globe_content.svg.png 2x" data-file-width="350" data-file-height="290" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">The examples and perspective in this article <b>may not represent a <a href="/wiki/Wikipedia:WikiProject_Countering_systemic_bias" title="Wikipedia:WikiProject Countering systemic bias">worldwide view</a> of the subject</b>. The specific issue is: <b>US perspective completely neglected, George Dantzig gets a passing mention only</b><span class="hide-when-compact"> You may <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Operations_research&action=edit">improve this article</a>, discuss the issue on the <a href="/wiki/Talk:Operations_research" title="Talk:Operations research">talk page</a>, or <a href="/wiki/Wikipedia:Article_wizard" title="Wikipedia:Article wizard">create a new article</a>, as appropriate.</span> <span class="date-container"><i>(<span class="date">December 2020</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p> <b>Operations research</b> (<a href="/wiki/British_English_language" class="mw-redirect" title="British English language">British English</a>: <span lang="en-GB"><b>operational research</b></span>) (U.S. <a href="/wiki/Air_Force_Specialty_Code" title="Air Force Specialty Code">Air Force Specialty Code</a>: Operations Analysis), often shortened to the <a href="/wiki/Initialism" class="mw-redirect" title="Initialism">initialism</a> <b>OR</b>, is a branch of applied mathematics that deals with the development and application of analytical methods to improve management and decision-making.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Although the term <a href="/wiki/Management_science" title="Management science">management science</a> is sometimes used similarly, the two fields differ in their scope and emphasis. </p><p>Employing techniques from other mathematical sciences, such as <a href="/wiki/Mathematical_model" title="Mathematical model">modeling</a>, <a href="/wiki/Statistics" title="Statistics">statistics</a>, and <a href="/wiki/Mathematical_optimization" title="Mathematical optimization">optimization</a>, operations research arrives at optimal or near-optimal solutions to <a href="/wiki/Decision-making" title="Decision-making">decision-making</a> problems. Because of its emphasis on practical applications, operations research has overlapped with many other disciplines, notably <a href="/wiki/Industrial_engineering" title="Industrial engineering">industrial engineering</a>. Operations research is often concerned with determining the extreme values of some real-world objective: the <a href="/wiki/Maxima_and_minima" class="mw-redirect" title="Maxima and minima">maximum</a> (of profit, performance, or yield) or minimum (of loss, risk, or cost). Originating in military efforts before <a href="/wiki/World_War_II" title="World War II">World War II</a>, its techniques have grown to concern problems in a variety of industries.<sup id="cite_ref-hsor.org_3-0" class="reference"><a href="#cite_note-hsor.org-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Overview">Overview</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Operations_research&action=edit&section=1" title="Edit section: Overview"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Operations research (OR) encompasses the development and the use of a wide range of <a href="/wiki/Problem_solving" title="Problem solving">problem-solving</a> techniques and methods applied in the pursuit of improved decision-making and efficiency, such as <a href="/wiki/Simulation" title="Simulation">simulation</a>, <a href="/wiki/Mathematical_optimization" title="Mathematical optimization">mathematical optimization</a>, <a href="/wiki/Queueing_theory" title="Queueing theory">queueing theory</a> and other <a href="/wiki/Stochastic_process" title="Stochastic process">stochastic-process</a> models, <a href="/wiki/Markov_Decision_Process" class="mw-redirect" title="Markov Decision Process">Markov decision processes</a>, <a href="/wiki/Econometrics" title="Econometrics">econometric methods</a>, <a href="/wiki/Data_envelopment_analysis" title="Data envelopment analysis">data envelopment analysis</a>, <a href="/wiki/Ordinal_Priority_Approach" class="mw-redirect" title="Ordinal Priority Approach">ordinal priority approach</a>, <a href="/wiki/Artificial_neural_network" class="mw-redirect" title="Artificial neural network">neural networks</a>, <a href="/wiki/Expert_System" class="mw-redirect" title="Expert System">expert systems</a>, <a href="/wiki/Decision_analysis" title="Decision analysis">decision analysis</a>, and the <a href="/wiki/Analytic_hierarchy_process" title="Analytic hierarchy process">analytic hierarchy process</a>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Nearly all of these techniques involve the construction of mathematical models that attempt to describe the system. Because of the computational and statistical nature of most of these fields, OR also has strong ties to <a href="/wiki/Computer_science" title="Computer science">computer science</a> and <a href="/wiki/Analytics" title="Analytics">analytics</a>. Operational researchers faced with a new problem must determine which of these techniques are most appropriate given the nature of the system, the goals for improvement, and constraints on time and computing power, or develop a new technique specific to the problem at hand (and, afterwards, to that type of problem). </p><p>The major sub-disciplines (but not limited to) in modern operational research, as identified by the journal <i>Operations Research</i><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> and <i>The Journal of the Operational Research Society</i> <sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> are: </p> <ul><li>Computing and information technologies</li> <li><a href="/wiki/Financial_engineering" title="Financial engineering">Financial engineering</a></li> <li><a href="/wiki/Manufacturing" title="Manufacturing">Manufacturing</a>, <a href="/wiki/Service_science" class="mw-redirect" title="Service science">service sciences</a>, and <a href="/wiki/Supply_chain_management" title="Supply chain management">supply chain management</a></li> <li>Policy modeling and public sector work</li> <li><a href="/wiki/Revenue_management" title="Revenue management">Revenue management</a></li> <li><a href="/wiki/Simulation" title="Simulation">Simulation</a></li> <li><a href="/wiki/Stochastics" class="mw-redirect" title="Stochastics">Stochastic models</a></li> <li><a href="/wiki/Transportation_theory_(mathematics)" title="Transportation theory (mathematics)">Transportation theory</a></li> <li><a href="/wiki/Game_theory" title="Game theory">Game theory</a> for strategies</li> <li><a href="/wiki/Linear_programming" title="Linear programming">Linear programming</a></li> <li><a href="/wiki/Nonlinear_programming" title="Nonlinear programming">Nonlinear programming</a></li> <li><a href="/wiki/Integer_programming" title="Integer programming">Integer programming</a> in <a href="/wiki/NP-complete_problem" class="mw-redirect" title="NP-complete problem">NP-complete problem</a> specially for 0-1 integer linear programming for binary</li> <li><a href="/wiki/Dynamic_programming" title="Dynamic programming">Dynamic programming</a> in <a href="/wiki/Aerospace_engineering" title="Aerospace engineering">Aerospace engineering</a> and <a href="/wiki/Economics" title="Economics">Economics</a></li> <li><a href="/wiki/Information_theory" title="Information theory">Information theory</a> used in <a href="/wiki/Cryptography" title="Cryptography">Cryptography</a>, <a href="/wiki/Quantum_computing" title="Quantum computing">Quantum computing</a></li> <li><a href="/wiki/Quadratic_programming" title="Quadratic programming">Quadratic programming</a> for solutions of <a href="/wiki/Quadratic_equation" title="Quadratic equation">Quadratic equation</a> and <a href="/wiki/Quadratic_function" title="Quadratic function">Quadratic function</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Operations_research&action=edit&section=2" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the decades after the two world wars, the tools of operations research were more widely applied to problems in business, industry, and society. Since that time, operational research has expanded into a field widely used in industries ranging from petrochemicals to airlines, finance, logistics, and government, moving to a focus on the development of mathematical models that can be used to analyse and optimize sometimes complex systems, and has become an area of active academic and industrial research.<sup id="cite_ref-hsor.org_3-1" class="reference"><a href="#cite_note-hsor.org-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Historical_origins">Historical origins</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Operations_research&action=edit&section=3" title="Edit section: Historical origins"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the 17th century, mathematicians <a href="/wiki/Blaise_Pascal" title="Blaise Pascal">Blaise Pascal</a> and <a href="/wiki/Christiaan_Huygens" title="Christiaan Huygens">Christiaan Huygens</a> solved problems involving sometimes complex decisions (<a href="/wiki/Problem_of_points" title="Problem of points">problem of points</a>) by using <a href="/wiki/Game_theory" title="Game theory">game-theoretic</a> ideas and <a href="/wiki/Expected_value" title="Expected value">expected values</a>; others, such as <a href="/wiki/Pierre_de_Fermat" title="Pierre de Fermat">Pierre de Fermat</a> and <a href="/wiki/Jacob_Bernoulli" title="Jacob Bernoulli">Jacob Bernoulli</a>, solved these types of problems using <a href="/wiki/Combinatorics" title="Combinatorics">combinatorial reasoning</a> instead.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Charles_Babbage" title="Charles Babbage">Charles Babbage</a>'s research into the cost of transportation and sorting of mail led to England's <a href="/wiki/Uniform_Penny_Post" title="Uniform Penny Post">universal "Penny Post"</a> in 1840, and to studies into the dynamical behaviour of railway vehicles in defence of the <a href="/wiki/Great_Western_Railway" title="Great Western Railway">GWR</a>'s broad gauge.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Beginning in the 20th century, study of inventory management could be considered<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Manual_of_Style/Words_to_watch#Unsupported_attributions" title="Wikipedia:Manual of Style/Words to watch"><span title="The material near this tag may use weasel words or too-vague attribution. (November 2019)">by whom?</span></a></i>]</sup> the origin of modern operations research with <a href="/wiki/Economic_order_quantity" title="Economic order quantity">economic order quantity</a> developed by <a href="/wiki/Ford_W._Harris" class="mw-redirect" title="Ford W. Harris">Ford W. Harris</a> in 1913. Operational research may<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:No_original_research" title="Wikipedia:No original research"><span title="The material near this tag possibly contains original research. (November 2019)">original research?