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4177. Cost Allocation Mechanisms in a Capacitated Economic Lot-Sizing Game

Invited abstract in session TC-49: Lot-sizing with game theory aspects, stream Lot Sizing, Lot Scheduling and Production Planning.

Tuesday, 12:30-14:00
Room: M1 (building: 101)

Authors (first author is the speaker)

1. Basak Altan
Department of Economics, Ozyegin University

Abstract

In this paper, we consider a capacitated economic lot-sizing problem where companies determine the optimal joint order plan in order to meet their demands in the most cost effective manner for a given planning horizon. After determining the minimum cost solution of the collaboration, the resulting joint-cost is to be allocated among the collaborators appropriately in order to sustain the collaboration. We first prove that the core of the corresponding cooperative game may be empty. Next, we establish the necessary and sufficient conditions for this game to have a non-empty core and show that when these conditions are satisfied, we can obtain a core allocation by solving a dual problem of a tight LP-relaxation. We also establish the equivalency of the dual optimal solution set and the core allocations when they exist and satisfy equal treatment of equals. Finally, we propose five different cost allocation mechanisms: (i) marginal allocation, (ii) dual linear programming based mechanism, (iii) the Shapley Value, (iv) the Nucleolus, and finally (v) pattern-based mechanism. Based on an extensive computational study, we observe that the pattern-based allocation mechanism significantly outperforms the other mechanisms with respect to the fairness of the cost allocations.

Keywords

Status: accepted

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