Cutting plane method for the facility location problem with probabilistic constraints

This study shows the effectiveness of the cutting plane method by applying it to the facility location problem with probabilistic constraints. Probabilistic constraints are those that should be satisfied at a certain probabilistic level and can consider the uncertainty of the parameters involved in the problem. Problems with such probabilistic constraints are generally difficult to solve. Therefore, based on previous research, we consider transforming a problem with probabilistic constraints into a 0–1 mixed integer programming problem under special conditions. Thereafter, we introduce the cutting plane method using a valid inequality of the feasible region.