</span></a></i>]</sup> have originated in the efforts of military planners during <a href="/wiki/World_War_I" title="World War I">World War I</a> (convoy theory and <a href="/wiki/Lanchester%27s_laws" title="Lanchester's laws">Lanchester's laws</a>). <a href="/wiki/Percy_Bridgman" class="mw-redirect" title="Percy Bridgman">Percy Bridgman</a> brought operational research to bear on problems in physics in the 1920s and would later attempt to extend these to the social sciences.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>Modern operational research originated at the <a href="/wiki/Telecommunications_Research_Establishment" title="Telecommunications Research Establishment">Bawdsey Research Station</a> in the UK in 1937 as the result of an initiative of the station's superintendent, <a href="/wiki/Albert_Percival_Rowe" class="mw-redirect" title="Albert Percival Rowe">A. P. Rowe</a> and <a href="/wiki/Robert_Watson-Watt" title="Robert Watson-Watt">Robert Watson-Watt</a>.<sup id="cite_ref-Beginning_10-0" class="reference"><a href="#cite_note-Beginning-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> Rowe conceived the idea as a means to analyse and improve the working of the UK's <a href="/wiki/Early-warning_radar" title="Early-warning radar">early-warning radar</a> system, code-named "<a href="/wiki/Chain_Home" title="Chain Home">Chain Home</a>" (CH). Initially, Rowe analysed the operating of the radar equipment and its communication networks, expanding later to include the operating personnel's behaviour. This revealed unappreciated limitations of the CH network and allowed remedial action to be taken.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>Scientists in the United Kingdom (including <a href="/wiki/Patrick_Maynard_Stuart_Blackett" class="mw-redirect" title="Patrick Maynard Stuart Blackett">Patrick Blackett</a> (later Lord Blackett OM PRS), <a href="/w/index.php?title=Cecil_Gordon_(scientist)&action=edit&redlink=1" class="new" title="Cecil Gordon (scientist) (page does not exist)">Cecil Gordon</a>, <a href="/wiki/Solly_Zuckerman,_Baron_Zuckerman" title="Solly Zuckerman, Baron Zuckerman">Solly Zuckerman</a>, (later Baron Zuckerman OM, KCB, FRS), <a href="/wiki/Conrad_Hal_Waddington" class="mw-redirect" title="Conrad Hal Waddington">C. H. Waddington</a>, <a href="/wiki/Owen_Wansbrough-Jones" title="Owen Wansbrough-Jones">Owen Wansbrough-Jones</a>, <a href="/wiki/Frank_Yates" title="Frank Yates">Frank Yates</a>, <a href="/wiki/Jacob_Bronowski" title="Jacob Bronowski">Jacob Bronowski</a> and <a href="/wiki/Freeman_Dyson" title="Freeman Dyson">Freeman Dyson</a>), and in the United States (<a href="/wiki/George_Dantzig" title="George Dantzig">George Dantzig</a>) looked for ways to make better decisions in such areas as <a href="/wiki/Logistics" title="Logistics">logistics</a> and training schedules. </p> <div class="mw-heading mw-heading3"><h3 id="Second_World_War">Second World War</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Operations_research&action=edit&section=4" title="Edit section: Second World War"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The modern field of operational research arose during World War II.<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Accuracy_dispute#Disputed_statement" title="Wikipedia:Accuracy dispute"><span title="The material near this tag is possibly inaccurate or nonfactual. (March 2019)">dubious</span></a> – <a href="/wiki/Talk:Operations_research" title="Talk:Operations research">discuss</a></i>]</sup> In the World War II era, operational research was defined as "a scientific method of providing executive departments with a quantitative basis for decisions regarding the operations under their control".<sup id="cite_ref-C67-3-4-48-para-1_12-0" class="reference"><a href="#cite_note-C67-3-4-48-para-1-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> Other names for it included operational analysis (UK Ministry of Defence from 1962)<sup id="cite_ref-PROCATWO291_13-0" class="reference"><a href="#cite_note-PROCATWO291-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> and quantitative management.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p><p>During the <a href="/wiki/World_War_II" title="World War II">Second World War</a> close to 1,000 men and women in Britain were engaged in operational research. About 200 operational research scientists worked for the <a href="/wiki/British_Army" title="British Army">British Army</a>.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Patrick_Blackett" title="Patrick Blackett">Patrick Blackett</a> worked for several different organizations during the war. Early in the war while working for the <a href="/wiki/Royal_Aircraft_Establishment" title="Royal Aircraft Establishment">Royal Aircraft Establishment</a> (RAE) he set up a team known as the "Circus" which helped to reduce the number of <a href="/wiki/Anti-aircraft_artillery" class="mw-redirect" title="Anti-aircraft artillery">anti-aircraft artillery</a> rounds needed to shoot down an enemy aircraft from an average of over 20,000 at the start of the <a href="/wiki/Battle_of_Britain" title="Battle of Britain">Battle of Britain</a> to 4,000 in 1941.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Liberator_B_Mk.I_in_RAF_service_23_03_05.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Liberator_B_Mk.I_in_RAF_service_23_03_05.jpg/220px-Liberator_B_Mk.I_in_RAF_service_23_03_05.jpg" decoding="async" width="220" height="138" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/98/Liberator_B_Mk.I_in_RAF_service_23_03_05.jpg/330px-Liberator_B_Mk.I_in_RAF_service_23_03_05.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/98/Liberator_B_Mk.I_in_RAF_service_23_03_05.jpg/440px-Liberator_B_Mk.I_in_RAF_service_23_03_05.jpg 2x" data-file-width="1744" data-file-height="1091" /></a><figcaption>A <a href="/wiki/Consolidated_B-24_Liberator" title="Consolidated B-24 Liberator">Liberator</a> in standard RAF green/dark earth/black night bomber finish as originally used by Coastal Command</figcaption></figure> <p>In 1941, Blackett moved from the RAE to the Navy, after first working with <a href="/wiki/RAF_Coastal_Command" title="RAF Coastal Command">RAF Coastal Command</a>, in 1941 and then early in 1942 to the <a href="/wiki/British_Admiralty" class="mw-redirect" title="British Admiralty">Admiralty</a>.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> Blackett's team at Coastal Command's Operational Research Section (CC-ORS) included two future <a href="/wiki/Nobel_Prize" title="Nobel Prize">Nobel Prize</a> winners and many other people who went on to be pre-eminent in their fields.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-dyson_19-0" class="reference"><a href="#cite_note-dyson-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> They undertook a number of crucial analyses that aided the war effort. Britain introduced the <a href="/wiki/Convoy" title="Convoy">convoy</a> system to reduce shipping losses, but while the principle of using warships to accompany merchant ships was generally accepted, it was unclear whether it was better for convoys to be small or large. Convoys travel at the speed of the slowest member, so small convoys can travel faster. It was also argued that small convoys would be harder for German <a href="/wiki/U-boat" title="U-boat">U-boats</a> to detect. On the other hand, large convoys could deploy more warships against an attacker. Blackett's staff showed that the losses suffered by convoys depended largely on the number of escort vessels present, rather than the size of the convoy. Their conclusion was that a few large convoys are more defensible than many small ones.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p><p><span class="anchor" id="RAF_Coastal_Command's_Operational_Research_Section"></span> While performing an analysis of the methods used by <a href="/wiki/RAF_Coastal_Command" title="RAF Coastal Command">RAF Coastal Command</a> to hunt and destroy submarines, one of the analysts asked what colour the aircraft were. As most of them were from Bomber Command they were painted black for night-time operations. At the suggestion of CC-ORS a test was run to see if that was the best colour to camouflage the aircraft for daytime operations in the grey North Atlantic skies. Tests showed that aircraft painted white were on average not spotted until they were 20% closer than those painted black. This change indicated that 30% more submarines would be attacked and sunk for the same number of sightings.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> As a result of these findings Coastal Command changed their aircraft to using white undersurfaces. </p><p>Other work by the CC-ORS indicated that on average if the trigger depth of aerial-delivered <a href="/wiki/Depth_charge" title="Depth charge">depth charges</a> were changed from 100 to 25 feet, the kill ratios would go up. The reason was that if a U-boat saw an aircraft only shortly before it arrived over the target then at 100 feet the charges would do no damage (because the U-boat wouldn't have had time to descend as far as 100 feet), and if it saw the aircraft a long way from the target it had time to alter course under water so the chances of it being within the 20-foot kill zone of the charges was small. It was more efficient to attack those submarines close to the surface when the targets' locations were better known than to attempt their destruction at greater depths when their positions could only be guessed. Before the change of settings from 100 to 25 feet, 1% of submerged U-boats were sunk and 14% damaged. After the change, 7% were sunk and 11% damaged; if submarines were caught on the surface but had time to submerge just before being attacked, the numbers rose to 11% sunk and 15% damaged. Blackett observed "there can be few cases where such a great operational gain had been obtained by such a small and simple change of tactics".<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Kammhuber_Line_Map_-_Agent_Tegal.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Kammhuber_Line_Map_-_Agent_Tegal.png/170px-Kammhuber_Line_Map_-_Agent_Tegal.png" decoding="async" width="170" height="242" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Kammhuber_Line_Map_-_Agent_Tegal.png/255px-Kammhuber_Line_Map_-_Agent_Tegal.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/33/Kammhuber_Line_Map_-_Agent_Tegal.png/340px-Kammhuber_Line_Map_-_Agent_Tegal.png 2x" data-file-width="800" data-file-height="1141" /></a><figcaption>Map of <i><a href="/wiki/Kammhuber_Line" title="Kammhuber Line">Kammhuber Line</a></i></figcaption></figure> <p><span class="anchor" id="RAF_Bomber_Command's_Operational_Research_Section"></span> Bomber Command's Operational Research Section (BC-ORS), analyzed a report of a survey carried out by <a href="/wiki/RAF_Bomber_Command" title="RAF Bomber Command">RAF Bomber Command</a>.