Abstract:

A new concept called the t*-optimal integral differential solution for a two-person interaction programming problem(IPP) was introduced,　where t* is a non-negative constant. It can be shown that the t*-optimal integral differential solution is equivalent to the optimal solution for another mathematical programming problem. In addition,  the t*-optimal integral differential solution that the giving-up value of each decision maker is different was discussed,　the relation between the t*-optimal integral differential solution and the s-optimal joint solution was also presented. A numerical example illustrated that the method presented here is efficient for solving a two-person interaction programming problem.

Key words: interaction programming problem; s-optimal joint solution; t*-optimal integral differential solution