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M.</a>; <a href="/authors/pardalos.panos-m" title="Author Profile">Pardalos, P. M.</a></div> <h2 class="title"> <strong>Minimum concave-cost network flow problems: Applications, complexity, and algorithms.</strong> <i>(English)</i> <a class="label nowrap" href="/0724.90022">Zbl 0724.90022</a> </h2> <div class="source"> <a href="/serials/1319" title="Journal Profile">Ann. Oper. Res.</a> <a href="/?q=in%3A182855" title="Articles in this Issue">25, No. 1-4, 75-100 (1990)</a>. </div> <div class="abstract">The paper is an overview of applications of minimum-cost network flow problems (MCNFP) economic problems and algorithms, a summary of known results in the complexity of the problem and some new results in the complexity area. At the end of the paper 108 references are given. <br class="zbmathjax-paragraph">Some of the applications are described in detail, others are just mentioned with further reference to the literature. The description of the algorithms is restricted to explaining the main ideas without going into details. The new complexity results are: (1) MCNFP is NP-hard if the objective function is strictly convex (even for bipartite networks), and (2) for capacitated MCNFP there is no pseudopolynomial algorithm in the sum of the arc capacities (unless \(P=NP\), of course).<div class="reviewer"> Reviewer: <a href="/authors/?q=rv%3A4855">H.W.Hamacher (Kaiserslautern)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A4195681">Cited in <strong>51</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A90B10" title="MSC2020">90B10</a> </td> <td class="space"> Deterministic network models in operations research </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C60" title="MSC2020">90C60</a> </td> <td class="space"> Abstract computational complexity for mathematical programming problems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C30" title="MSC2020">90C30</a> </td> <td class="space"> Nonlinear programming </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A90C35" title="MSC2020">90C35</a> </td> <td class="space"> Programming involving graphs or networks </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aminimum-cost+network+flow+problems">minimum-cost network flow problems</a>; <a href="/?q=ut%3Apseudopolynomial+algorithm">pseudopolynomial algorithm</a></div> <!-- Modal used to show zbmath metadata in different output formats--> <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;"> <!-- alert for connection errors etc --> </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function"> <!-- Button trigger metadata modal --> <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 0724.90022" data-ciurl="/ci/04195681" data-biburl="/bibtex/04195681.bib" data-amsurl="/amsrefs/04195681.bib" data-xmlurl="/xml/04195681.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/04195681.pdf" title="Zbl 0724.90022 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1007/BF02283688" aria-label="DOI for “Minimum concave-cost network flow problems: Applications, complexity, and algorithms”" title="10.1007/BF02283688">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">U. Akinc and B.M. Khumawala, An efficient branch and bound algorithm for the capacitated warehouse location problem, Management Sci. 23 (1977) 585–594. · <a href="/0348.90157" class="nowrap">Zbl 0348.90157</a> · <a href="https://doi.org/10.1287/mnsc.23.6.585" class="nowrap">doi:10.1287/mnsc.23.6.585</a></td> </tr><tr> <td>[2]</td> <td class="space">A. Balakrishnan and S.C. Graves, A composite algorithm for a concave-cost network flow problem, Networks 19 (1989) 175–202. · <a href="/0673.90034" class="nowrap">Zbl 0673.90034</a> · <a href="https://doi.org/10.1002/net.3230190202" class="nowrap">doi:10.1002/net.3230190202</a></td> </tr><tr> <td>[3]</td> <td class="space">M.L. Balinski, Fixed cost transportation problems, Naval Res. Logistics Quarterly 8 (1961) 41–54. · <a href="/0106.34801" class="nowrap">Zbl 0106.34801</a> · <a href="https://doi.org/10.1002/nav.3800080104" class="nowrap">doi:10.1002/nav.3800080104</a></td> </tr><tr> <td>[4]</td> <td class="space">M.L. Balinski and R.E. Quandt, On an integer program for a delivery