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (February 2007)">citation needed</span></a></i>]</sup> For the survey, Bomber Command inspected all bombers returning from bombing raids over Germany over a particular period. All damage inflicted by German <a href="/wiki/Anti-aircraft_warfare" title="Anti-aircraft warfare">air defenses</a> was noted and the recommendation was given that armor be added in the most heavily damaged areas. This <a href="/wiki/Survivorship_bias#Military" title="Survivorship bias">recommendation</a> was not adopted because the fact that the aircraft were able to return with these areas damaged indicated the areas were not vital, and adding armor to non-vital areas where damage is acceptable reduces aircraft performance. Their suggestion to remove some of the crew so that an aircraft loss would result in fewer personnel losses, was also rejected by RAF command. Blackett's team made the logical recommendation that the armor be placed in the areas which were completely untouched by damage in the bombers who returned. They reasoned that the survey was biased, since it only included aircraft that returned to Britain. The areas untouched in returning aircraft were probably vital areas, which, if hit, would result in the loss of the aircraft.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> This story has been disputed,<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> with a similar damage assessment study completed in the US by the <a href="/wiki/Statistical_Research_Group" title="Statistical Research Group">Statistical Research Group</a> at <a href="/wiki/Columbia_University" title="Columbia University">Columbia University</a>,<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> the result of work done by <a href="/wiki/Abraham_Wald" title="Abraham Wald">Abraham Wald</a>.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> </p><p>When Germany organized its air defences into the <a href="/wiki/Kammhuber_Line" title="Kammhuber Line">Kammhuber Line</a>, it was realized by the British that if the RAF bombers were to fly in a <a href="/wiki/Bomber_stream" title="Bomber stream">bomber stream</a> they could overwhelm the night fighters who flew in individual cells directed to their targets by ground controllers. It was then a matter of calculating the statistical loss from collisions against the statistical loss from night fighters to calculate how close the bombers should fly to minimize RAF losses.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> </p><p>The "exchange rate" ratio of output to input was a characteristic feature of operational research. By comparing the number of flying hours put in by Allied aircraft to the number of U-boat sightings in a given area, it was possible to redistribute aircraft to more productive patrol areas. Comparison of exchange rates established "effectiveness ratios" useful in planning. The ratio of 60 <a href="/wiki/Mine_(naval)" class="mw-redirect" title="Mine (naval)">mines</a> laid per ship sunk was common to several campaigns: German mines in British ports, British mines on German routes, and United States mines in Japanese routes.<sup id="cite_ref-Proceedings_28-0" class="reference"><a href="#cite_note-Proceedings-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </p><p>Operational research doubled the on-target bomb rate of <a href="/wiki/B-29" class="mw-redirect" title="B-29">B-29s</a> bombing Japan from the <a href="/wiki/Marianas_Islands" class="mw-redirect" title="Marianas Islands">Marianas Islands</a> by increasing the training ratio from 4 to 10 percent of flying hours; revealed that wolf-packs of three United States submarines were the most effective number to enable all members of the pack to engage targets discovered on their individual patrol stations; revealed that glossy enamel paint was more effective camouflage for night fighters than conventional dull camouflage paint finish, and a smooth paint finish increased airspeed by reducing skin friction.<sup id="cite_ref-Proceedings_28-1" class="reference"><a href="#cite_note-Proceedings-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </p><p>On land, the operational research sections of the Army Operational Research Group (AORG) of the <a href="/wiki/Ministry_of_Supply" title="Ministry of Supply">Ministry of Supply</a> (MoS) were landed in <a href="/wiki/Operation_Overlord" title="Operation Overlord">Normandy in 1944</a>, and they followed British forces in the advance across Europe. They analyzed, among other topics, the effectiveness of artillery, aerial bombing and anti-tank shooting. </p> <div class="mw-heading mw-heading3"><h3 id="After_World_War_II">After World War II</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Operations_research&action=edit&section=5" title="Edit section: After World War II"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1947, under the auspices of the <a href="/wiki/British_Association" class="mw-redirect" title="British Association">British Association</a>, a symposium was organized in <a href="/wiki/Dundee" title="Dundee">Dundee</a>. In his opening address, Watson-Watt offered a definition of the aims of OR: </p> <dl><dd>"To examine quantitatively whether the user organization is getting from the operation of its equipment the best attainable contribution to its overall objective."<sup id="cite_ref-Beginning_10-1" class="reference"><a href="#cite_note-Beginning-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup></dd></dl> <p>With expanded techniques and growing awareness of the field at the close of the war, operational research was no longer limited to only operational, but was extended to encompass equipment procurement, training, <a href="/wiki/Logistics" title="Logistics">logistics</a> and infrastructure. Operations research also grew in many areas other than the military once scientists learned to apply its principles to the civilian sector. The development of the <a href="/wiki/Simplex_algorithm" title="Simplex algorithm">simplex algorithm</a> for <a href="/wiki/Linear_programming" title="Linear programming">linear programming</a> was in 1947.<sup id="cite_ref-pitt.edu_29-0" class="reference"><a href="#cite_note-pitt.edu-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> </p><p>In the 1950s, the term Operations Research was used to describe heterogeneous mathematical methods such as <a href="/wiki/Game_theory" title="Game theory">game theory</a>, dynamic programming, linear programming, warehousing, <a href="/w/index.php?title=Spare_parts_theory&action=edit&redlink=1" class="new" title="Spare parts theory (page does not exist)">spare parts theory</a>, <a href="/wiki/Queueing_theory" title="Queueing theory">queue theory</a>, simulation and production control, which were used primarily in civilian industry. Scientific societies and journals on the subject of operations research were founded in the 1950s, such as the <a href="/wiki/Institute_for_Operations_Research_and_the_Management_Sciences" title="Institute for Operations Research and the Management Sciences">Operation Research Society of America</a> (ORSA) in 1952 and the Institute for Management Science (TIMS) in 1953.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> Philip Morse, the head of the Weapons Systems Evaluation Group of the Pentagon, became the first president of ORSA and attracted the companies of the <a href="/wiki/Military%E2%80%93industrial_complex" title="Military–industrial complex">military-industrial complex</a> to ORSA, which soon had more than 500 members. In the 1960s, ORSA reached 8000 members.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (July 2023)">citation needed</span></a></i>]</sup> Consulting companies also founded OR groups. In 1953, Abraham Charnes and William Cooper published the first textbook on Linear Programming.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (July 2023)">citation needed</span></a></i>]</sup> </p><p>In the 1950s and 1960s, chairs of operations research were established in the U.S. and United Kingdom (from 1964 in Lancaster) in the management faculties of universities. Further influences from the U.S. on the development of operations research in Western Europe can be traced here. The authoritative<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (July 2023)">citation needed</span></a></i>]</sup> OR textbooks from the U.S. were published in Germany in German language and in France in French (but not in Italian<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (July 2023)">citation needed</span></a></i>]</sup>), such as the book by George Dantzig "Linear Programming"(1963) and the book by <a href="/wiki/C._West_Churchman" title="C. West Churchman">C. West Churchman</a> et al. "Introduction to Operations Research"(1957). The latter was also published in Spanish in 1973, opening at the same time Latin American readers to Operations Research. <a href="/wiki/NATO" title="NATO">NATO</a> gave important impulses for the spread of Operations Research in Western Europe; NATO headquarters (SHAPE) organised four conferences on OR in the 1950s – the one in 1956 with 120 participants – bringing OR to mainland Europe. Within NATO, OR was also known as "Scientific Advisory" (SA) and was grouped together in the Advisory Group of Aeronautical Research and Development (AGARD). SHAPE and AGARD organized an OR conference in April 1957 in Paris. When <a href="/wiki/Withdrawal_from_NATO#France" title="Withdrawal from NATO">France withdrew from the NATO military command structure</a>, the transfer of NATO headquarters from France to Belgium led to the institutionalization of OR in Belgium, where Jacques Drèze founded CORE, the Center for Operations Research and Econometrics at the <a href="/wiki/Catholic_University_of_Leuven_(1834%E2%80%931968)" title="Catholic University of Leuven (1834–1968)">Catholic University of Leuven</a> in 1966.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (July 2023)">citation needed</span></a></i>]</sup> </p><p>With the development of computers over the next three decades, Operations Research can now solve problems with hundreds of thousands of variables and constraints. Moreover, the large volumes of data required for such problems can be stored and manipulated very efficiently."<sup id="cite_ref-pitt.edu_29-1" class="reference"><a href="#cite_note-pitt.edu-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> Much of operations research (modernly known as 'analytics') relies upon stochastic variables and a therefore access to truly random numbers. Fortunately, the cybernetics field also required the same level of randomness. The development of increasingly better random number generators has been a boon to both disciplines. Modern applications of operations research includes city planning, football strategies, emergency planning, optimizing all facets of industry and economy, and undoubtedly with the likelihood of the inclusion of terrorist attack planning and definitely counterterrorist attack planning. More recently, the research approach of operations research, which dates back to the 1950s, has been criticized for being collections of mathematical models but lacking an empirical basis of data collection for applications. How to collect data is not presented in the textbooks. Because of the lack of data, there are also no computer applications in the textbooks.