The robust multi-plant capacitated lot-sizing problem

In this paper, we study the robust multi-plant capacitated lot-sizing problem with uncertain demands, processing and setup times. This problem consists of a production system with more than one production plant, in which each plant can produce items to meet its demand or transfer items to other plants. The objective is to determine a minimum-cost production and transfer plan considering the compromise between production, inventory, and transfer costs. Using a static robust optimization approach, we propose two different robust mixed-integer programming formulations for the problem. The first formulation applies the standard duality technique to the constraints involving uncertain parameters while the second applies the duality technique only to the time constraints and introduces new parameters, accumulating the worst-case demand realizations, to the inventory balance constraints. This second formulation has the advantage of resulting from a more intuitive and straightforward approach. We perform extensive computational experiments to compare the performance of the formulations and to assess the effect of different budgets of uncertainty on the solutions. Moreover, we observe that demand, processing and setup times have different impacts when taking uncertainty into account.