problem. Oper. Res. 12 (1964) 300–304. · <a href="https://doi.org/10.1287/opre.12.2.300" class="nowrap">doi:10.1287/opre.12.2.300</a></td> </tr><tr> <td>[5]</td> <td class="space">R.S. Barr, F. Glover and D. Klingman, A new optimization method for large scale fixed charge transportation problems. Oper. Res. 29 (1981) 448–463. · <a href="/0455.90055" class="nowrap">Zbl 0455.90055</a> · <a href="https://doi.org/10.1287/opre.29.3.448" class="nowrap">doi:10.1287/opre.29.3.448</a></td> </tr><tr> <td>[6]</td> <td class="space">W.J. Baumol and P. Wolfe, A warehouse-location problem Oper. Res. 6 (1958) 252–263. · <a href="https://doi.org/10.1287/opre.6.2.252" class="nowrap">doi:10.1287/opre.6.2.252</a></td> </tr><tr> <td>[7]</td> <td class="space">I. Baybars and R.H. Edahl, A heuristic method for facility planning in telecommunications networks with multiple alternate routes, Naval Res. Logistics Quarterly 35 (1988) 503–528. · <a href="/0643.90022" class="nowrap">Zbl 0643.90022</a> · <a href="https://doi.org/10.1002/1520-6750(198808)35:4<503::AID-NAV3220350406>3.0.CO;2-N" class="nowrap">doi:10.1002/1520-6750(198808)35:4<503::AID-NAV3220350406>3.0.CO;2-N</a></td> </tr><tr> <td>[8]</td> <td class="space">D.P. Bertsekas and J.N. Tsitsiklis,Parallel and Distributed Computation (Prentice Hall, New Jersey, 1989). · <a href="/0743.65107" class="nowrap">Zbl 0743.65107</a></td> </tr><tr> <td>[9]</td> <td class="space">H.L. Bhatia, Indefinite quadratic solid transportation problem, J. Inform. Optimiz. Sci. 2 (1981) 297–303. · <a href="/0468.90043" class="nowrap">Zbl 0468.90043</a></td> </tr><tr> <td>[10]</td> <td class="space">C.T. Bornstein and R. Rust, Minimizing a sum of staircase functions under linear constraints, Optimization 19 (1988) 181–190. · <a href="/0651.90088" class="nowrap">Zbl 0651.90088</a> · <a href="https://doi.org/10.1080/02331938808843335" class="nowrap">doi:10.1080/02331938808843335</a></td> </tr><tr> <td>[11]</td> <td class="space">V.P. Bulatov, The immersion method for the global minimization of functions on the convex polyhedra,Int. Symp. on Engineering, Mathematics, and Applications, Beijing, PR China (July 1988) pp. 335–338.</td> </tr><tr> <td>[12]</td> <td class="space">A.V. Cabot and S.S. Erenguc, Some branch-and-bound procedures for fixed-cost transportation problems, Naval Res. Logistics Quarterly 31 (1984) 145–154. · <a href="/0537.90074" class="nowrap">Zbl 0537.90074</a> · <a href="https://doi.org/10.1002/nav.3800310115" class="nowrap">doi:10.1002/nav.3800310115</a></td> </tr><tr> <td>[13]</td> <td class="space">L. Cooper and C. Drebes, An approximate solution method for the fixed-charge problem. Naval Res. Logistics Quarterly 14 (1968) 101–113. · <a href="/0154.19601" class="nowrap">Zbl 0154.19601</a> · <a href="https://doi.org/10.1002/nav.3800140110" class="nowrap">doi:10.1002/nav.3800140110</a></td> </tr><tr> <td>[14]</td> <td class="space">G. Daeninck and Y. Smeers, Using shortest paths in some transshipment problems with concave costs, Math. Programming (1977) 18–25. · <a href="/0368.90128" class="nowrap">Zbl 0368.90128</a></td> </tr><tr> <td>[15]</td> <td class="space">G.B. Dantzig,Linear Programming and Extensions (Princeton University Press, Princeton, New Jersey, 1963).</td> </tr><tr> <td>[16]</td> <td class="space">P.S. Davis and T.L. Ray, A branch-and-bound algorithm for the capacitated facilities locations problem, Naval Res. Logistics Quarterly 16 (1969) 331–344. · <a href="/0186.24905" class="nowrap">Zbl 0186.24905</a></td> </tr><tr> <td>[17]</td> <td class="space">D.R. Denzler, An approximate algorithm for the fixed charge problems, Naval Res. Logistics Quarterly 16 (1969) 411–416. · <a href="/0186.24102" class="nowrap">Zbl 0186.24102</a></td> </tr><tr> <td>[18]</td> <td class="space">N. Driebeek, An algorithm for the solution of mixed integer programming problems. Management Sci. 12 (1966) 576–587. · <a href="https://doi.org/10.1287/mnsc.12.7.576" class="nowrap">doi:10.1287/mnsc.12.7.576</a></td> </tr><tr> <td>[19]</td> <td class="space">M.A. Efroymson and T.L. Ray, A branch-and-bound algorithm for plant location. Oper. Res. 14 (1966) 361–368. · <a href="https://doi.org/10.1287/opre.14.3.361" class="nowrap">doi:10.1287/opre.14.3.361</a></td> </tr><tr> <td>[20]</td> <td