两人多目标交叉规划的s-最优联合解

s-Optimal joint solutions for two-person multi-objective interaction programming

在现实生活中存在许多具有相互影响的多人决策问题,如供应链中的采购库存问题,决策者之间不仅存在自己决定的变量,也存在着决策者共同决策的变量,这类问题可以用交叉规划来建立模型,它要比一般的对策模型更加复杂.笔者将两人单目标交叉规划问题推广到多目标交叉规划问题,引进了具有相同联合值的s-最优联合解,并得到了它的若干有关性质,证明了可以通过求解等价的数学规划问题作为此类问题的s-最优联合解,这样大大地降低了求解多目标交叉规划的难度.

In real life,there are many multi-person decision making problems with interaction effect,such as ordering and inventorying problem in supply chain.There are not only the variables decided by decision maker himself,but also the variables decided by other decision makers.The problem can be modeled with interaction programming,which is more complex than strategy model.In this paper,we extend the two-person single-objective interaction programming to the multi-objective interaction programming.An s-optimal joint solution with the same joint value is proposed and some related properties can be gotten.It has been certificated that the s-optimal joint problem can be soluted as equivalent mathematical programming problem.It can greatly reduce the difficulty of multi-objective cross programming.