Coalition formation in a multi-agent inventory problem with two acquisition costs

Resumo

A multi-agent inventory problem is a situation in which several agents face individual inventory problems and make an agreement to coordinate their orders with the objective of reducing costs. Fiestras-Janeiro et al. (2015) propose a model to deal with a multiagent inventory problem in which several farmers cooperate to make joint orders of animal feed, the cost of the usual feeding ration being similar to the cost of the shortage feeding ration. However, in some situations the latter cost may be significantly smaller than the former cost since the shortage feeding ration is produced in the farm. When this happens each farm faces a continuous-review inventory problem, with a deterministic and linear demand, with no holding costs, with a limited capacity warehouse, with shortages and with two acquisition costs. In this work, we present a cooperative multi-agent inventory model to describe and analyze the system in which a group of farms cooperate by placing joint orders under these assumptions. If two acquisition costs are considered, the model and the procedure for the analysis are significantly different. The optimal inventory policies for this model are established, and a procedure to obtain a stable coalitional structure is proposed (following Elomri et al, 2012). In addition, an allocation rule for sharing the optimal costs is introduced and its performance is illustrated in a farming community in the North West of Spain.