class="space">H.G. Eggleston,Convexity, Cambridge Tracts in Mathematics and Mathematical Physics No. 47 (Cambridge University Press, Cambridge, MA, 1963). · <a href="/0117.39502" class="nowrap">Zbl 0117.39502</a></td> </tr><tr> <td>[21]</td> <td class="space">R.E. Erickson, C.L. Monma and A.F. Veinott, Jr., Send-and-split method for minimum-con-cave-cost network flows, Math. Oper. Res. 12 (1987) 634–664. · <a href="/0667.90036" class="nowrap">Zbl 0667.90036</a> · <a href="https://doi.org/10.1287/moor.12.4.634" class="nowrap">doi:10.1287/moor.12.4.634</a></td> </tr><tr> <td>[22]</td> <td class="space">D. Erlenkotter, Two producing areas–dynamic programming solutions, in:Investment for Capacity Expansion: Size, Location and Time Phasing, ed. A.S. Manne (MIT Press, Cambridge, MA, 1967) pp. 210–227.</td> </tr><tr> <td>[23]</td> <td class="space">J.E. Falk and R.M. Soland, An algorithm for separable nonconvex programming problems. Management Sci. 15 (1969) 550–569. · <a href="/0172.43802" class="nowrap">Zbl 0172.43802</a> · <a href="https://doi.org/10.1287/mnsc.15.9.550" class="nowrap">doi:10.1287/mnsc.15.9.550</a></td> </tr><tr> <td>[24]</td> <td class="space">M. Florian, An introduction to network models used in transportation planning,Transportation Planning Models (Elsevier, New York, 1984). · <a href="/0591.90092" class="nowrap">Zbl 0591.90092</a></td> </tr><tr> <td>[25]</td> <td class="space">M. Florian, Nonlinear cost network models in transportation analysis, Math. Programming Study 26 (1986) 167–196. · <a href="/0607.90029" class="nowrap">Zbl 0607.90029</a></td> </tr><tr> <td>[26]</td> <td class="space">M. Florian and M. Klein, Deterministic production planning with concave costs and capacity constraints. Management Sci. 18 (1971) 12–20. · <a href="/0273.90023" class="nowrap">Zbl 0273.90023</a> · <a href="https://doi.org/10.1287/mnsc.18.1.12" class="nowrap">doi:10.1287/mnsc.18.1.12</a></td> </tr><tr> <td>[27]</td> <td class="space">M. Florian, J.K. Lenstra and A.H.G. Rinnooy Kan. Deterministic production planning: algorithms and complexity, Management Sci. 26 (1980) 669–679. · <a href="/0445.90025" class="nowrap">Zbl 0445.90025</a> · <a href="https://doi.org/10.1287/mnsc.26.7.669" class="nowrap">doi:10.1287/mnsc.26.7.669</a></td> </tr><tr> <td>[28]</td> <td class="space">M. Florian and P. Robillard, An implicit enumeration algorithm for the concave cost network flow problem, Management Sci. 18 (1971) 184–193. · <a href="/0238.90075" class="nowrap">Zbl 0238.90075</a> · <a href="https://doi.org/10.1287/mnsc.18.3.184" class="nowrap">doi:10.1287/mnsc.18.3.184</a></td> </tr><tr> <td>[29]</td> <td class="space">M. Florian, M. Rossin-Arthiat, and D. de Werra, A property of minimum concave cost flows in capacitated networks, Can. J. Oper. Res. 9 (1971) 293–304. · <a href="/0222.90016" class="nowrap">Zbl 0222.90016</a></td> </tr><tr> <td>[30]</td> <td class="space">C.O. Fong and M.R. Rao, Capacity expansion with two producing regions and concave costs, Management Sci. 22 (1975) 331–339. · <a href="/0324.90032" class="nowrap">Zbl 0324.90032</a> · <a href="https://doi.org/10.1287/mnsc.22.3.331" class="nowrap">doi:10.1287/mnsc.22.3.331</a></td> </tr><tr> <td>[31]</td> <td class="space">L.R. Ford, jr. and D.R. Fulkerson,Flows in Networks (Princeton University Press, Princeton, New Jersey, 1962). · <a href="/0106.34802" class="nowrap">Zbl 0106.34802</a></td> </tr><tr> <td>[32]</td> <td class="space">G. Gallo, C. Sandi and C. Sodini, An algorithm for the min concave-cost flow problem, Europ. J. Oper. Res. 4 (1980) 249–255. · <a href="/0439.90092" class="nowrap">Zbl 0439.90092</a> · <a href="https://doi.org/10.1016/0377-2217(80)90109-5" class="nowrap">doi:10.1016/0377-2217(80)90109-5</a></td> </tr><tr> <td>[33]</td> <td class="space">G. Gallo and C. Sodini, Adjacent extreme flows and application to min concave-cost flow problems. Networks 9 (1979) 95–121. · <a href="/0419.90078" class="nowrap">Zbl 0419.90078</a> · <a href="https://doi.org/10.1002/net.3230090202" class="nowrap">doi:10.1002/net.3230090202</a></td> </tr><tr> <td>[34]</td> <td class="space">M.R. Garey and D.S. Johnson,Computers and Intractability: A Guide to the Theory of