A Mixed-Discrete Bilevel Programming Problem

We investigate a special mixed-discrete bilevel programming problem resulting from the task to compute cash-out penalties due to the supply of incorrect amounts of natural gas through large gas networks. For easier solution we move the discreteness demand from the lower to the upper levels. This clearly changes the problem and it is our aim to investigate the relations between both problems. After the move, a parametric generalized transportation problem arises in the lower level for which the formulation of conditions for the existence of an optimal solution is our first task. In the second part of the paper, requirements guaranteeing that an optimal solution of the original problem is obtained by solving the modified one as well as bounds for the optimal value of the original problem are derived.