抄録
In this article, we discuss multi-production planning problem under the framework of cooperative game theory. Shapley value is employed to evaluate allocated risk, and the average value-at-risk (AVaR), a function managing risk mainly used to evaluate a loss distribution, is defined as characteristic function for singular player and respective coalitions. Opposite to the conventional Shapley value we treat the problem using quadratic programming models. Three models are proposed, namely Model 1.1 where production constraints are added directly to Shapley value [11]; Model 2 or Constrained Model using Shapley value and production constraints without considering individual rationality and Model 3, similar to the second, but with a weighting factor, w{9, controled by decision-maker. Hence, the scheme proposed in this study seeks to satisfy, essentially, individual rationality and group rationality properties. The concept of penalty for each period is introduced, and by quantifying its value the decision-maker can forecast the production volume for those periods efficiently. A numerical illustration is also considered. Abstract In this article, we discuss multi-production planning problem under theory. Shapley value is employed to evaluate allocated risk, and the tion managing risk mainly used to evaluate a loss distribution, is defined singular player and respective coalitions. Opposite to the conventional using quadratic programming models. Three models are proposed, namely straints are added directly to Shapley value [11]; Model 2 or Constrained production constraints without considering individual rationality and with a weighting factor, w{9, controled by decision-maker. Hence, the scsatisfy, essentially, individual rationality and group rationality properties. period is introduced, and by quantifying its value the decision-maker can those periods efficiently. A numerical illustration is also considered.