NP-Completeness (W.H. Freeman, San Francisco, CA, 1979). · <a href="/0411.68039" class="nowrap">Zbl 0411.68039</a></td> </tr><tr> <td>[35]</td> <td class="space">S.C. Graves and J.B. Orlin, A minimum concave-cost dynamic network flow problem with an application to lot-sizing. Networks, 15 (1985) 59–71. · <a href="/0579.90032" class="nowrap">Zbl 0579.90032</a> · <a href="https://doi.org/10.1002/net.3230150107" class="nowrap">doi:10.1002/net.3230150107</a></td> </tr><tr> <td>[36]</td> <td class="space">P. Gray, Exact solution of the site selection problem by mixed integer programming, in:Applications of Mathematical Programming Techniques, ed. E.M.L. Beale (The English Universities Press, London, 1970) pp. 262–270.</td> </tr><tr> <td>[37]</td> <td class="space">P. Gray, Exact solution of the fixed-charge transportation problem. Oper. Res. 19 (1971) 1529–1538. · <a href="/0224.90036" class="nowrap">Zbl 0224.90036</a> · <a href="https://doi.org/10.1287/opre.19.6.1529" class="nowrap">doi:10.1287/opre.19.6.1529</a></td> </tr><tr> <td>[38]</td> <td class="space">G.M. Guisewite and P.M. Pardalos, Algorithms for the uncapacitated single-source minimum concave-cost network flow problem, Technical Report, Department of Computer Science, Pennsylvania State University (1990). · <a href="/0724.90022" class="nowrap">Zbl 0724.90022</a></td> </tr><tr> <td>[39]</td> <td class="space">K.B. Haley, The solid transportation problem, Oper. Res. Quarterly 10 (1962) 448–463. · <a href="/0109.13904" class="nowrap">Zbl 0109.13904</a> · <a href="https://doi.org/10.1287/opre.10.4.448" class="nowrap">doi:10.1287/opre.10.4.448</a></td> </tr><tr> <td>[40]</td> <td class="space">R.W. Hall, Graphical interpretation of the transportation problem, Transportation Sci. 23 (1988) 37–45. · <a href="/0672.90085" class="nowrap">Zbl 0672.90085</a> · <a href="https://doi.org/10.1287/trsc.23.1.37" class="nowrap">doi:10.1287/trsc.23.1.37</a></td> </tr><tr> <td>[41]</td> <td class="space">G.L. Hefley and B.O. Barr, Fixed charge transportation problem: a survey, presented to the 43rd ORSA National Meeting in Milwaukee, Wisconsin (May 1973).</td> </tr><tr> <td>[42]</td> <td class="space">D.S. Hochbaum and A. Segev. Analysis of a flow problem with fixed charges. Networks 19 (1989) 291–312. · <a href="/0673.90035" class="nowrap">Zbl 0673.90035</a> · <a href="https://doi.org/10.1002/net.3230190304" class="nowrap">doi:10.1002/net.3230190304</a></td> </tr><tr> <td>[43]</td> <td class="space">R. Horst and H. Tuy,Global Optimization: Deterministic Approaches. (Springer, 1989) to be published. · <a href="/0704.90057" class="nowrap">Zbl 0704.90057</a></td> </tr><tr> <td>[44]</td> <td class="space">T. Ibaraki and N. Katoh,Resource Allocation Problems, Algorithmic Approaches (The MIT Press, Cambridge, MA., 1988). · <a href="/0786.90067" class="nowrap">Zbl 0786.90067</a></td> </tr><tr> <td>[45]</td> <td class="space">J.J. Jarvis, V.E. Unger, R.L. Rardin and R.W. Moore, Optimal design of regional wastewater systems: a fixed charge network flow model. Oper. Res. 26 (1978) 538–550. · <a href="/0385.90075" class="nowrap">Zbl 0385.90075</a> · <a href="https://doi.org/10.1287/opre.26.4.538" class="nowrap">doi:10.1287/opre.26.4.538</a></td> </tr><tr> <td>[46]</td> <td class="space">R. Jogannathan and M.R. Rao, A class of deterministic production planning models, Management Sci. 19 (1973) 1295–1300. · <a href="https://doi.org/10.1287/mnsc.19.11.1295" class="nowrap">doi:10.1287/mnsc.19.11.1295</a></td> </tr><tr> <td>[47]</td> <td class="space">L.A. Johnson and D.C. Montgomery,Operations Research in Production Planning, Scheduling, and Inventory Control. (Wiley, New York, 1974) pp. 212–224.</td> </tr><tr> <td>[48]</td> <td class="space">D. Kennedy, Some branch-and-bound techniques for nonlinear optimization, Math. Programming 42 (1988) 147–169. · <a href="/0639.90078" class="nowrap">Zbl 0639.90078</a> · <a href="https://doi.org/10.1007/BF01589399" class="nowrap">doi:10.1007/BF01589399</a></td> </tr><tr> <td>[49]</td> <td class="space">J. Kennington, The fixed-charge transportation problem: a computational study with a branch-and-bound code. AIIE Trans. 8 (1976) 241–247.