EFFICIENT RESOURCE ALLOCATION IN A BILEVEL HIERARCHY WITH KNAPSACK AND ASSIGNMENT LOWER-LEVEL PROBLEMS

Bilevel optimization problems model a decision-making process with a two-level hierarchy of independent decision-makers, namely, the leader and the follower. The decisions are performed in a predetermined sequence with the leader acting first. Consequently, the follower solves an optimization problem which contains parameters (e.g., the right-hand sides of the follower's constraints) that are functionally dependent on the leader's decisions. On the other hand, the leader's objective and, possibly, constraints are also functions of both the leader's and follower's decision variables. Therefore, in the course of the decision-making process the leader should take into account the follower's rational response, i.e., optimal solutions to the follower's optimization problem. This dissertation is focused on the development of exact solution approaches for bilevel programs with combinatorial structures in the lower-level problems. In particular, we consider models arising in resource distribution systems that involve bilevel decision-making hierarchies with knapsack and assignment constraints. We discuss design and implementation of novel solution techniques, which exploit structural properties of the underlying optimization problems. The superiority of the proposed approaches is demonstrated through extensive computational experiments