<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Problems_addressed">Problems addressed</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Operations_research&action=edit&section=6" title="Edit section: Problems addressed"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Critical_path_analysis" class="mw-redirect" title="Critical path analysis">Critical path analysis</a> or <a href="/wiki/Project_planning" title="Project planning">project planning</a>: identifying those processes in a multiple-dependency project which affect the overall duration of the project</li> <li><a href="/wiki/Floorplanning" class="mw-redirect" title="Floorplanning">Floorplanning</a>: designing the layout of equipment in a factory or components on a <a href="/wiki/Computer_chip" class="mw-redirect" title="Computer chip">computer chip</a> to reduce <a href="/wiki/Manufacturing" title="Manufacturing">manufacturing</a> time (therefore reducing cost)</li> <li><a href="/wiki/Telecommunications_network" title="Telecommunications network">Network optimization</a>: for instance, setup of telecommunications or power system networks to maintain quality of service during outages</li> <li><a href="/wiki/Resource_allocation" title="Resource allocation">Resource allocation</a> problems</li> <li><a href="/wiki/Optimal_facility_location" title="Optimal facility location">Facility location</a></li> <li>Assignment Problems: <ul><li><a href="/wiki/Assignment_problem" title="Assignment problem">Assignment problem</a></li> <li><a href="/wiki/Generalized_assignment_problem" title="Generalized assignment problem">Generalized assignment problem</a></li> <li><a href="/wiki/Quadratic_assignment_problem" title="Quadratic assignment problem">Quadratic assignment problem</a></li> <li><a href="/wiki/Weapon_target_assignment_problem" title="Weapon target assignment problem">Weapon target assignment problem</a></li></ul></li> <li><a href="/wiki/Bayesian_search_theory" title="Bayesian search theory">Bayesian search theory</a>: looking for a target</li> <li><a href="/wiki/Search_theory" title="Search theory">Optimal search</a></li> <li><a href="/wiki/Routing" title="Routing">Routing</a>, such as determining the routes of buses so that as few buses are needed as possible</li> <li><a href="/wiki/Supply_chain_management" title="Supply chain management">Supply chain management</a>: managing the flow of raw materials and products based on uncertain demand for the finished products</li> <li>Project production activities: managing the flow of work activities in a capital project in response to system variability through operations research tools for variability reduction and buffer allocation using a combination of allocation of capacity, inventory and time<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup></li> <li>Efficient messaging and customer response tactics</li> <li><a href="/wiki/Automation" title="Automation">Automation</a>: automating or integrating robotic systems in human-driven operations processes</li> <li><a href="/wiki/Globalization" title="Globalization">Globalization</a>: globalizing operations processes in order to take advantage of cheaper materials, labor, land or other productivity inputs</li> <li>Transportation: managing <a href="/wiki/Freight" class="mw-redirect" title="Freight">freight</a> transportation and delivery systems (Examples: <a href="/wiki/Less-than-truckload_shipping" title="Less-than-truckload shipping">LTL shipping</a>, <a href="/wiki/Intermodal_freight_transport" title="Intermodal freight transport">intermodal freight transport</a>, <a href="/wiki/Travelling_salesman_problem" title="Travelling salesman problem">travelling salesman problem</a>, <a href="/wiki/Driver_scheduling_problem" title="Driver scheduling problem">driver scheduling problem</a>)</li> <li><a href="/wiki/Scheduling_(computing)" title="Scheduling (computing)">Scheduling</a>: <ul><li><a href="/wiki/Nurse_scheduling_problem" title="Nurse scheduling problem">Personnel staffing</a></li> <li>Manufacturing steps</li> <li><a href="/wiki/Project_management" title="Project management">Project tasks</a></li> <li>Network data traffic: these are known as <a href="/wiki/Queueing_model" class="mw-redirect" title="Queueing model">queueing models</a> or queueing systems.</li> <li>Sports events and their television coverage</li></ul></li> <li>Blending of raw materials in oil refineries</li> <li>Determining optimal prices, in many retail and B2B settings, within the disciplines of <a href="/wiki/Pricing_science" title="Pricing science">pricing science</a></li> <li><a href="/wiki/Cutting_stock_problem" title="Cutting stock problem">Cutting stock problem</a>: Cutting small items out of bigger ones.</li> <li>Finding the optimal parameter (weights) setting of an algorithm that generates the realisation of a <a href="/wiki/Figured_bass" title="Figured bass">figured bass</a> in <a href="/wiki/Baroque" title="Baroque">Baroque</a> compositions (classical music) by using weighted local cost and transition cost rules</li></ul> <p>Operational research is also used extensively in government where <a href="/wiki/Evidence-based_policy" title="Evidence-based policy">evidence-based policy</a> is used. </p> <div class="mw-heading mw-heading2"><h2 id="Management_science">Management science</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Operations_research&action=edit&section=7" title="Edit section: Management science"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Management_science" title="Management science">Management science</a></div> <p>The field of management science (MS) is known as using operations research models in business.<sup id="cite_ref-UTK_34-0" class="reference"><a href="#cite_note-UTK-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Stafford_Beer" title="Stafford Beer">Stafford Beer</a> characterized this in 1967.<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> Like operational research itself, management science is an interdisciplinary branch of applied mathematics devoted to optimal decision planning, with strong links with economics, business, engineering, and other <a href="/wiki/Science" title="Science">sciences</a>. It uses various <a href="/wiki/Science" title="Science">scientific</a> <a href="/wiki/Research" title="Research">research</a>-based principles, <a href="/wiki/Strategy" title="Strategy">strategies</a>, and <a href="/wiki/Analytical_method" class="mw-redirect" title="Analytical method">analytical methods</a> including <a href="/wiki/Mathematical_model" title="Mathematical model">mathematical modeling</a>, statistics and <a href="/wiki/Numerical_algorithm" class="mw-redirect" title="Numerical algorithm">numerical algorithms</a> to improve an organization's ability to enact rational and meaningful management decisions by arriving at optimal or near-optimal solutions to sometimes complex decision problems. Management scientists help businesses to achieve their goals using the scientific methods of operational research. </p><p>The management scientist's mandate is to use rational, systematic, science-based techniques to inform and improve decisions of all kinds. Of course, the techniques of management science are not restricted to business applications but may be applied to military, medical, public administration, charitable groups, political groups or community groups. </p><p>Management science is concerned with developing and applying <a href="/wiki/Scientific_modeling" class="mw-redirect" title="Scientific modeling">models</a> and <a href="/wiki/Concept" title="Concept">concepts</a> that may prove useful in helping to illuminate management issues and solve managerial problems, as well as designing and developing new and better models of organizational excellence.<sup id="cite_ref-LS_36-0" class="reference"><a href="#cite_note-LS-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Related_fields">Related fields</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Operations_research&action=edit&section=8" title="Edit section: Related fields"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Some of the fields that have considerable overlap with Operations Research and Management Science include:<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> </p> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 13em;"> <ul><li><a href="/wiki/Artificial_Intelligence" class="mw-redirect" title="Artificial Intelligence">Artificial Intelligence</a></li> <li><a href="/wiki/Business_analytics" title="Business analytics">Business analytics</a></li> <li><a href="/wiki/Computer_science" title="Computer science">Computer science</a></li> <li><a href="/wiki/Data_mining" title="Data mining">Data mining</a>/<a href="/wiki/Data_science" title="Data science">Data science</a>/<a href="/wiki/Big_data" title="Big data">Big data</a></li> <li><a href="/wiki/Decision_analysis" title="Decision analysis">Decision analysis</a></li> <li><a href="/wiki/Decision_intelligence" title="Decision intelligence">Decision intelligence</a></li> <li><a href="/wiki/Engineering" title="Engineering">Engineering</a></li> <li><a href="/wiki/Financial_engineering" title="Financial engineering">Financial engineering</a></li> <li><a href="/wiki/Forecasting" title="Forecasting">Forecasting</a></li> <li><a href="/wiki/Game_theory" title="Game theory">Game theory</a></li> <li><a href="/wiki/Geography" title="Geography">Geography</a>/<a href="/wiki/Geographic_information_science" title="Geographic information science">Geographic information science</a></li> <li><a href="/wiki/Graph_theory" title="Graph theory">Graph theory</a></li> <li><a href="/wiki/Industrial_engineering" title="Industrial engineering">Industrial engineering</a></li> <li><a href="/wiki/Inventory_control" title="Inventory control">Inventory control</a></li> <li><a href="/wiki/Logistics" title="Logistics">Logistics</a></li> <li><a href="/wiki/Mathematical_modeling" class="mw-redirect" title="Mathematical modeling">Mathematical modeling</a></li> <li><a href="/wiki/Mathematical_optimization" title="Mathematical optimization">Mathematical optimization</a></li> <li><a href="/wiki/Probability" title="Probability">Probability</a> and <a href="/wiki/Statistics" title="Statistics">statistics</a></li> <li><a href="/wiki/Project_management" title="Project management">Project management</a></li> <li><a href="/wiki/Policy_analysis" title="Policy analysis">Policy analysis</a></li> <li><a href="/wiki/Queueing_theory" title="Queueing theory">Queueing theory</a></li> <li><a href="/wiki/Simulation" title="Simulation">Simulation</a></li> <li><a href="/wiki/Social_network" title="Social network">Social network</a>/<a href="/wiki/Transportation_forecasting" title="Transportation forecasting">Transportation forecasting</a> models</li> <li><a href="/wiki/Stochastic_processes" class="mw-redirect" title="Stochastic processes">Stochastic processes</a></li> <li><a href="/wiki/Supply_chain_management" title="Supply chain management">Supply chain management</a></li> <li><a href="/wiki/Systems_engineering" title="Systems engineering">Systems engineering</a></li></ul> </div> <div class="mw-heading mw-heading3"><h3 id="Applications">Applications</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Operations_research&action=edit&section=9" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Applications are abundant such as in airlines, manufacturing companies, <a href="/wiki/Service_organization" class="mw-redirect" title="Service organization">service organizations</a>, military branches, and government. The range of problems and issues to which it has contributed insights and solutions is vast. It includes:<sup id="cite_ref-LS_36-1" class="reference"><a href="#cite_note-LS-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> </p> <ul><li>Scheduling (of airlines, trains, buses etc.)