# On horizontal cooperation in linear production processes with a supplier that controls a limited resource

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## Abstract

In this paper we consider a two-echelon supply chain with one supplier that controls a limited resource and a finite set of manufacturers who need to purchase this resource. We analyze the effect of the limited resource on the horizontal cooperation of manufacturers. To this end, we use cooperative game theory and the existence of stable distributions of the total profit among the manufacturers as a measure of the possibilities of cooperation. The game theoretical model that describes the horizontal cooperation involves externalities, which arise because of the possible scarcity of the limited resource and the possible coalition structures that can be formed. Furthermore, manufacturers do not know how the supplier will allocate the limited resource, therefore, how much of this resource they will obtain is uncertain for all concerned. Nevertheless, when the limited resource is not scarce for the grand coalition, the existence of stable distributions of the total profit is guaranteed and consequently the collaboration among the manufacturers is profitable for them all. In the event that the limited resource is insufficient for the grand coalition, we introduce a new cooperative game that assesses the expectations of each coalition of manufacturers regarding the amount of the limited resource they can obtain. We analyze two extreme expectations: the optimistic and the pessimistic. In the optimistic case, we cannot reach a conclusion regarding the full cooperation of the manufacturers. In the pessimistic case, with one reasonable assumption, the existence of stable distributions of the total profit is guaranteed and as a result the collaboration among manufacturers is a win–win deal.

## Keywords

Linear production processes Limited resource Horizontal cooperation Externalities## Notes

### Acknowledgements

First of all, the authors thank two anonymous referees and an associate editor for their helpful comments and suggestions to improve the contents of the paper. Financial support from the Ministerio de Economia y Competitividad (MINECO) of Spain and FEDER funds under Projects MTM2014-53395-C3-3-P and MTM2014-54199-P and from Fundacion Seneca de la Region de Murcia through Grant 19320/PI/14 are gratefully acknowledged.

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