A method for solving group multi objective decision problems

This paper introduces a new concept called s-optimal coalition solutions for group multi objective decision problems (GMDP), where s is a nonnegative constant. Its practical meaning is to achieve the optimality within a same value in each objective for each decision maker. This value is called the giving-up value. We show that to solve s-optimal coalition solutions is equivalent to solve a single objective programming. Based on this, we easily prove the existence of s-optimal coalition solutions under some conditions. We also discuss s-optimal coalition solutions when the giving-up value is a vector, i.e., the value in each objective is different. Numerical examples illustrate that the method presented here is efficient for GMDP. This paper presents a new way to solve the group multi objective decision problems.