Models, Algorithms and Approximation Results for a Bi-Level Synchronized Knapsack Problem

Abstract

We describe here a bi-level Knapsack problem which involves an Eater/Feeder interaction between 2 Knapsack systems and expresses the collaboration between a local resource provider and a consumer. We first describe the SFEK: Synchronized Feeder/Eater Knapsack problem in an accurate way, and set an ILP model, enhanced with additional valid cuts. Next we focus on the complexity issue. We design a Dynamic Programming algorithm which allows us to state that SFEK is pseudo-polynomial and derive for this problem a polynomial time approximation scheme. We conclude with a brief discussion about the Collaborative issue.