The Stochastic Bilevel Continuous Knapsack Problem with Uncertain Follower’s Objective

Abstract We consider a bilevel continuous knapsack problem where the leader controls capacity of knapsack, while follower chooses feasible packing maximizing his own profit. The leader’s aim is to optimize linear objective function in and follower’s solution, but with respect different item values. address stochastic version this profits are uncertain from perspective, only probability distribution known. Assuming that aims at optimizing expected value her function, we first observe tractable as long possible scenarios given explicitly part input, which also allows deal general distributions using sample average approximation. For case independently uniformly distributed values, show #P-hard general, same true even for evaluating function. Nevertheless, present pseudo-polynomial time algorithms case, running total size items. Based on this, derive an additive approximation scheme runs time.