</li> <li>Assignment (assigning crew to flights, trains or buses; employees to projects; commitment and dispatch of power generation facilities)</li> <li>Facility location (deciding most appropriate location for new facilities such as warehouses; factories or fire station)</li> <li>Hydraulics & Piping Engineering (managing flow of water from reservoirs)</li> <li>Health Services (information and supply chain management)</li> <li>Game Theory (identifying, understanding; developing strategies adopted by companies)</li> <li>Urban Design</li> <li>Computer Network Engineering (packet routing; timing; analysis)</li> <li>Telecom & Data Communication Engineering (packet routing; timing; analysis)</li></ul> <p><sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> </p><p>Management is also concerned with so-called soft-operational analysis which concerns methods for <a href="/wiki/Strategic_planning" title="Strategic planning">strategic planning</a>, strategic <a href="/wiki/Decision_support" class="mw-redirect" title="Decision support">decision support</a>, <a href="/wiki/Problem_structuring_methods" title="Problem structuring methods">problem structuring methods</a>. In dealing with these sorts of challenges, mathematical <a href="/wiki/Modeling_and_simulation" title="Modeling and simulation">modeling and simulation</a> may not be appropriate or may not suffice. Therefore, during the past 30 years<sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Vagueness" title="Wikipedia:Vagueness"><span title="This information is too vague. (November 2017)">vague</span></a></i>]</sup>, a number of non-quantified modeling methods have been developed. These include:<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (June 2016)">citation needed</span></a></i>]</sup> </p> <ul><li>stakeholder based approaches including <a href="/wiki/Metagame_analysis" title="Metagame analysis">metagame analysis</a> and <a href="/wiki/Drama_theory" title="Drama theory">drama theory</a></li> <li><a href="/wiki/Morphological_analysis_(problem-solving)" title="Morphological analysis (problem-solving)">morphological analysis</a> and various forms of <a href="/wiki/Influence_diagram" title="Influence diagram">influence diagrams</a></li> <li>cognitive mapping</li> <li>strategic choice</li> <li>robustness analysis</li></ul> <div class="mw-heading mw-heading2"><h2 id="Societies_and_journals">Societies and journals</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Operations_research&action=edit&section=10" title="Edit section: Societies and journals"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Societies">Societies</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Operations_research&action=edit&section=11" title="Edit section: Societies"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/International_Federation_of_Operational_Research_Societies" title="International Federation of Operational Research Societies">International Federation of Operational Research Societies</a> (IFORS)<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> is an <a href="/wiki/Umbrella_organization" title="Umbrella organization">umbrella organization</a> for operational research societies worldwide, representing approximately 50 national societies including those in the US,<sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Operational_Research_Society" title="Operational Research Society">UK</a>,<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> France,<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> Germany, <a href="/wiki/Italian_Operations_Research_Society" title="Italian Operations Research Society">Italy</a>,<sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> Canada,<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> Australia,<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> New Zealand,<sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> Philippines,<sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> India,<sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> Japan and South Africa.<sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> For the institutionalization of Operations Research, the foundation of IFORS in 1960 was of decisive importance, which stimulated the foundation of national OR societies in Austria, Switzerland and Germany. IFORS held important international conferences every three years since 1957.<sup id="cite_ref-50" class="reference"><a href="#cite_note-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> The constituent members of IFORS form regional groups, such as that in Europe, the <a href="/wiki/Association_of_European_Operational_Research_Societies" title="Association of European Operational Research Societies">Association of European Operational Research Societies</a> (EURO).<sup id="cite_ref-51" class="reference"><a href="#cite_note-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> Other important operational research organizations are <a href="/wiki/Simulation_Interoperability_Standards_Organization" title="Simulation Interoperability Standards Organization">Simulation Interoperability Standards Organization</a> (SISO)<sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/Interservice/Industry_Training,_Simulation_and_Education_Conference" title="Interservice/Industry Training, Simulation and Education Conference">Interservice/Industry Training, Simulation and Education Conference</a> (I/ITSEC)<sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup> </p><p>In 2004, the US-based organization INFORMS began an initiative to market the OR profession better, including a website entitled <i>The Science of Better</i><sup id="cite_ref-54" class="reference"><a href="#cite_note-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> which provides an introduction to OR and examples of successful applications of OR to industrial problems. This initiative has been adopted by the <a href="/wiki/Operational_Research_Society" title="Operational Research Society">Operational Research Society</a> in the UK, including a website entitled <i>Learn About OR</i>.<sup id="cite_ref-55" class="reference"><a href="#cite_note-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Journals_of_INFORMS">Journals of INFORMS</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Operations_research&action=edit&section=12" title="Edit section: Journals of INFORMS"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Institute_for_Operations_Research_and_the_Management_Sciences" title="Institute for Operations Research and the Management Sciences">Institute for Operations Research and the Management Sciences</a> (INFORMS) publishes thirteen scholarly journals about operations research, including the top two journals in their class, according to 2005 <a href="/wiki/Journal_Citation_Reports" title="Journal Citation Reports">Journal Citation Reports</a>.<sup id="cite_ref-56" class="reference"><a href="#cite_note-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup> They are: </p> <ul><li><i>Decision Analysis</i><sup id="cite_ref-57" class="reference"><a href="#cite_note-57"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup></li> <li><i>Information Systems Research</i><sup id="cite_ref-58" class="reference"><a href="#cite_note-58"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup></li> <li><i>INFORMS Journal on Computing</i><sup id="cite_ref-59" class="reference"><a href="#cite_note-59"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup></li> <li><i>INFORMS Transactions on Education</i><sup id="cite_ref-60" class="reference"><a href="#cite_note-60"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup> (an open access journal)</li> <li><i>Interfaces</i><sup id="cite_ref-61" class="reference"><a href="#cite_note-61"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup></li> <li><i><a href="/wiki/Management_Science_(journal)" title="Management Science (journal)">Management Science</a></i></li> <li><i><a href="/wiki/Manufacturing_%26_Service_Operations_Management" title="Manufacturing & Service Operations Management">Manufacturing & Service Operations Management</a></i></li> <li><i><a href="/wiki/Marketing_Science_(journal)" title="Marketing Science (journal)">Marketing Science</a></i></li> <li><i><a href="/wiki/Mathematics_of_Operations_Research" title="Mathematics of Operations Research">Mathematics of Operations Research</a></i></li> <li><i><a href="/wiki/Operations_Research_(journal)" title="Operations Research (journal)">Operations Research</a></i></li> <li><i>Organization Science</i><sup id="cite_ref-62" class="reference"><a href="#cite_note-62"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup></li> <li><i>Service Science</i><sup id="cite_ref-63" class="reference"><a href="#cite_note-63"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup></li> <li><i><a href="/wiki/Transportation_Science" title="Transportation Science">Transportation Science</a></i></li></ul> <div class="mw-heading mw-heading3"><h3 id="Other_journals">Other journals</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Operations_research&action=edit&section=13" title="Edit section: Other journals"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>These are listed in alphabetical order of their titles. </p> <ul><li><i><a href="/wiki/4OR" title="4OR">4OR</a>-A Quarterly Journal of Operations Research</i>: jointly published the Belgian, French and Italian Operations Research Societies (Springer);</li> <li><i><a href="/wiki/Decision_Sciences" title="Decision Sciences">Decision Sciences</a></i> published by <a href="/wiki/Wiley-Blackwell" title="Wiley-Blackwell">Wiley-Blackwell</a> on behalf of the <a href="/wiki/Decision_Sciences_Institute" title="Decision Sciences Institute">Decision Sciences Institute</a></li> <li><i><a href="/wiki/European_Journal_of_Operational_Research" title="European Journal of Operational Research">European Journal of Operational Research</a> (EJOR)</i>: Founded in 1975 and is presently<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Manual_of_Style/Dates_and_numbers#Chronological_items" title="Wikipedia:Manual of Style/Dates and numbers"><span title="The time period mentioned near this tag is ambiguous. (March 2019)">when?</span></a></i>]</sup> by far the largest operational research journal in the world, with its around 9,000 pages of published papers per year. In 2004, its total number of citations was the second largest amongst Operational Research and Management Science journals;</li> <li><i>INFOR Journal</i>: published and sponsored by the Canadian Operational Research Society;</li> <li><i>Journal of Defense Modeling and Simulation (JDMS): Applications, Methodology, Technology</i>: a quarterly journal devoted to advancing the science of modeling and simulation as it relates to the military and defense.