Croce
- Rosario Scatamacchia
title: A new exact approach for the Bilevel Knapsack with Interdiction Constraints
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Bilevel Knapsack with Interdiction Constraints ,Exact approach ,Bilevel programming

Introduction {#sec:Intro}
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In the recent years, a growing attention has been centered to multilevel programming. This emerging field considers optimization problems with a hierarchal structure where many decision makers sequentially operate to reach conflicting objectives. Each agent takes decisions that may affect objectives and decisions of the agents at lower levels. At the same time, the latter decisions impact on the objectives of the agents at upper levels. Hierarchal contexts arise in many real-life applications in supply chains, energy sector, logistics and telecommunication networks among others. The presence of many decision levels makes these problems very challenging to solve.\
The most relevant research in the field has been pursued for bilevel optimization where two agents, denoted as a leader and a follower, play a Stackelberg game ([@St52]). In this game, the leader takes the first decision and then the follower reacts taking into account the leader’s strategy. Eventually, the agents receive a pay-off which depends on both leader’s and follower’s choices. The goal is typically to find a strategy for the leader that 