Abstract
A linear production programming problem in which multiple decisionmakers have resources and produce several kinds of products in collaboration is considered. It is formulated as a problem in which the objective function is the income obtained by selling several kinds of products, and the objective is to maximize the income under the resource constraint. The problem also includes the fair allocation (imputation) of the obtained common income. This paper discusses the linear production programming problem with multiple decisionmakers in a multiobjective environment. The multicommodity game is derived from the multiobjective production programming problem, and the nonemptiness of the core of the multicommodity game is demonstrated, based on the special property of the game. It is shown that when the multiobjective production programming problem is the primal problem, payoffs belonging to the core can be calculated from the optimal solution of the dual problem. The validity of the approach is shown by a numerical example. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 82(5): 29–38, 1999
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