</td> </tr><tr> <td>[50]</td> <td class="space">J. Kennington and E. Unger, The group-theoretic structure in the fixed-charge transportation problem. Oper. Res. 21 (1973) 1142–1152. · <a href="/0272.90051" class="nowrap">Zbl 0272.90051</a> · <a href="https://doi.org/10.1287/opre.21.5.1142" class="nowrap">doi:10.1287/opre.21.5.1142</a></td> </tr><tr> <td>[51]</td> <td class="space">J. Kennington and E. Unger, A new branch-and-bound algorithm for the fixed-charge transportation algorithm. Management Sci. 22 (1976) 1116–1126. · <a href="/0329.90039" class="nowrap">Zbl 0329.90039</a> · <a href="https://doi.org/10.1287/mnsc.22.10.1116" class="nowrap">doi:10.1287/mnsc.22.10.1116</a></td> </tr><tr> <td>[52]</td> <td class="space">B.M. Khumawala, An efficient branch-and-bound algorithm for the warehouse location problem. Management Sci. 18 (1972) B718-B731. · <a href="/0238.90048" class="nowrap">Zbl 0238.90048</a> · <a href="https://doi.org/10.1287/mnsc.18.12.B718" class="nowrap">doi:10.1287/mnsc.18.12.B718</a></td> </tr><tr> <td>[53]</td> <td class="space">D. Klingman, P.H. Randolph and S.W. Fuller, A cotton ginning problem, Oper. Res. 24 (1976) 700–717. · <a href="https://doi.org/10.1287/opre.24.4.700" class="nowrap">doi:10.1287/opre.24.4.700</a></td> </tr><tr> <td>[54]</td> <td class="space">H. Konno, Minimum concave series production system with deterministic demands: a backlogging case. J. Oper. Res. Soc. Jpn. 16 (1973) 246–253. · <a href="/0277.90027" class="nowrap">Zbl 0277.90027</a></td> </tr><tr> <td>[55]</td> <td class="space">H. Konno, Minimum concave cost production system: multi-echelon model. Math. Programming 41 (1988) 185–193. · <a href="/0662.90037" class="nowrap">Zbl 0662.90037</a> · <a href="https://doi.org/10.1007/BF01580763" class="nowrap">doi:10.1007/BF01580763</a></td> </tr><tr> <td>[56]</td> <td class="space">H.W. Kuhn and W.J. Baumol, An approximate algorithm for the fixed-charge transportation problem, Naval Res. Logistics Quarterly 9 (1962) 1–16. · <a href="/0109.13903" class="nowrap">Zbl 0109.13903</a> · <a href="https://doi.org/10.1002/nav.3800090102" class="nowrap">doi:10.1002/nav.3800090102</a></td> </tr><tr> <td>[57]</td> <td class="space">B. Lamar, An improved branch-and-bound algorithm for minimum concave cost network flow problems, Working Paper, Graduate School of Management and Institute of Transportation Studies, University of California, Irvine (1989).</td> </tr><tr> <td>[58]</td> <td class="space">L. LeBlanc, Global solutions for a non-convex, non-concave rail network model, Math. Sci. 23 (1978) 131–139.</td> </tr><tr> <td>[59]</td> <td class="space">S. Lee and P.H. Zipkin, A dynamic lot-size model with make-or-buy decisions. Management Sci. 35 (1989) 447–458. · <a href="/0666.90029" class="nowrap">Zbl 0666.90029</a> · <a href="https://doi.org/10.1287/mnsc.35.4.447" class="nowrap">doi:10.1287/mnsc.35.4.447</a></td> </tr><tr> <td>[60]</td> <td class="space">N. Linial, Hard enumeration problems in geometry and combinatorics, SIAM J. Alg. Discr. Meth. 7 (1986) 331–335. · <a href="/0596.68041" class="nowrap">Zbl 0596.68041</a> · <a href="https://doi.org/10.1137/0607036" class="nowrap">doi:10.1137/0607036</a></td> </tr><tr> <td>[61]</td> <td class="space">L.S. Linn and J. Allen, Minplex – a compactor that minimizes the bounding rectangle and individual rectangles in a layout,23rd Design Automation Conf. (1986) pp. 123–129.</td> </tr><tr> <td>[62]</td> <td class="space">S.A. Lippman, Optimal inventory policy with multiple setup costs. Management Sci. 16 (1969) 118–138. · <a href="/0184.44701" class="nowrap">Zbl 0184.44701</a> · <a href="https://doi.org/10.1287/mnsc.16.1.118" class="nowrap">doi:10.1287/mnsc.16.1.118</a></td> </tr><tr> <td>[63]</td> <td class="space">S.F. Love, A facilities in series inventory model with nested schedules. Management Sci. 18 (1972) 327–338. · <a href="/0237.90015" class="nowrap">Zbl 0237.90015</a> · <a href="https://doi.org/10.1287/mnsc.18.5.327" class="nowrap">doi:10.1287/mnsc.18.5.327</a></td> </tr><tr> <td>[64]</td> <td class="space">S.F. Love, Bounded production and inventory models with piecewise concave costs, Management Sci. 20 (1973) 313–318. · <a href="/0322.90028" class="nowrap">Zbl 0322.90028</a> · <a