APPLICATION OF A HEURISTIC ALGORITHM TO MIXED-INTEGER BI-LEVEL PROGRAMMING PROBLEMS

In this paper, we consider a mixed-integer bi-level linear programming (or a leader's) problem with one parameter in the right-hand side of the constraints in the lower level (or a follower's) problem. Motivated by the application to a natural yes cash-out problem, we consider a particular case that consists in minimizing the cash-out penalty costs for a natural gas shipping company. The functions are linear at both levels, and the proposed algorithm, is based upon an approximation of the optimal value function using the branch-and-bound method. Therefore, at every node of this branch-and-bound structure, we apply a new branch-and-bound technique to process the integrality condition.