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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"><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 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role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/40px-Edit-clear.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/60px-Edit-clear.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/80px-Edit-clear.svg.png 2x" data-file-width="48" data-file-height="48" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article's <b><a href="/wiki/Wikipedia:Manual_of_Style/Lead_section" title="Wikipedia:Manual of Style/Lead section">lead section</a> may be too long</b>.<span class="hide-when-compact"> Please read the <a href="/wiki/Wikipedia:Manual_of_Style/Lead_section#Length" title="Wikipedia:Manual of Style/Lead section">length guidelines</a> and help <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Johnson%27s_rule&action=edit">move details into the article's body</a>.</span> <span class="date-container"><i>(<span class="date">July 2019</span>)</i></span></div></td></tr></tbody></table> <p>In <a href="/wiki/Operations_research" title="Operations research">operations research</a>, <b>Johnson's rule</b> is a method of scheduling jobs in two work centers. Its <a href="/wiki/Primary_objective" class="mw-redirect" title="Primary objective">primary objective</a> is to find an optimal <a href="/wiki/Sequence" title="Sequence">sequence</a> of jobs to reduce <a href="/wiki/Makespan" title="Makespan">makespan</a> (the total amount of time it takes to complete all jobs). It also reduces the amount of <a href="/wiki/Idleness" title="Idleness">idle</a> time between the two work centers. The method minimizes the makespan in the case of two work centers. Furthermore, the method finds the shortest makespan in the case of three work centers if additional constraints are met.<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> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Algorithm">Algorithm</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Johnson%27s_rule&action=edit&section=1" title="Edit section: Algorithm"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Skill" title="Skill">technique</a> requires several <a href="/wiki/Preconditions" class="mw-redirect" title="Preconditions">preconditions</a>: </p> <ul><li>The time for each job must be invariant with respect to when it is done.</li> <li>Job times must be independent of the job <a href="/wiki/Sequence" title="Sequence">sequence</a>.</li> <li>All jobs must be processed in the first work center before going through the second work center.</li> <li>All jobs are equally prioritised.</li></ul> <p>Johnson's rule is as follows: </p> <ol><li>List the jobs and their times at each work center.</li> <li>Select the job with the shortest activity time. If that activity time is for the first work center, then schedule the job first. If that activity time is for the second work center then schedule the job last. Break ties <a href="/wiki/Arbitrariness" title="Arbitrariness">arbitrarily</a>.</li> <li>Eliminate the shortest job from further consideration.</li> <li>Repeat steps 2 and 3, working towards the center of the job schedule until all jobs have been scheduled.</li></ol> <p>Given significant <a href="/wiki/Idleness" title="Idleness">idle</a> time at the second work center (from waiting for the job to be finished at the first work center), job splitting may be used. </p><p>If there are three work centers, Johnson's rules can still be applied if the minimum processing time in the first (and/or the third) work center is not less than the maximum processing time in the second work center. If so, one can create two virtual work center then apply Johnson's rules like for the two work center case. </p> <div class="mw-heading mw-heading2"><h2 id="Example">Example</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Johnson%27s_rule&action=edit&section=2" title="Edit section: Example"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Each of five jobs needs to go through work center A and B. Find the optimum sequence of jobs using Johnson's rule. </p> <table class="wikitable" style="text-align:center; margin-left: auto; margin-right: auto; border: none;"> <caption>Job times (hours) </caption> <tbody><tr> <th>Job </th> <th>Work center A </th> <th>Work center B </th></tr> <tr> <td>A </td> <td>3.2 </td> <td>4.2 </td></tr> <tr> <td>B </td> <td>4.7 </td> <td>1.5 </td></tr> <tr> <td>C </td> <td>2.2 </td> <td>5.0 </td></tr> <tr> <td>D </td> <td>5.8 </td> <td>4.0 </td></tr> <tr> <td>E </td> <td>3.1 </td> <td>2.8 </td></tr></tbody></table> <div><ol><li>The smallest time is located in Job B (1.5 hours). Since the time is in Work Center B, schedule this job last. <p>Eliminate Job B from further consideration. </p> <table class="wikitable" style="text-align:center; margin-left: auto; margin-right: auto; border: none;"><tbody><tr style="vertical-align:top"><td> ?</td><td> ?</td><td> ?</td><td> ?</td><td> B</td></tr></tbody></table></li><li>The next smallest time is located in Job C (2.2 hours). Since the time is in Work Center A, schedule this job first. <p>Eliminate Job C from further consideration. </p> <table class="wikitable" style="text-align:center; margin-left: auto; margin-right: auto; border: none;"><tbody><tr style="vertical-align:top"><td> C</td><td> ?