href="https://doi.org/10.1287/mnsc.20.3.313" class="nowrap">doi:10.1287/mnsc.20.3.313</a></td> </tr><tr> <td>[65]</td> <td class="space">D.D. Lozovanu, Properties of optimal solutions of a grid transport problem with concave function of the flows on the arcs. Engineering Cybernetics 20 (1983) 34–38. · <a href="/0527.90070" class="nowrap">Zbl 0527.90070</a></td> </tr><tr> <td>[66]</td> <td class="space">T.L. Magnanti and R.T. Wong. Network design and transportation planning: models and algorithms, Transportation Sci. 18 (1984) 1–55. · <a href="https://doi.org/10.1287/trsc.18.1.1" class="nowrap">doi:10.1287/trsc.18.1.1</a></td> </tr><tr> <td>[67]</td> <td class="space">A.S. Manne and A.F. Veinott, Jr., Optimal plant size with arbitrary increasing time paths of demand, in:Investments for Capacity Expansion: Size, Location and Time Phasing, ed. A.S. Manne (MIT Press, Cambridge, MA, 1967) pp. 178–190.</td> </tr><tr> <td>[68]</td> <td class="space">P. McKeown, A vertex ranking procedure for solving the linear fixed-charge problem Oper. Res. 23 (1975) 1183–1191. · <a href="/0329.90041" class="nowrap">Zbl 0329.90041</a> · <a href="https://doi.org/10.1287/opre.23.6.1183" class="nowrap">doi:10.1287/opre.23.6.1183</a></td> </tr><tr> <td>[69]</td> <td class="space">K.G. Murty, Solving the fixed charge problem by ranking the extreme points. Oper. Res. 16 (1968) 268–279. · <a href="/0249.90041" class="nowrap">Zbl 0249.90041</a> · <a href="https://doi.org/10.1287/opre.16.2.268" class="nowrap">doi:10.1287/opre.16.2.268</a></td> </tr><tr> <td>[70]</td> <td class="space">K.G. Murty and S.N. Kabadi, Some NP-complete problems in quadratic and non-linear programming. Math. Programming 39 (1987) 117–129. · <a href="/0637.90078" class="nowrap">Zbl 0637.90078</a> · <a href="https://doi.org/10.1007/BF02592948" class="nowrap">doi:10.1007/BF02592948</a></td> </tr><tr> <td>[71]</td> <td class="space">P.M. Pardalos, Enumerative techniques for solving some nonconvex global optimization problems. OR Spectrum 10 (1988) 29–35. · <a href="/0643.90082" class="nowrap">Zbl 0643.90082</a></td> </tr><tr> <td>[72]</td> <td class="space">P.M. Pardalos, J.H. Glick and J.B. Rosen, Global minimization of indefinite quadratic problems, Computing 39 (1987) 281–291. · <a href="/0627.65072" class="nowrap">Zbl 0627.65072</a> · <a href="https://doi.org/10.1007/BF02239972" class="nowrap">doi:10.1007/BF02239972</a></td> </tr><tr> <td>[73]</td> <td class="space">P.M. Pardalos, A.T. Phillips and J.B. Rosen,Parallel Computing in Mathematical Programming, (SIAM, Philadelphia, PA, 1990) to appear. · <a href="/0784.65059" class="nowrap">Zbl 0784.65059</a></td> </tr><tr> <td>[74]</td> <td class="space">P.M. Pardalos and J.B. Rosen, Global minimization of large-scale constrained concave quadratic problems by separable programming, Math. Programming 34 (1986) 163–174. · <a href="/0597.90066" class="nowrap">Zbl 0597.90066</a> · <a href="https://doi.org/10.1007/BF01580581" class="nowrap">doi:10.1007/BF01580581</a></td> </tr><tr> <td>[75]</td> <td class="space">P.M. Pardalos and J.B. Rosen. Global concave minimization: a bibliographic survey. SIAM Rev. 28 (1986) 367–379. · <a href="/0602.90105" class="nowrap">Zbl 0602.90105</a> · <a href="https://doi.org/10.1137/1028106" class="nowrap">doi:10.1137/1028106</a></td> </tr><tr> <td>[76]</td> <td class="space">P.M. Pardalos and J.B. Rosen.Constrained Global Optimization: Algorithms and Applications. Lecture Notes in Computer Science 268 (Springer, Berlin, 1987). · <a href="/0638.90064" class="nowrap">Zbl 0638.90064</a></td> </tr><tr> <td>[77]</td> <td class="space">P.M. Pardalos and G. Schnitger, Checking local optimality in constrained quadratic programming is NP-hard, Oper. Res. Lett. 7 (1988) 33–35. · <a href="/0644.90067" class="nowrap">Zbl 0644.90067</a> · <a href="https://doi.org/10.1016/0167-6377(88)90049-1" class="nowrap">doi:10.1016/0167-6377(88)90049-1</a></td> </tr><tr> <td>[78]</td> <td class="space">A.T. Phillips, Parallel algorithms for constrained optimization, Ph.D. Dissertation, University of Minnesota (1988). · <a href="/0665.90071" class="nowrap">Zbl 0665.90071</a></td> </tr><tr> <td>[79]</td> <td class="space">A.T. Phillips and J.B. Rosen, A parallel algorithm for constrained concave quadratic global minimization. Math. Programming 42 (1988) 421–448. · <a href="/0665.90071" class="nowrap">Zbl 0665.90071</a> · <a href="https://doi.org/10.1007/BF01589415" class="nowrap">doi:10.1007/BF01589415</a></td> </tr><tr> <td>[80]</td> <td class="space">J. Plasil and P. Chlebnican, A new algorithm for the concave cost flow problem, Working Paper, Technical University of Transport and Communications. Zilina, Czechoslovakia (1989).