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

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.