A two-level lot sizing and scheduling problem applied to a cosmetic industry

Abstract

In this paper we address a novel variant of the two-level lot-sizing and scheduling problem inspired by a cosmetic industry in Brazil. In this problem, we seek to optimize production activities in an environment consisting of two dependent levels and an intermediate inventory between them. We consider sequence-dependent setup in the first level, non-sequence dependent setup in the second level, and a different number of machines by level. Furthermore, following the mandatory requirements in the cosmetic industry, we also consider that each job must be stored for a minimum time limit and cannot exceeds a maximum time limit in the intermediate inventory. These practical requirements ensure a certain level of quality of the items produced. To solve the problem, we propose Mixed Integer Linear Programming (MILP) formulations and a hybrid exact method combining the traditional Branch and Bound (B&B) algorithm with Local Search (LS) procedures using a sequential framework. Our procedures apply several strategies of the Fix and Optimize (F&O) heuristic and Variable Neighborhood Descent (VND) principles. All methods were evaluated using a set of instances based on a real case scenario. The computational experiments indicated that our hybrid method can achieve competitive solutions, outperforming the results provided by the optimization of the MILP model.