</td> </tr><tr> <td>[81]</td> <td class="space">R. Polyak, On a nonconvex problem, Sov. Math. Doklady 17a (1968) 786–789.</td> </tr><tr> <td>[82]</td> <td class="space">P. Rech and L.G. Barton, A non-convex transportation algorithm, in:Applications of Mathematical Programming Techniques, ed. E.M.L. Beale (The English Universities Press, London, 1970) pp. 250–260.</td> </tr><tr> <td>[83]</td> <td class="space">C. Revelle, D. Marks and J.C. Liebman, An analysis of private and public sector location models, Management Sci. 16 (1970) 692–707. · <a href="/0195.21901" class="nowrap">Zbl 0195.21901</a> · <a href="https://doi.org/10.1287/mnsc.16.11.692" class="nowrap">doi:10.1287/mnsc.16.11.692</a></td> </tr><tr> <td>[84]</td> <td class="space">J.B. Rosen, Global minimization of a linearly constrained concave function by partition of feasible domain. Math. Oper. Res. 8 (1983) 215–230. · <a href="/0526.90072" class="nowrap">Zbl 0526.90072</a> · <a href="https://doi.org/10.1287/moor.8.2.215" class="nowrap">doi:10.1287/moor.8.2.215</a></td> </tr><tr> <td>[85]</td> <td class="space">M.J. Sobel, Smoothing start-up and shut-down costs: concave case, Management Sci. 17 (1970) 78–91. · <a href="/0211.22901" class="nowrap">Zbl 0211.22901</a> · <a href="https://doi.org/10.1287/mnsc.17.1.78" class="nowrap">doi:10.1287/mnsc.17.1.78</a></td> </tr><tr> <td>[86]</td> <td class="space">R.M. Soland, Optimal facility location with concave costs. Oper. Res. 22 (1974) 373–382. · <a href="/0278.90079" class="nowrap">Zbl 0278.90079</a> · <a href="https://doi.org/10.1287/opre.22.2.373" class="nowrap">doi:10.1287/opre.22.2.373</a></td> </tr><tr> <td>[87]</td> <td class="space">K. Spielberg. An algorithm for the simple plant location problem with some side conditions, Oper. Res. 17 (1969) 85–111. · <a href="/0165.54104" class="nowrap">Zbl 0165.54104</a> · <a href="https://doi.org/10.1287/opre.17.1.85" class="nowrap">doi:10.1287/opre.17.1.85</a></td> </tr><tr> <td>[88]</td> <td class="space">K. Spielberg, Plant location with generalized search origin. Management Sci. 16 (1969) 165–178. · <a href="https://doi.org/10.1287/mnsc.16.3.165" class="nowrap">doi:10.1287/mnsc.16.3.165</a></td> </tr><tr> <td>[89]</td> <td class="space">K. Spielberg, On solving plant location problems, in:Applications of Mathematical Programming Techniques, ed. E.M.L. Beale (The English Universities Press, London, 1970) pp. 216–234.</td> </tr><tr> <td>[90]</td> <td class="space">J.W. Stroup, Allocation of launch vehicles to space missions: a fixed-cost transportation problem. Oper. Res. 15 (1967) 1157–1163. · <a href="https://doi.org/10.1287/opre.15.6.1157" class="nowrap">doi:10.1287/opre.15.6.1157</a></td> </tr><tr> <td>[91]</td> <td class="space">C. Swoveland, A deterministic multi-period production planning model with piecewise concave production and holding-backorder costs. Management Sci. 21 (1975) 1007–1013. · <a href="/0328.90033" class="nowrap">Zbl 0328.90033</a> · <a href="https://doi.org/10.1287/mnsc.21.9.1007" class="nowrap">doi:10.1287/mnsc.21.9.1007</a></td> </tr><tr> <td>[92]</td> <td class="space">H.A. Taha, Concave minimization over a convex polyhedron. Naval Res. Logistics Quarterly 20 (1973) 533–548. · <a href="/0286.90052" class="nowrap">Zbl 0286.90052</a> · <a href="https://doi.org/10.1002/nav.3800200313" class="nowrap">doi:10.1002/nav.3800200313</a></td> </tr><tr> <td>[93]</td> <td class="space">P.T. Thach, An efficient method for min concave cost flow problems under circuitless single-source uncapacitated networks, Technical Report. Technical University of Graz. Austria (1989).