Abstract
We investigate algorithms, applications, and complexity issues for the single-source uncapacitated (SSU) version of the minimum concave-cost network flow problem (MCNFP). We present applications arising from production planning, and prove complexity results for both global and local search. We formally state the local search algorithm of Gallo and Sodini [5], and present alternative local search algorithms. Computational results are provided to compare the various local search algorithms proposed and the effects of initial solution techniques.
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References
Dantzig, G. B. (1963), Linear Programming and Extensions, Princeton University Press, Princeton, New Jersey.
Denzler, D. R. (1969), An Approximate Solution for the Fixed Charge Problem, Naval Research Logistics Quarterly 16, 411–416.
Eggleston, H. G. (1963), Convexity, Cambridge Tracts in Mathematics and Mathematical Physics No. 47, Cambridge University Press, Cambridge, Mass.
Erickson, R. E., Monma, C. L., and VeinottJr., A. F. (1987), Send-and-Split Method for Minimum-Concave-Cost Network Flows, Mathematics of Operations Research 12(4), 634–664.
Gallo, G. and Sodini, C. (1979), Adjacent Extreme Flows and Application to Min Concave-Cost Flow Problems, Networks 9, 95–121.
Garey, M. R. and Johnson, D.S. (1979), Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman and Company, San Francisco, CA.
Guisewite, G. M. and Pardalos, P. M. (1990), Uncapacitated Single-Source Minimum Concave-Cost Network Flow Problem, Working Paper, Department of Computer Science, Pennsylvania State University.
Guisewite, G. M. and Pardalos, P. M. (1990), Minimum Concave-Cost Network Flow Problems: Applications, Complexity, and Algorithms, Annals of Operations Research 28, 75–100.
Lozovanu, D. D. (1983), Properties of Optimal Solutions of a Grid Transport Problem with Concave Function of the Flows on the Arcs, Engineering Cybernetics 20, 34–38.
Pardalos, P. M. and Rosen, J. B. (1987), Constrained Global Optimization; Algorithms and Applications, Lecture Notes in Computer Science 268, Springer-Verlag, Berlin.
Pardalos, P. M. and Schnitger, G. (1988), Checking Local Optimality in Constrained Quadratic Programming is NP-Hard, Operations Research Letters 7(1), 33–35.
Plasil, J. and Chlebnican, P. (1990), A New Algorithm for the Min Concaye Cost Flow Problem, Working paper, Technical University of Transport and Communications, Czechoslovakia.
Steinberg, D. I. (1970), The Fixed Charge Problem, Naval Research Logistics Quarterly 17, 217–236.
Thach, P.T. (1989), An Efficient Method for Min Concave Cost Flow Problems Under Circuitless Single-Source Uncapacitated Networks, Technical Report, Technical University of Graz, Austria:
Valiant, L. G. and Vazirani, V. V. (1985), NP Is as Easy as Detecting Unique Solutions, 17'th STOC of the ACM, 458–463.
Wagner, H.M. (1960), A Postscript to ‘Dynamic Problems in the Theory of the Firm’, Naval Research Logistics Quarterly 7, 7–12.
Wagner, H. M. and Whitin, T. M. (1958), Dynamic Version of the Economic Lot Size Model, Management Science 5(1), 89–96.
Walker, W. E. (1976), A Heuristic Adjacent Extreme Point Algorithm for the Fixed Charge Problem, Management Science 22(5) 587–596.
YagedJr., B. (1971), Minimum Cost Routing for Static Network Models, Networks 1, 139–172.
Zangwill, W. I. (1966), A Deterministic Multi-Period Production Scheduling Model with Backlogging, Management Science 13(1) 105–119.
Zangwill, W. I. (1968), Minimum Concave-Cost Flows in Certain Networks, Management Science 14(7) 429–450.
Zangwill, W. I. (1969), A Backlogging Model and a Multi-Echelon Model of a Economic Lot Size Production System — A Network Approach, Management Science 15(9) 506–527.
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Guisewite, G.M., Pardalos, P.M. Algorithms for the single-source uncapacitated minimum concave-cost network flow problem. J Glob Optim 1, 245–265 (1991). https://doi.org/10.1007/BF00119934
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DOI: https://doi.org/10.1007/BF00119934