Linear two-level programming problems with single imprecise follower's objective functions and its solution method

摘要

In this paper, we discuss linear two-level programming problems with single imprecise follower's objective functions. Because of the imprecision of the follower's objective function coefficients, the leader cannot predict the follower's reaction but a set of possible reactions. Based on the max-mm strategy, we formulate such a problem as a max-mm problem with a non-convex feasible set. Analizing the problem, we show that the optimal solution exists in the vertex set of the original feasible set. Some solution algorithms based on the Kth-Best approach are proposed and compared the computational efficiency by a numerical experiment.