</td> </tr><tr> <td>[94]</td> <td class="space">N.V. Thoai and H. Tuy. Convergent algorithms for minimizing a concave function. Math. Oper. Res. 5 (1980) 556–566. · <a href="/0472.90054" class="nowrap">Zbl 0472.90054</a> · <a href="https://doi.org/10.1287/moor.5.4.556" class="nowrap">doi:10.1287/moor.5.4.556</a></td> </tr><tr> <td>[95]</td> <td class="space">J.A. Tomlin, Minimum-cost multicommodity network flows. Oper. Res. 14 (1966) 45–51. · <a href="https://doi.org/10.1287/opre.14.1.45" class="nowrap">doi:10.1287/opre.14.1.45</a></td> </tr><tr> <td>[96]</td> <td class="space">H. Tuy, Concave-programming under linear constraints. Sov. Math. Doklady (1964) 1437–1440. · <a href="/0132.40103" class="nowrap">Zbl 0132.40103</a></td> </tr><tr> <td>[97]</td> <td class="space">A.F. Veinott, Jr., Minimum concave-cost solution of Leontief substitution models of multifacility inventory systems. Oper. Res. 17 (1969) 262–291. · <a href="/0175.17602" class="nowrap">Zbl 0175.17602</a> · <a href="https://doi.org/10.1287/opre.17.2.262" class="nowrap">doi:10.1287/opre.17.2.262</a></td> </tr><tr> <td>[98]</td> <td class="space">H.M. Wagner, On a class of capacitated transportation problems, Management. Sci. 5 (1959) 304–318. · <a href="/0995.90513" class="nowrap">Zbl 0995.90513</a> · <a href="https://doi.org/10.1287/mnsc.5.3.304" class="nowrap">doi:10.1287/mnsc.5.3.304</a></td> </tr><tr> <td>[99]</td> <td class="space">H.M. Wagner, A postscript to: Dynamic problems in the theory of the firm. Naval Res. Logistics Quarterly 7 (1960) 7–12. · <a href="https://doi.org/10.1002/nav.3800070103" class="nowrap">doi:10.1002/nav.3800070103</a></td> </tr><tr> <td>[100]</td> <td class="space">H.M. Wagner and T.M. Whitin, Dynamic version of the economic lot size model, Management Sci. 5 (1958) 89–96. · <a href="https://doi.org/10.1287/mnsc.5.1.89" class="nowrap">doi:10.1287/mnsc.5.1.89</a></td> </tr><tr> <td>[101]</td> <td class="space">W.E. Walker, A heuristic adjacent extreme point algorithm for the fixed charge problem, Management Sci. 22 (1976) 587–596. · <a href="/0316.90041" class="nowrap">Zbl 0316.90041</a> · <a href="https://doi.org/10.1287/mnsc.22.5.587" class="nowrap">doi:10.1287/mnsc.22.5.587</a></td> </tr><tr> <td>[102]</td> <td class="space">B. Yaged, Jr., Minimum cost routing for static network models, Networks 1 (1971) 139–172. · <a href="/0228.90011" class="nowrap">Zbl 0228.90011</a> · <a href="https://doi.org/10.1002/net.3230010205" class="nowrap">doi:10.1002/net.3230010205</a></td> </tr><tr> <td>[103]</td> <td class="space">N. Zadeh, On building minimum cost communication networks. Networks 3 (1973) 315–331. · <a href="/0375.90029" class="nowrap">Zbl 0375.90029</a> · <a href="https://doi.org/10.1002/net.3230030404" class="nowrap">doi:10.1002/net.3230030404</a></td> </tr><tr> <td>[104]</td> <td class="space">N. Zadeh, On building minimum cost communication networks over time, Networks 4 (1974) 19–34. · <a href="/0284.90031" class="nowrap">Zbl 0284.90031</a> · <a href="https://doi.org/10.1002/net.3230040104" class="nowrap">doi:10.1002/net.3230040104</a></td> </tr><tr> <td>[105]</td> <td class="space">W.I. Zangwill, A deterministic multi-period production scheduling model with backlogging, Management Sci. 13 (1966) 105–119. · <a href="/0143.22101" class="nowrap">Zbl 0143.22101</a> · <a href="https://doi.org/10.1287/mnsc.13.1.105" class="nowrap">doi:10.1287/mnsc.13.1.105</a></td> </tr><tr> <td>[106]</td> <td class="space">W.I. Zangwill, Production smoothing of economic lot sizes with non-decreasing requirements. Management Sci. 13 (1966) 191–209. · <a href="/0204.20503" class="nowrap">Zbl 0204.20503</a> · <a href="https://doi.org/10.1287/mnsc.13.3.191" class="nowrap">doi:10.1287/mnsc.13.3.191</a></td> </tr><tr> <td>[107]</td> <td class="space">W.I. Zangwill, Minimum concave-cost flows in certain networks Management Sci. 14 (1968) 429–450. · <a href="/0159.49102" class="nowrap">Zbl 0159.49102</a> · <a href="https://doi.org/10.1287/mnsc.14.7.429" class="nowrap">doi:10.1287/mnsc.14.7.429</a></td> </tr><tr> <td>[108]</td> <td class="space">W.I. Zangwill, A backlogging model and a multi-echelon model of an economic lot size production system – a network approach, Management Sci. 15 (1969) 506–527. · <a href="/0172.44603" class="nowrap">Zbl 0172.44603</a> · <a href="https://doi.org/10.1287/mnsc.15.9.506" class="nowrap">doi:10.1287/mnsc.15.9.506</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>