Annals of Operations Research

, Volume 261, Issue 1–2, pp 255–273 | Cite as

On coalition formation in a non-convex multi-agent inventory problem

  • A. Saavedra-NievesEmail author
  • I. García-Jurado
  • M. G. Fiestras-Janeiro
Original Paper


A multi-agent inventory problem is a situation in which several agents face individual inventory problems and can coordinate their orders to reduce costs. This paper analyses a multi-agent inventory problem in which each agent faces a continuous-review inventory problem, with a deterministic linear demand, no holding costs and a limited capacity warehouse. In the case under study, shortages are allowed as follows. Goods are bought from an external supplier and then they are stored in each agent’s warehouse. These stored goods usually satisfy demand. However, each agent may alternative produce their own goods, which are less costly but of lower quality. When a shortage of the purchased goods occurs, demand is satisfied with the produced goods until a new order arrives. The problem under study herein arises in a farming community, and is a variation of a problem addressed by Fiestras-Janeiro et al. (2015). However, the existence of two acquisition costs makes it substantially different from Fiestras-Janeiro et al.’s problem and significantly complicates its analysis since the resulting cost functions may now be non-convex. This paper establishes the optimal inventory policies for our problem and obtains a stable order structure when agents allocate the joint costs using a proportional rule. In addition, it illustrates the performance of our model and results in an example.


Multi-agent systems Optimal inventory policy Non-convex optimization Allocation rule Cooperative game 



Authors acknowledge the financial support of Ministerio de Economía y Competitividad through projects MTM2011-27731-C03-01, MTM2011-27731-C03-03, MTM2014-53395-C3-1-P, MTM2014-53395-C3-2-P and MTM2014-53395-C3-3-P, and of Xunta de Galicia through the ERDF (Grupos de Referencia Competitiva ED431C-2016-015 and ED431C-2016-040, and Centro Singular de Investigación de Galicia ED431G/01).


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • A. Saavedra-Nieves
    • 1
    Email author
  • I. García-Jurado
    • 2
  • M. G. Fiestras-Janeiro
    • 3
  1. 1.Departamento de Estatística, Análise Matemática e OptimizaciónUniversidade de Santiago de CompostelaSantiago de CompostelaSpain
  2. 2.Departamento de MatemáticasUniversidade da CoruñaA CoruñaSpain
  3. 3.Departamento de Estatística e Investigación OperativaUniversidade de VigoVigoSpain

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