Polymatroid Optimization, Submodularity, and Joint Replenishment Games

References

• Anily S., Haviv M. The cost allocation problem for the first order interaction joint replenishment model. Oper. Res. (2007) 55(2):292–302Link, Google Scholar
• Edmonds J. Submodular functions, matroid, and certain polyhedra. Combinatorial Structures and Their Applications (1970) (Gordon & Breach, New York) 69–87Google Scholar
• European Chemical Transport Association Cooperation and collaboration between logistic service providors (LSP's): Threat or opportunity? (2006) . White paper, European Chemical Transport Association, BrusselsGoogle Scholar
• Faigle U., Kern W., Kuipers J. On the computation of the nucleolus of a cooperative game. Internat. J. Game Theory (2001) 30(1):79–98Crossref, Google Scholar
• Federgruen A., Groenevelt H. The greedy procedure for resource allocation problems: Necessary and sufficient conditions for optimality. Oper. Res. (1986) 34(6):909–918Link, Google Scholar
• Federgruen A., Zheng Y. S. The joint replenishment problem with general joint cost structures. Oper. Res. (1992) 40(2):384–403Link, Google Scholar
• Federgruen A., Queyranne M., Zheng Y.-S. Simple power-of-two policies are close to optimal in general class of production/distribution networks with general joint setup costs. Math. Oper. Res. (1992) 17(4):951–963Link, Google Scholar
• Garbe R., Glazebrook K. D. Submodular returns and greedy heuristics for queueing scheduling problems. Oper. Res. (1998) 46(3):336–346Link, Google Scholar
• Hochbaum D. S., Hong S.-P. About strongly polynomial time algorithms for quadratic optimization over submodular constraints. Math. Programming (1995) 69:269–309Crossref, Google Scholar
• Hochbaum D. S., Shanthikumar J. G. Convex separable optimization is not much harder than linear optimization. J. ACM (1990) 37:843–862Crossref, Google Scholar
• Lovász L., Bachem A., Grötschel M., Korte B. Submodular functions and convexity. Mathematical Programming: The State of the Art (1983) (Springer-Verlag, New York) 235–257Crossref, Google Scholar
• Nagarajan M., Sošić G. Game-theoretical analysis of cooperation among supply chain agents: Review and extensions. Eur. J. Oper. Res. (2008) 187(3):719–745Crossref, Google Scholar
• Nerve Wire Inc. Collaborative commerce: Compelling benefits, significant obstacles. (2002) . White paper, NerveWire Inc., Newton, MAGoogle Scholar
• Peleg B., Sudholter P.Introduction to the Theory of Cooperative Games (2003) (Kluwer Academic Publishers, Boston) Crossref, Google Scholar
• Puerto J., Tamir A. Locating tree-shaped facilities using the ordered median objective. Math. Programming (2005) 102:313–338Crossref, Google Scholar
• Rockafellar R. T.Convex Analysis (1970) (Princeton University Press, Princeton, NJ) Crossref, Google Scholar
• Roundy R. 98%-effective integer-ratio lot-sizing for one-warehouse multi-retailer systems. Management Sci. (1985) 31(11):1416–1430Link, Google Scholar
• Schulz A. S., Uhan N. A. Sharing supermodular costs. Oper. Res. (2010) 58(4):1051–1056Link, Google Scholar
• Shapley L. S. Cores of convex games. Internat. J. Game Theory (1971) 1:11–26Crossref, Google Scholar
• Sharkey W. W. Cooperative games with large cores. Internat. J. Game Theory (1982) 11:175–182Crossref, Google Scholar
• Topkis D. M.Supermodularity and Complementarity (1998) (Princeton University Press, Princeton, NJ) Crossref, Google Scholar
• Tse D., Hanly V. Multiaccess fading channels—-Part I: Polymatroid structure, optimal resource allocation, and throughput capacities. IEEE Trans. Inform. Theory (1998) 44:2796–2815Crossref, Google Scholar
• Wolsey L. A. Maximising real-valued submodular functions: Primal and dual heuristics for location problems. Math. Oper. Res. (1982) 7(3):410–425Link, Google Scholar
• Yao D. D., Calzarossa M., Tucci S. Dynamic scheduling via polymatroid optimization. Lecture Notes in Computer Science (2002) 2459(Springer-Verlag, Berlin) 89–113Crossref, Google Scholar
• Zhang J. Joint replenishment game and maximizing an H-Schur concave function over a polymatroid. (2008) . Working paper, New York University, New YorkGoogle Scholar
• Zhang J. Cost allocation for joint replenishment models. Oper. Res. (2009) 57(1):146–156Link, Google Scholar