以機遇限制規劃模式求解可能性最小生成樹問題

Solving Possibilistic Minimum Spanning Tree Problems by Using Chance-Constrained Models

本文在探討，當聯結權數為模糊數時，如何以機遇限制規劃模式求解最小生成樹問題。在模式中，聯結權數為受限於機遇限制的決策變數，要求實際的聯結權數不大於規劃的聯結權數之可能性不低於預定的信賴水準。依決策者的特性，所提出模式分為Minimin模式與Maximin模式兩種。本文指出當聯結權數為具無互動性的模糊數時，可將問題轉成傳統的最小生成樹問題。

In this paper, two possibilistic chance-constrained models for solving the minimum spanning tree problem with fuzzy arc weights are proposed. In these models, the arc weights used in planning are treated as decision variables and subject to a set of chance constraints. These constraints require the possibilities that the arc weights used in planning are sufficient are not less than the specified levels. According to the characteristic of the decision maker, there are two kinds of chance-constrained model, the minimin model and the maximin model. It is shown that when the arc weights are non-interactive, these two models can be transformed into the classical minimum spanning tree problems easily.