Cooperative Linear Production Planning with Pooling of Resources

Abstract

In this paper, we deal with a cooperative production planning model in which multiple firms mutually pool a part of resources procured by themselves. Although the firms are cooperative in the sense that pooling of the resources is allowed, we consider an equilibrium model in which the firms maximize their own profits and a Nash equilibrium point with respect to their profits is calculated. Finally, we show allocation schemes based on a cooperative game arising from the cooperative linear production planning with pooling of the resources because the total profit of all the firms in the cooperative production planning model is larger than that in the independent production planning model without pooling. Calculating the Nash equilibrium points of a numerical example with various pooling rates and the corresponding profit allocations, we demonstrate the validity of the proposed cooperative production planning model.