A primal-dual algorithm for computing a cost allocation in the core of economic lot-sizing games

Abstract We consider the economic lot-sizing game with general concave ordering cost functions. It is well-known that the core of this game is nonempty when the inventory holding costs are linear. The main contribution of this work is a combinatorial, primal–dual algorithm that computes a cost allocation in the core of these games in polynomial time. We also show that this algorithm can be used to compute a cost allocation in the core of economic lot-sizing games with remanufacturing under certain assumptions.

[1]  Lloyd S. Shapley,et al.  On balanced sets and cores , 1967 .

[2]  Stéphane Dauzère-Pérès,et al.  Single item lot sizing problems , 2006, Eur. J. Oper. Res..

[3]  Harvey M. Wagner,et al.  Dynamic Version of the Economic Lot Size Model , 2004, Manag. Sci..

[4]  Justo Puerto,et al.  Production-inventory games: A new class of totally balanced combinatorial optimization games , 2024, Games Econ. Behav..

[5]  T. Magnanti,et al.  Strongly Polynomial Primal-Dual Algorithms for Concave Cost Combinatorial Optimization Problems , 2012, 1202.2654.

[6]  K. Richter,et al.  The reverse Wagner/Whitin model with variable manufacturing and remanufacturing cost , 2001 .

[7]  Donald B. Gillies,et al.  3. Solutions to General Non-Zero-Sum Games , 1959 .

[8]  Herbert Hamers,et al.  Economic Lot-Sizing Games , 2004, Eur. J. Oper. Res..

[9]  Knut Richter,et al.  Remanufacturing planning for the reverse Wagner/Whitin models , 2000, Eur. J. Oper. Res..

[10]  W. Zangwill.  A Backlogging Model and a Multi-Echelon Model of a Dynamic Economic Lot Size Production System---A Network Approach , 1969 .

[11]  Alf Kimms,et al.  Lot sizing and scheduling -- Survey and extensions , 1997 .

[12]  Dachuan Xu,et al.  A cost-sharing method for an economic lot-sizing game , 2009, Oper. Res. Lett..

[13]  Xin Chen,et al.  Duality Approaches to Economic Lot‐Sizing Games , 2007 .

[14]  Justo Puerto,et al.  Production-inventory games and PMAS-games: Characterizations of the Owen point , 2008, Math. Soc. Sci..

[15]  Thomas Demuynck.  A general extension result with applications to convexity, homotheticity and monotonicity , 2009, Math. Soc. Sci..