The effect of consolidated periods in heterogeneous lot-sizing games

Luis A. Guardiola (), Ana Meca () and Justo Puerto ()
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Luis A. Guardiola: Universidad de Alicante
Ana Meca: Universidad Miguel Hernández, Edificio Torretamarit
Justo Puerto: Mathematical Research Institute of the University of Seville (IMUS)

TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 2022, vol. 30, issue 2, No 7, 380-404

Abstract: Abstract We consider a cooperative game defined by an economic lot-sizing problem with heterogeneous costs over a finite time horizon, in which each firm faces demand for a single product in each period and coalitions can pool orders. The model of cooperation works as follows: ordering channels and holding and backlogging technologies are shared among the members of the coalitions. This implies that each firm uses the best ordering channel and holding technology provided by the participants in the consortium. That is, they produce, hold inventory, pay backlogged demand and make orders at the minimum cost of the coalition members. Thus, firms aim at satisfying their demand over the planing horizon with minimal operation cost. Our contribution is to show that there exist fair allocations of the overall operation cost among the firms so that no group of agents profit from leaving the consortium. Then we propose a parametric family of cost allocations and provide sufficient conditions for this to be a stable family against coalitional defections of firms. Finally, we focus on those periods of the time horizon that are consolidated and we analyze their effect on the stability of cost allocations.

Keywords: Cost-sharing; Lot-sizing; Heterogeneous costs; Consolidated period; Cooperative game; 91A12; 90B05 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11750-021-00614-0

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