<sup id="cite_ref-64" class="reference"><a href="#cite_note-64"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup></li> <li><i><a href="/wiki/Journal_of_the_Operational_Research_Society" title="Journal of the Operational Research Society">Journal of the Operational Research Society</a> (JORS)</i>: an official journal of <a href="/wiki/The_OR_Society" class="mw-redirect" title="The OR Society">The OR Society</a>; this is the oldest continuously published journal of OR in the world, published by <a href="/wiki/Taylor_%26_Francis" title="Taylor & Francis">Taylor & Francis</a>;</li> <li><i>Military Operations Research (MOR)</i>: published by the <a href="/wiki/Military_Operations_Research_Society" title="Military Operations Research Society">Military Operations Research Society</a>;</li> <li><i>Omega - The International Journal of Management Science</i>;</li> <li><i><a href="/wiki/Operations_Research_Letters" title="Operations Research Letters">Operations Research Letters</a></i>;</li> <li><i>Opsearch</i>: official journal of the Operational Research Society of India;</li> <li><i>OR Insight</i>: a quarterly journal of The OR Society published by Palgrave;<sup id="cite_ref-The_OR_Society_65-0" class="reference"><a href="#cite_note-The_OR_Society-65"><span class="cite-bracket">[</span>65<span class="cite-bracket">]</span></a></sup></li> <li><i>Pesquisa Operacional</i>, the official journal of the Brazilian Operations Research Society</li> <li><i><a href="/wiki/Production_and_Operations_Management" title="Production and Operations Management">Production and Operations Management</a></i>, the official journal of the Production and Operations Management Society</li> <li><i>TOP</i>: the official journal of the <a href="/wiki/Spanish_Statistics_and_Operations_Research_Society" title="Spanish Statistics and Operations Research Society">Spanish Statistics and Operations Research Society</a>.<sup id="cite_ref-66" class="reference"><a href="#cite_note-66"><span class="cite-bracket">[</span>66<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Operations_research&action=edit&section=14" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1216972533">.mw-parser-output .col-begin{border-collapse:collapse;padding:0;color:inherit;width:100%;border:0;margin:0}.mw-parser-output .col-begin-small{font-size:90%}.mw-parser-output .col-break{vertical-align:top;text-align:left}.mw-parser-output .col-break-2{width:50%}.mw-parser-output .col-break-3{width:33.3%}.mw-parser-output .col-break-4{width:25%}.mw-parser-output .col-break-5{width:20%}@media(max-width:720px){.mw-parser-output .col-begin,.mw-parser-output .col-begin>tbody,.mw-parser-output .col-begin>tbody>tr,.mw-parser-output .col-begin>tbody>tr>td{display:block!important;width:100%!important}.mw-parser-output .col-break{padding-left:0!important}}</style><div> <table class="col-begin" role="presentation"> <tbody><tr> <td class="col-break"> <dl><dt>Operations research topics</dt></dl> <ul><li><a href="/wiki/Black_box" title="Black box">Black box analysis</a></li> <li><a href="/wiki/Dynamic_programming" title="Dynamic programming">Dynamic programming</a></li> <li><a href="/wiki/Inventory_theory" title="Inventory theory">Inventory theory</a></li> <li><a href="/wiki/Optimal_maintenance" title="Optimal maintenance">Optimal maintenance</a></li> <li><a href="/wiki/Real_options_valuation" title="Real options valuation">Real options valuation</a></li> <li><a href="/wiki/Artificial_intelligence" title="Artificial intelligence">Artificial intelligence</a></li></ul> </td> <td class="col-break"> <dl><dt>Operations researchers</dt></dl> <ul><li><a href="/wiki/Category:Operations_researchers" title="Category:Operations researchers">Operations researchers</a> (category)</li> <li><a href="/wiki/George_Dantzig" title="George Dantzig">George Dantzig</a></li> <li><a href="/wiki/Leonid_Kantorovich" title="Leonid Kantorovich">Leonid Kantorovich</a></li> <li><a href="/wiki/Tjalling_Koopmans" title="Tjalling Koopmans">Tjalling Koopmans</a></li> <li><a href="/wiki/Russell_L._Ackoff" title="Russell L. Ackoff">Russell L. Ackoff</a></li> <li><a href="/wiki/Stafford_Beer" title="Stafford Beer">Stafford Beer</a></li> <li><a href="/wiki/Alfred_Blumstein" title="Alfred Blumstein">Alfred Blumstein</a></li> <li><a href="/wiki/C._West_Churchman" title="C. West Churchman">C. West Churchman</a></li></ul> </td> <td class="col-break"> <ul><li><a href="/wiki/William_W._Cooper" title="William W. Cooper">William W. Cooper</a></li> <li><a href="/wiki/Robert_Dorfman" title="Robert Dorfman">Robert Dorfman</a></li> <li><a href="/wiki/Richard_M._Karp" title="Richard M. Karp">Richard M. Karp</a></li> <li><a href="/wiki/Ramayya_Krishnan" title="Ramayya Krishnan">Ramayya Krishnan</a></li> <li><a href="/wiki/Frederick_W._Lanchester" title="Frederick W. Lanchester">Frederick W. Lanchester</a></li> <li><a href="/wiki/Thomas_L._Magnanti" title="Thomas L. Magnanti">Thomas L. Magnanti</a></li> <li><a href="/wiki/Alvin_E._Roth" title="Alvin E. Roth">Alvin E. Roth</a></li> <li><a href="/wiki/Peter_Whittle_(mathematician)" title="Peter Whittle (mathematician)">Peter Whittle</a></li></ul> </td> <td class="col-break"> <dl><dt>Related fields</dt></dl> <ul><li><a href="/wiki/Behavioral_operations_research" class="mw-redirect" title="Behavioral operations research">Behavioral operations research</a></li> <li><a href="/wiki/Big_data" title="Big data">Big data</a></li> <li><a href="/wiki/Business_engineering" class="mw-redirect" title="Business engineering">Business engineering</a></li> <li><a href="/wiki/Business_process_management" title="Business process management">Business process management</a></li> <li><a href="/wiki/Database_normalization" title="Database normalization">Database normalization</a></li> <li><a href="/wiki/Engineering_management" title="Engineering management">Engineering management</a></li> <li><a href="/wiki/Geographic_information_system" title="Geographic information system">Geographic information systems</a></li> <li><a href="/wiki/Industrial_engineering" title="Industrial engineering">Industrial engineering</a></li> <li><a href="/wiki/Industrial_organization" title="Industrial organization">Industrial organization</a></li> <li><a href="/wiki/Managerial_economics" title="Managerial economics">Managerial economics</a></li></ul> </td> <td class="col-break"> <ul><li><a href="/wiki/Military_simulation" title="Military simulation">Military simulation</a></li> <li><a href="/wiki/Operational_level_of_war" title="Operational level of war">Operational level of war</a></li> <li><a href="/wiki/Power_system_simulation" title="Power system simulation">Power system simulation</a></li> <li><a href="/wiki/Project_production_management" title="Project production management">Project production management</a></li> <li><a href="/wiki/Reliability_engineering" title="Reliability engineering">Reliability engineering</a></li> <li><a href="/wiki/Scientific_management" title="Scientific management">Scientific management</a></li> <li><a href="/wiki/Search-based_software_engineering" title="Search-based software engineering">Search-based software engineering</a></li> <li><a href="/wiki/Simulation_modeling" title="Simulation modeling">Simulation modeling</a></li> <li><a href="/wiki/Strategic_management" title="Strategic management">Strategic management</a></li> <li><a href="/wiki/Supply_chain_engineering" title="Supply chain engineering">Supply chain engineering</a></li> <li><a href="/wiki/System_safety" title="System safety">System safety</a></li> <li><a href="/wiki/Wargaming" class="mw-redirect" title="Wargaming">Wargaming</a></li></ul> <p>  </p> </td></tr></tbody></table></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Operations_research&action=edit&section=15" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output 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"In January 1962 the name was changed to Army Operational Research Establishment (AORE). Following the creation of a unified Ministry of Defence, a tri-service operational research organisation was established: the <a href="/w/index.php?title=Defence_Operational_Analysis_Establishment&action=edit&redlink=1" class="new" title="Defence Operational Analysis Establishment (page does not exist)">Defence Operational Research Establishment</a> (DOAE) which was formed in 1965, and it absorbed the Army Operational Research Establishment based at West Byfleet."</span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20110812213540/http://brochure.unisa.ac.za/myunisa/data/subjects/Quantitative%20Management.pdf">"Archived copy"</a> <span class="cs1-format">(PDF)</span>. Archived from <a rel="nofollow" class="external text" href="http://brochure.unisa.ac.za/myunisa/data/subjects/Quantitative%20Management.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 12 August 2011<span class="reference-accessdate">. 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Scs.org. Archived from <a rel="nofollow" class="external text" href="http://www.scs.org/pubs/jdms/jdms.html">the original</a> on 23 August 2009<span class="reference-accessdate">. Retrieved <span class="nowrap">13 November</span> 2011</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=JDMS&rft.pub=Scs.org&rft.au=The+Society+for+Modeling+%26+Simulation+International&rft_id=http%3A%2F%2Fwww.scs.org%2Fpubs%2Fjdms%2Fjdms.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOperations+research" class="Z3988"></span></span> </li> <li id="cite_note-The_OR_Society-65"><span class="mw-cite-backlink"><b><a href="#cite_ref-The_OR_Society_65-0">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.orsoc.org.uk">The OR Society</a> <a rel="nofollow" class="external text" href="http://webarchive.loc.gov/all/20060424161729/http://www.orsoc.org.uk/">Archived</a> 24 April 2006 at the <a href="/wiki/Library_of_Congress" title="Library of Congress">Library of Congress</a> Web Archives;</span> </li> <li id="cite_note-66"><span class="mw-cite-backlink"><b><a href="#cite_ref-66">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.springer.com/east/home/business/operations+research?SGWID=5-40521-70-173677307-detailsPage=journal%7Cdescription">"TOP"</a>. Springer.com<span class="reference-accessdate">. Retrieved <span class="nowrap">13 November</span> 2011</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=TOP&rft.pub=Springer.com&rft_id=https%3A%2F%2Fwww.springer.com%2Feast%2Fhome%2Fbusiness%2Foperations%2Bresearch%3FSGWID%3D5-40521-70-173677307-detailsPage%3Djournal%257Cdescription&rfr_id=info%3Asid%2Fen.wikipedia.org%3AOperations+research" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Operations_research&action=edit&section=16" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Classic_books_and_articles">Classic books and articles</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Operations_research&action=edit&section=17" title="Edit section: Classic books and articles"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>R. E. Bellman, <i>Dynamic Programming</i>, Princeton University Press, Princeton, 1957</li> <li>Abraham Charnes, William W. Cooper, <i>Management Models and Industrial Applications of Linear Programming</i>, Volumes I and II, New York, John