The core of multiobjective linear production programming games

A linear production programming problem in which multiple decisionmakers ha ve resources and produce several kinds of products in collaboration is cons idered. It is formulated as a problem in which the objective function is th e income obtained by selling several kinds of products, and the objective i s to maximize the income under the resource constraint. The problem also in cludes the fair allocation (imputation) of the obtained common income. This paper discusses the linear production programming problem with multiple de cisionmakers in a multiobjective environment. The multicommodity game is de rived from the multiobjective production programming problem, and the nonem ptiness of the core of the multicommodity game is demonstrated, based on th e special property of the game. It is shown that when the multiobjective pr oduction programming problem is the primal problem, payoffs belonging to th e core can be calculated from the optimal solution of the dual problem. The validity of the approach is shown by a numerical example. (C) 1999 Scripta Technica.