Capacity planning with competitive decision-makers: trilevel MILP formulation and solution approaches

Abstract

Capacity expansion addresses the decision problem of a producer investing on infrastructure intended to fulfill future demand at the highest profit. The simplest formulation of such a problem assumes passive competitors (if any) and a market purchasing products according to the interest of the main producer. Such an approach disregards the rational behavior of the two other decision-makers on play. Namely, the customer usually prefers to buy at the lowest available cost and the competitors might also expand their capacity to capture a higher share of the market. The discrepancy between the previous model and the actual behavior of the other players might lead to wrong decisions and serious economic losses. This thesis proposes a trilevel formulation that takes into account a fully competitive environment. It presents a bi-level reformulation, with integer variables in both levels and introduces two novel algorithms able to solve such a challenging problem. To illustrate the value of using a multilevel model, an illustrative instance and an industrial example are presented. When comparing performances of the algorithms, it is shown that each one outperforms the other in one of the examples. Also the impact of degeneracy on a multilevel framework is analyzed; each algorithm is proven to offer one of the two different solution types according to the definition of optimistic solution. Finally, a possible generalization of one of the algorithms and its application to another trilevel problem from the literature is reported.