Wiley & Sons, 1961</li> <li>Abraham Charnes, William W. Cooper, A. Henderson, <i>An Introduction to Linear Programming</i>, New York, John Wiley & Sons, 1953</li> <li>C. West Churchman, Russell L. Ackoff & E. L. Arnoff, <i>Introduction to Operations Research</i>, New York: J. Wiley and Sons, 1957</li> <li>George B. Dantzig, <i>Linear Programming and Extensions</i>, Princeton, Princeton University Press, 1963</li> <li>Lester K. Ford, Jr., D. Ray Fulkerson, <i>Flows in Networks</i>, Princeton, Princeton University Press, 1962</li> <li>Jay W. Forrester, <i>Industrial Dynamics</i>, Cambridge, MIT Press, 1961</li> <li>L. V. Kantorovich, "Mathematical Methods of Organizing and Planning Production" <i>Management Science</i>, 4, 1960, 266–422</li> <li>Ralph Keeney, Howard Raiffa, <i>Decisions with Multiple Objectives: Preferences and Value Tradeoffs</i>, New York, John Wiley & Sons, 1976</li> <li>H. W. Kuhn, "The Hungarian Method for the Assignment Problem," <i>Naval Research Logistics Quarterly</i>, 1–2, 1955, 83–97</li> <li>H. W. Kuhn, A. W. Tucker, "Nonlinear Programming," pp. 481–492 in <i>Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability</i></li> <li>B. O. Koopman, <i>Search and Screening: General Principles and Historical Applications</i>, New York, Pergamon Press, 1980</li> <li>Tjalling C. Koopmans, editor, <i>Activity Analysis of Production and Allocation</i>, New York, John Wiley & Sons, 1951</li> <li>Charles C. Holt, Franco Modigliani, John F. Muth, Herbert A. Simon, <i>Planning Production, Inventories, and Work Force</i>, Englewood Cliffs, NJ, Prentice-Hall, 1960</li> <li>Philip M. Morse, George E. Kimball, <i>Methods of Operations Research</i>, New York, MIT Press and John Wiley & Sons, 1951</li> <li>Robert O. Schlaifer, Howard Raiffa, <i>Applied Statistical Decision Theory</i>, Cambridge, Division of Research, Harvard Business School, 1961</li></ul> <div class="mw-heading mw-heading3"><h3 id="Classic_textbooks">Classic textbooks</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Operations_research&action=edit&section=18" title="Edit section: Classic textbooks"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Taha, Hamdy A., "Operations Research: An Introduction", Pearson, 10th Edition, 2016</li> <li>Frederick S. Hillier & Gerald J. Lieberman, <i>Introduction to Operations Research</i>, McGraw-Hill: Boston MA; 10th Edition, 2014</li> <li>Robert J. Thierauf & Richard A. Grosse, "Decision Making Through Operations Research", John Wiley & Sons, INC, 1970</li> <li>Harvey M. Wagner, <i>Principles of Operations Research</i>, Englewood Cliffs, Prentice-Hall, 1969</li> <li><a href="/wiki/Elena_Ventsel" class="mw-redirect" title="Elena Ventsel">Wentzel (Ventsel), E. S.</a> <i>Introduction to Operations Research</i>, Moscow: Soviet Radio Publishing House, 1964.</li></ul> <div class="mw-heading mw-heading3"><h3 id="History_2">History</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Operations_research&action=edit&section=19" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Saul I. Gass, Arjang A. Assad, <i>An Annotated Timeline of Operations Research: An Informal History</i>. New York, Kluwer Academic Publishers, 2005.</li> <li>Saul I. Gass (Editor), Arjang A. Assad (Editor), <i>Profiles in Operations Research: Pioneers and Innovators</i>. Springer, 2011</li> <li>Maurice W. Kirby (Operational Research Society (Great Britain)). Operational Research in War and Peace: The British Experience from the 1930s to 1970, Imperial College Press, 2003. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1-86094-366-7" title="Special:BookSources/1-86094-366-7">1-86094-366-7</a>, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-86094-366-9" title="Special:BookSources/978-1-86094-366-9">978-1-86094-366-9</a></li> <li>J. K. Lenstra, A. H. G. Rinnooy Kan, A. Schrijver (editors) <i>History of Mathematical Programming: A Collection of Personal Reminiscences</i>, North-Holland, 1991</li> <li>Charles W. McArthur, <i>Operations Analysis in the U.S. Army Eighth Air Force in World War II</i>, History of Mathematics, Vol. 4, Providence, American Mathematical Society, 1990</li> <li>C. H. Waddington, <i>O. R. in World War 2: Operational Research Against the U-boat</i>, London, Elek Science, 1973.</li> <li>Richard Vahrenkamp: <i>Mathematical Management – Operations Research in the United States and Western Europe, 1945 – 1990</i>, in: Management Revue – Socio-Economic Studies, vol. 34 (2023), issue 1, pp. 69–91.</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Operations_research&action=edit&section=20" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output 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psychology">Psychology</a></li> <li><a href="/wiki/Systems_theory" title="Systems theory">Theory</a> (<a href="/wiki/Systems_thinking" title="Systems thinking">Systems thinking</a>)</li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/List_of_systems_scientists" title="List of systems scientists">Scientists</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Russell_L._Ackoff" title="Russell L. Ackoff">Russell L. Ackoff</a></li> <li><a href="/wiki/Victor_Aladjev" title="Victor Aladjev">Victor Aladjev</a></li> <li><a href="/wiki/William_Ross_Ashby" class="mw-redirect" title="William Ross Ashby">William Ross Ashby</a></li> <li><a href="/wiki/Ruzena_Bajcsy" title="Ruzena Bajcsy">Ruzena Bajcsy</a></li> <li><a href="/wiki/B%C3%A9la_H._B%C3%A1n%C3%A1thy" title="Béla H. Bánáthy">Béla H. Bánáthy</a></li> <li><a href="/wiki/Gregory_Bateson" title="Gregory Bateson">Gregory Bateson</a></li> <li><a href="/wiki/Anthony_Stafford_Beer" class="mw-redirect" title="Anthony Stafford Beer">Anthony Stafford Beer</a></li> <li><a href="/wiki/Richard_E._Bellman" title="Richard E. Bellman">Richard E. Bellman</a></li> <li><a href="/wiki/Ludwig_von_Bertalanffy" title="Ludwig von Bertalanffy">Ludwig von Bertalanffy</a></li> <li><a href="/wiki/Margaret_Boden" title="Margaret Boden">Margaret Boden</a></li> <li><a href="/wiki/Alexander_Bogdanov" title="Alexander Bogdanov">Alexander Bogdanov</a></li> <li><a href="/wiki/Kenneth_E._Boulding" title="Kenneth E. Boulding">Kenneth E. Boulding</a></li> <li><a href="/wiki/Murray_Bowen" title="Murray Bowen">Murray Bowen</a></li> <li><a href="/wiki/Kathleen_Carley" title="Kathleen Carley">Kathleen Carley</a></li> <li><a href="/wiki/Mary_Cartwright" title="Mary Cartwright">Mary Cartwright</a></li> <li><a href="/wiki/C._West_Churchman" title="C. West Churchman">C. West Churchman</a></li> <li><a href="/wiki/Manfred_Clynes" title="Manfred Clynes">Manfred Clynes</a></li> <li><a href="/wiki/George_Dantzig" title="George Dantzig">George Dantzig</a></li> <li><a href="/wiki/Edsger_W._Dijkstra" title="Edsger W. Dijkstra">Edsger W. Dijkstra</a></li> <li><a href="/wiki/Fred_Emery" title="Fred Emery">Fred Emery</a></li> <li><a href="/wiki/Heinz_von_Foerster" title="Heinz von Foerster">Heinz von Foerster</a></li> <li><a href="/wiki/Stephanie_Forrest" title="Stephanie Forrest">Stephanie Forrest</a></li> <li><a href="/wiki/Jay_Wright_Forrester" title="Jay Wright Forrester">Jay Wright Forrester</a></li> <li><a href="/wiki/Barbara_J._Grosz" title="Barbara J. Grosz">Barbara Grosz</a></li> <li><a href="/wiki/Charles_A._S._Hall" title="Charles A. S. Hall">Charles A. S. Hall</a></li> <li><a href="/wiki/Mike_Jackson_(systems_scientist)" title="Mike Jackson (systems scientist)">Mike Jackson</a></li> <li><a href="/wiki/Lydia_Kavraki" title="Lydia Kavraki">Lydia Kavraki</a></li> <li><a href="/wiki/James_J._Kay" title="James J. Kay">James J. Kay</a></li> <li><a href="/wiki/Faina_Mihajlovna_Kirillova" class="mw-redirect" title="Faina Mihajlovna Kirillova">Faina M. Kirillova</a></li> <li><a href="/wiki/George_Klir" title="George Klir">George Klir</a></li> <li><a href="/wiki/Allenna_Leonard" title="Allenna Leonard">Allenna Leonard</a></li> <li><a href="/wiki/Edward_Norton_Lorenz" title="Edward Norton Lorenz">Edward Norton Lorenz</a></li> <li><a href="/wiki/Niklas_Luhmann" title="Niklas Luhmann">Niklas Luhmann</a></li> <li><a href="/wiki/Humberto_Maturana" title="Humberto Maturana">Humberto Maturana</a></li> <li><a href="/wiki/Margaret_Mead" title="Margaret Mead">Margaret Mead</a></li> <li><a href="/wiki/Donella_Meadows" title="Donella Meadows">Donella Meadows</a></li> <li><a href="/wiki/Mihajlo_D._Mesarovic" title="Mihajlo D. Mesarovic">Mihajlo D. Mesarovic</a></li> <li><a href="/wiki/James_Grier_Miller" title="James Grier Miller">James Grier Miller</a></li> <li><a href="/wiki/Radhika_Nagpal" title="Radhika Nagpal">Radhika Nagpal</a></li> <li><a href="/wiki/Howard_T._Odum" title="Howard T. Odum">Howard T. Odum</a></li> <li><a href="/wiki/Talcott_Parsons" title="Talcott Parsons">Talcott Parsons</a></li> <li><a href="/wiki/Ilya_Prigogine" title="Ilya Prigogine">Ilya Prigogine</a></li> <li><a href="/wiki/Qian_Xuesen" title="Qian Xuesen">Qian Xuesen</a></li> <li><a href="/wiki/Anatol_Rapoport" title="Anatol Rapoport">Anatol Rapoport</a></li> <li><a href="/wiki/John_Seddon" title="John Seddon">John Seddon</a></li> <li><a href="/wiki/Peter_Senge" title="Peter Senge">Peter Senge</a></li> <li><a href="/wiki/Claude_Shannon" title="Claude Shannon">Claude Shannon</a></li> <li><a href="/wiki/Katia_Sycara" title="Katia Sycara">Katia Sycara</a></li> <li><a href="/wiki/Eric_Trist" title="Eric Trist">Eric Trist</a></li> <li><a href="/wiki/Francisco_Varela" title="Francisco Varela">Francisco Varela</a></li> <li><a href="/wiki/Manuela_M._Veloso" title="Manuela M. Veloso">Manuela M. Veloso</a></li> <li><a href="/wiki/Kevin_Warwick" title="Kevin Warwick">Kevin Warwick</a></li> <li><a href="/wiki/Norbert_Wiener" title="Norbert Wiener">Norbert Wiener</a></li> <li><a href="/wiki/Jennifer_Wilby" title="Jennifer Wilby">Jennifer Wilby</a></li> <li><a href="/wiki/Anthony_Wilden" title="Anthony Wilden">Anthony Wilden</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Applications</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Systems_theory_in_anthropology" title="Systems theory in anthropology">Systems theory in anthropology</a></li> <li><a href="/wiki/Systems_theory_in_archaeology" title="Systems theory in archaeology">Systems theory in archaeology</a></li> <li><a href="/wiki/Systems_theory_in_political_science" title="Systems theory in political science">Systems theory in political science</a></li></ul> </div></td></tr><tr><th 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src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span> <b><a href="https://commons.wikimedia.org/wiki/Category:Systems_theory" class="extiw" title="commons:Category:Systems theory">Commons</a></b></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Major_mathematics_areas1051" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Areas_of_mathematics" title="Template:Areas of mathematics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Areas_of_mathematics" title="Template talk:Areas of mathematics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Areas_of_mathematics" title="Special:EditPage/Template:Areas of mathematics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Major_mathematics_areas1051" style="font-size:114%;margin:0 4em">Major <a