</td><td> ?</td><td> ?</td><td> B</td></tr></tbody></table></li><li>The next smallest time after that is located in Job E (2.8 hours). Since the time is in Work Center B, schedule this job last. <p>Eliminate Job E from further consideration. </p> <table class="wikitable" style="text-align:center; margin-left: auto; margin-right: auto; border: none;"><tbody><tr style="vertical-align:top"><td> C</td><td> ?</td><td> ?</td><td> E</td><td> B</td></tr></tbody></table></li><li>The next smallest time after is located in Job A (3.2 hours). Since the time is in Work Center A, schedule this job first. <p>Eliminate Job A from further consideration. </p> <table class="wikitable" style="text-align:center; margin-left: auto; margin-right: auto; border: none;"><tbody><tr style="vertical-align:top"><td> C</td><td> A</td><td> ?</td><td> E</td><td> B</td></tr></tbody></table></li><li>The only job left to consider is Job D. <table class="wikitable" style="text-align:center; margin-left: auto; margin-right: auto; border: none;"><tbody><tr style="vertical-align:top"><td> C</td><td> A</td><td> D</td><td> E</td><td> B</td></tr></tbody></table></li></ol></div> <p>So, the jobs must be processed in the order C → A → D → E → B, and must be processed in the same order on both work centers. </p> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Johnson%27s_rule&action=edit&section=3" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><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 .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFJohnson1954" class="citation journal cs1">Johnson, S. M. (1954). <a rel="nofollow" class="external text" href="https://www.rand.org/content/dam/rand/pubs/papers/2008/P402.pdf">"Optimal Two- and Three-Stage Production Schedules With Set-up Time Included"</a> <span class="cs1-format">(PDF)</span>. <i>Naval Research Logistics Quarterly</i>. <b>1</b>: 61–68. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fnav.3800010110">10.1002/nav.3800010110</a><span class="reference-accessdate">. Retrieved <span class="nowrap">4 June</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Naval+Research+Logistics+Quarterly&rft.atitle=Optimal+Two-+and+Three-Stage+Production+Schedules+With+Set-up+Time+Included&rft.volume=1&rft.pages=61-68&rft.date=1954&rft_id=info%3Adoi%2F10.1002%2Fnav.3800010110&rft.aulast=Johnson&rft.aufirst=S.+M.&rft_id=https%3A%2F%2Fwww.rand.org%2Fcontent%2Fdam%2Frand%2Fpubs%2Fpapers%2F2008%2FP402.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJohnson%27s+rule" class="Z3988"></span></span> </li> </ol></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=Johnson%27s_rule&action=edit&section=4" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMortonPentico2001" class="citation book cs1">Morton, Thomas; Pentico, David W. (2001-07-20). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=6ORuBRNk_Z8C&pg=PA302"><i>Heuristic Scheduling Systems: With Applications to Production Systems and ... - Thomas Morton, David W. Pentico - Google Książki</i></a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780471578192" title="Special:BookSources/9780471578192"><bdi>9780471578192</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">2012-09-26</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Heuristic+Scheduling+Systems%3A+With+Applications+to+Production+Systems+and+...+-+Thomas+Morton%2C+David+W.+Pentico+-+Google+Ksi%C4%85%C5%BCki&rft.date=2001-07-20&rft.isbn=9780471578192&rft.aulast=Morton&rft.aufirst=Thomas&rft.au=Pentico%2C+David+W.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D6ORuBRNk_Z8C%26pg%3DPA302&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJohnson%27s+rule" class="Z3988"></span> j</li></ul> <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=Johnson%27s_rule&action=edit&section=5" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>William J Stevenson, <i>Operations Management 9th Edition</i>, McGraw-Hill/Irwin, 2007</li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Johnson%27s_rule&oldid=1238895459">https://en.wikipedia.org/w/index.php?title=Johnson%27s_rule&oldid=1238895459</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Production_planning" title="Category:Production planning">Production planning</a></li><li><a href="/wiki/Category:Operations_research" title="Category:Operations research">Operations research</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Wikipedia_introduction_cleanup_from_July_2019" title="Category:Wikipedia introduction cleanup from July 2019">Wikipedia introduction cleanup from July 2019</a></li><li><a href="/wiki/Category:All_pages_needing_cleanup" title="Category:All pages needing cleanup">All pages needing cleanup</a></li><li><a href="/wiki/Category:Articles_covered_by_WikiProject_Wikify_from_July_2019" title="Category:Articles covered by WikiProject Wikify from July 2019">Articles covered by WikiProject Wikify from July 2019</a></li><li><a href="/wiki/Category:All_articles_covered_by_WikiProject_Wikify" title="Category:All articles covered by WikiProject Wikify">All articles covered by WikiProject Wikify</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 6 August 2024, at 07:34<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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