New partial cooperation model for ill-posed bilevel programming problem via satisfactory degree

摘要

Partial cooperation formulation is a more viable option than optimistic's and pessimistic's to solve an ill-posed bilevel programming problem. Aboussoror's partial cooperation model uses a constant as a cooperation index to describe the degree of follower's cooperation. The constant only indicates the leader's expectation coefficient for the follower's action, not the follower's own willingness. To solve this situation, a new model is proposed by using the follower's satisfactory degree as the cooperation degree. Then, because this new cooperation degree is a function which is dependent on the leader's choice and decided by the follower's satisfactory degree, this paper proves such proposed model not only leads an optimal value between the optimistic value and pessimistic's, but also leads a more satisfactory solution than Aboussoror's. Finally, a numerical experiment is given to demonstrate the feasibility of this new model.