Multisite capacity, production, and distribution planning with reactor modifications: MILP model, bilevel decomposition algorithm versus lagrangean decomposition scheme

We propose a multiperiod mixed-integer linear programming (MILP) model for the simultaneous capacity, production, and distribution planning for a multisite system including a number of production sites and markets. Multiple products are produced in several production trains that are located in different sites. The unique feature of the proposed model is that it considers the construction times of capacity modifications and takes into account the option of capacity transformation by modifying the reactor in a production train from producing one product family to producing another one. To solve the resulting large-scale MILP model, we present solution techniques based on Lagrangean decomposition and bilevel decomposition. Numerical examples are presented to illustrate the applicability of the model and the performance of the algorithms. It is shown that the bilevel decomposition is the superior solution approach in terms of faster computational times and smaller optimality gaps for the problem addressed in this work.