International Journal of Management Science and Engineering Management, MSEM, 2007, Vol.2 No.1, World Academic Union (World Academic Press)

In this paper, we present a class of interactional programming model (IPM) for the coexistence of competitions and cooperations problems, which can be regarded as decision making problems, such as supply chains. We introduce the optimal solution to the IPM, which is ideal and often does not exist. Therefore, we give a new concept of s-optimal solution, which always exists under some conditions. We prove that the soptimal solution to IPM can be obtained by solving a non-linear programming problem after we obtain some optimal solutions to the sub-problem of each decision maker. Some examples are given to explain how to compute an s-optimal solution.