href="/wiki/Mathematics" title="Mathematics">mathematics</a> areas</div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><a href="/wiki/History_of_mathematics" title="History of mathematics">History</a> <ul><li><a href="/wiki/Timeline_of_mathematics" title="Timeline of mathematics">Timeline</a></li> <li><a href="/wiki/Future_of_mathematics" title="Future of mathematics">Future</a></li></ul></li> <li><a href="/wiki/Lists_of_mathematics_topics" title="Lists of mathematics topics">Lists</a></li> <li><a href="/wiki/Glossary_of_mathematical_symbols" title="Glossary of mathematical symbols">Glossary</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Foundations_of_mathematics" title="Foundations of mathematics">Foundations</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Category_theory" title="Category theory">Category theory</a></li> <li><a href="/wiki/Information_theory" title="Information theory">Information theory</a></li> <li><a href="/wiki/Mathematical_logic" title="Mathematical logic">Mathematical logic</a></li> <li><a href="/wiki/Philosophy_of_mathematics" title="Philosophy of mathematics">Philosophy of mathematics</a></li> <li><a href="/wiki/Set_theory" title="Set theory">Set theory</a></li> <li><a href="/wiki/Type_theory" title="Type theory">Type theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Algebra" title="Algebra">Algebra</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Abstract_algebra" title="Abstract algebra">Abstract</a></li> <li><a href="/wiki/Commutative_algebra" title="Commutative algebra">Commutative</a></li> <li><a href="/wiki/Elementary_algebra" title="Elementary algebra">Elementary</a></li> <li><a href="/wiki/Group_theory" title="Group 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this template">e</abbr></a></li></ul></div><div id="Microeconomics291" style="font-size:114%;margin:0 4em"><a href="/wiki/Microeconomics" title="Microeconomics">Microeconomics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Major topics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Aggregation_problem" title="Aggregation problem">Aggregation</a></li> <li><a href="/wiki/Budget_set" title="Budget set">Budget set</a></li> <li><a href="/wiki/Consumer_choice" title="Consumer choice">Consumer choice</a></li> <li><a href="/wiki/Convexity_in_economics" title="Convexity in economics">Convexity</a> and <a href="/wiki/Non-convexity_(economics)" title="Non-convexity (economics)">non-convexity</a></li> <li><a href="/wiki/Economic_cost" title="Economic cost">Cost</a> <ul><li><a href="/wiki/Average_cost" title="Average cost">Average</a></li> <li><a href="/wiki/Marginal_cost" title="Marginal cost">Marginal</a></li> <li><a href="/wiki/Opportunity_cost" title="Opportunity cost">Opportunity</a> <ul><li><a href="/wiki/Implicit_cost" title="Implicit cost">Implicit</a></li></ul></li> <li><a href="/wiki/Social_cost" title="Social cost">Social</a></li> <li><a href="/wiki/Sunk_cost" title="Sunk cost">Sunk</a></li> <li><a href="/wiki/Transaction_cost" title="Transaction cost">Transaction</a></li></ul></li> <li><a href="/wiki/Cost%E2%80%93benefit_analysis" title="Cost–benefit analysis">Cost–benefit analysis</a></li> <li><a href="/wiki/Deadweight_loss" title="Deadweight loss">Deadweight loss</a></li> <li><a href="/wiki/Distribution_(economics)" title="Distribution (economics)">Distribution</a></li> <li><a href="/wiki/Economies_of_scale" title="Economies of scale">Economies of scale</a></li> <li><a href="/wiki/Economies_of_scope" title="Economies of scope">Economies of scope</a></li> <li><a href="/wiki/Elasticity_(economics)" title="Elasticity (economics)">Elasticity</a> <ul><li><a href="/wiki/Cross_elasticity_of_demand" title="Cross elasticity of demand">Cross elasticity of demand</a></li> <li><a href="/wiki/Income_elasticity_of_demand" title="Income elasticity of demand">Income elasticity of demand</a></li> <li><a href="/wiki/Price_elasticity_of_demand" title="Price elasticity of demand">Price elasticity of demand</a></li> <li><a href="/wiki/Price_elasticity_of_supply" title="Price elasticity of supply">Price elasticity of supply</a></li></ul></li> <li><a href="/wiki/Economic_equilibrium" title="Economic equilibrium">Equilibrium</a> <ul><li><a href="/wiki/General_equilibrium_theory" title="General equilibrium theory">General</a></li></ul></li> <li><a href="/wiki/Trade" title="Trade">Exchange</a></li> <li><a href="/wiki/Externality" title="Externality">Externality</a></li> <li><a href="/wiki/Theory_of_the_firm" title="Theory of the firm">Firms</a></li> <li><a href="/wiki/Goods_and_services" title="Goods and services">Goods and services</a> <ul><li><a href="/wiki/Goods" title="Goods">Goods</a></li> <li><a href="/wiki/Service_(economics)" title="Service (economics)">Service</a></li></ul></li> <li><a href="/wiki/Family_economics" title="Family economics">Household</a></li> <li><a href="/wiki/Income%E2%80%93consumption_curve" title="Income–consumption curve">Income–consumption curve</a></li> <li><a href="/wiki/Information_economics" title="Information economics">Information</a></li> <li><a href="/wiki/Indifference_curve" title="Indifference curve">Indifference curve</a></li> <li><a href="/wiki/Intertemporal_choice" title="Intertemporal choice">Intertemporal choice</a></li> <li><a href="/wiki/Market_(economics)" title="Market (economics)">Market</a></li> <li><a href="/wiki/Market_failure" title="Market failure">Market failure</a></li> <li><a href="/wiki/Market_structure" title="Market structure">Market structure</a> <ul><li><a href="/wiki/Competition_(economics)" title="Competition (economics)">Competition</a> <ul><li><a href="/wiki/Monopolistic_competition" title="Monopolistic competition">Monopolistic</a></li> <li><a href="/wiki/Perfect_competition" title="Perfect competition">Perfect</a></li></ul></li> <li><a href="/wiki/Duopoly" title="Duopoly">Duopoly</a></li> <li><a href="/wiki/Monopoly" title="Monopoly">Monopoly</a> <ul><li><a href="/wiki/Bilateral_monopoly" title="Bilateral monopoly">Bilateral</a></li> <li><a href="/wiki/Complementary_monopoly" title="Complementary monopoly">Complementary</a></li></ul></li> <li><a href="/wiki/Monopsony" title="Monopsony">Monopsony</a></li> <li><a href="/wiki/Oligopoly" title="Oligopoly">Oligopoly</a></li> <li><a href="/wiki/Oligopsony" title="Oligopsony">Oligopsony</a></li></ul></li> <li><a href="/wiki/Pareto_efficiency" title="Pareto efficiency">Pareto efficiency</a></li> <li><a href="/wiki/Preference_(economics)" title="Preference (economics)">Preferences</a></li> <li><a href="/wiki/Price" title="Price">Price</a> <ul><li><a href="/wiki/Price_controls" title="Price controls">Price controls</a></li> <li><a href="/wiki/Price_ceiling" title="Price ceiling">Price ceiling</a></li> <li><a href="/wiki/Price_floor" title="Price floor">Price floor</a></li> <li><a href="/wiki/Price_discrimination" title="Price discrimination">Price discrimination</a></li> <li><a href="/wiki/Price_signal" title="Price signal">Price signal</a></li> <li><a href="/wiki/Price_system" title="Price system">Price system</a>/<a href="/wiki/Free_price_system" title="Free price system">Free</a></li> <li><a href="/wiki/Pricing" title="Pricing">Pricing</a></li></ul></li> <li><a href="/wiki/Production_set" title="Production set">Production</a></li> <li><a href="/wiki/Profit_(economics)" title="Profit (economics)">Profit</a></li> <li><a href="/wiki/Public_good_(economics)" class="mw-redirect" title="Public good (economics)">Public goods</a></li> <li><a href="/wiki/Rationing" title="Rationing">Rationing</a></li> <li><a href="/wiki/Economic_rent" title="Economic rent">Rent</a></li> <li><a href="/wiki/Returns_to_scale" title="Returns to scale">Returns to scale</a></li> <li><a href="/wiki/Risk_aversion" title="Risk aversion">Risk aversion</a></li> <li><a href="/wiki/Scarcity" title="Scarcity">Scarcity</a></li> <li><a href="/wiki/Shortage" title="Shortage">Shortage</a>/<a href="/wiki/Excess_supply" title="Excess supply">Excess supply</a></li> <li><a href="/wiki/Substitution_effect" title="Substitution effect">Substitution effect</a></li> <li><a href="/wiki/Economic_surplus" title="Economic surplus">Surplus</a></li> <li><a href="/wiki/Social_choice_theory" title="Social choice theory">Social choice</a></li> <li><a href="/wiki/Supply_and_demand" title="Supply and demand">Supply and demand</a> <ul><li><a href="/wiki/Demand" title="Demand">Demand</a>/<a href="/wiki/Law_of_demand" title="Law of demand">Law of demand</a></li> <li><a href="/wiki/Supply_(economics)" title="Supply (economics)">Supply</a>/<a href="/wiki/Law_of_supply" title="Law of supply">Law of supply</a></li></ul></li> <li><a href="/wiki/Uncertainty" title="Uncertainty">Uncertainty</a></li> <li><a href="/wiki/Utility" title="Utility">Utility</a> <ul><li><a href="/wiki/Expected_utility_hypothesis" title="Expected utility hypothesis">Expected</a></li> <li><a href="/wiki/Marginal_utility" title="Marginal utility">Marginal</a></li></ul></li> <li><a href="/wiki/Wage" title="Wage">Wage</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Subfields</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Behavioral_economics" title="Behavioral economics">Behavioral</a></li> <li><a href="/wiki/Business_economics" title="Business economics">Business</a></li> <li><a href="/wiki/Computational_economics" title="Computational economics">Computational</a></li> <li><a href="/wiki/Development_economics" title="Development economics">Development</a></li> <li><a href="/wiki/Statistical_decision_theory" class="mw-redirect" title="Statistical decision theory">Statistical decision theory</a></li> <li><a href="/wiki/Econometrics" title="Econometrics">Econometrics</a></li> <li><a href="/wiki/Engineering_economics" title="Engineering economics">Engineering economics</a></li> <li><a href="/wiki/Engineering_economics_(civil_engineering)" title="Engineering economics (civil engineering)">Civil engineering economics</a></li> <li><a href="/wiki/Evolutionary_economics" title="Evolutionary economics">Evolutionary</a></li> <li><a href="/wiki/Experimental_economics" title="Experimental economics">Experimental</a></li> <li><a href="/wiki/Game_theory" title="Game theory">Game theory</a></li> <li><a href="/wiki/Green_economy" title="Green economy">Green</a></li> <li><a href="/wiki/Industrial_organization" title="Industrial organization">Industrial organization</a></li> <li><a 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<ul><li><a href="/wiki/Economics" title="Economics">Economics</a> <ul><li><a href="/wiki/Applied_economics" title="Applied economics">Applied</a></li></ul></li> <li><a href="/wiki/Macroeconomics" title="Macroeconomics">Macroeconomics</a></li> <li><a href="/wiki/Political_economy" title="Political economy">Political economy</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="nowrap"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Emblem-money.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Emblem-money.svg/16px-Emblem-money.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Emblem-money.svg/24px-Emblem-money.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Emblem-money.svg/32px-Emblem-money.svg.png 2x" data-file-width="48" data-file-height="48" /></a></span> </span><a 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