The core of multiobjective linear production programming games

A production model in which multiple decision makers pool resources to produce finished goods is considered. Such a production model, which is assumed to be linear, can be formulated as a multiobjective linear programming problem. In this paper, it is shown that a multi-commodity game arises from the multiobjective linear production programming problem with multiple decision makers. The characteristic sets in the game can be obtained by finding the set of Pareto maximal points of the multiobjective programming problem. It is proven that the core of the game is not empty, and points in the core are computed by using the duality theory of multiobjective linear programming problems. Numerical examples illustrate multi-commodity games arising from production programming problems and computing points in the core.