Control Method of Effect of Robust Optimization in Multi-Player Multi-Objective Decision-Making

Abstract

In the real situations of supply chain, there are different parts such as facilities, logistics warehouses and retail stores and they handle common kinds of products. In this research, these situations are focused on as the background of this research. They deal with the common quantities of their products, but due to their different environments, the optimal production quantity of one part can be unacceptable to another part and it may suffer a heavy loss. To avoid that kind of unacceptable situations, the common production quantities should be acceptable to all parts in one supply chain. Therefore, the motivation of this research is the necessity of the method to find the production quantities that make all decision makers acceptable is needed. However, it is difficult to find the production quantities that make all decision makers acceptable. Moreover, their acceptable ranges do not always have common ranges. In the decision making of car design, there are similar situations to this type of decision making. The performance of a car consists of purposes such as fuel efficiency, size and so on. Improving one purpose makes another worse and the relationship between these purposes is tradeoff. In these cases, Suriawase process is applied. This process consists of negotiations and reviews of the requirements of the purposes. In the step of negotiations, the requirements of the purposes are share among all decision makers and the solution that makes them as satisfied as possible. In the step of reviews of the requirements, they are reviewed based on the result of the negotiation if the result is unacceptable to some of decision makers. Therefore, through the iterations of the two steps, the solution that makes all decision makers satisfied is obtained. However, in the previous research, the effects that one decision maker reviews requirements in Suriawase process are quantified, but the mathematical model to modify the ranges of production quantities of all decision makers simultaneously is not shown. Therefore, in this research, based on Suriawase process, the mathematical model of multi-player multi-objective decision making is proposed. The mathematical model of multi-player multi-objective decision making by using linear physical programming (LPP) and robust optimization (RO) in the previous research is the basis of the methods of this research. LPP is one of the multi-objective optimization methods and RO is used to make the balance of the preference levels among decision makers. In LPP, the preference ranges of all objective functions are needed, so as the hypothesis of this research. In the research referred in this research, the method to control the effect of RO is not shown. If the effect of RO is too big, the average of the preference level becomes worse. The purpose of this research is to reproduce the mathematical model of multi-player multi-objective decision making based on Suriawase process and propose the method to control the effect of RO. In the proposed model, a set of the solutions of the negotiation problem is obtained and it is proved by the result of the numerical experiment. Therefore, the conclusion that the proposed model is available to obtain a set of the solutions of the negotiation problems in supply chain.