ABSTRACT In this paper, we propose a novel MIP-based heuristic method to deal with a lot sizing and scheduling problem with multiple heterogeneous production lines in a production setting with perishable items. The problem is inspired by the production processes adopted by some Brazilian food industries and it considers that several production lines share the same scarce production resources. Therefore, only a subset of those lines can simultaneously operate in each production period. Moreover, the production environment is characterized by the existence of sequence-dependent setup times and costs, and by the production of perishable items which can be stocked for a short period only. Firstly, we propose a facility location reformulation for a model previously proposed in the literature. Secondly, we propose a heuristic composed of two phases. The first phase has an elaborated approach to building feasible solutions solving initially an aggregated lot sizing problem to decide which production lines to assemble, followed by the resolution of the various single line lot sizing and scheduling problems. The second phase applies improvement heuristics exploring principles of fix-and-optimize and local branching procedures. Computational results carried out using a data set proposed in the literature are presented in order to study the efficiency of the proposed approach. The results demonstrate that our heuristics provide superior results when benchmarked with a heuristic from the literature specifically developed to solve the problem under consideration, and with a commercial MIP solver.

ABSTRACT This research addresses a lot sizing and scheduling problem inspired by a real-world production environment where the customers make advanced orders and the industry need to decide which orders will be accepted with the aim of maximizing the profit respecting the production capacity constraints. Orders are composed of different types of items which must be delivered within a given time interval and, moreover, such orders cannot be split. A mixed integer programming (MIP) model is proposed to represent the problem and a MIP-based heuristic is also proposed to deliver good solutions at an acceptable computational time. The heuristic is composed of three phases (construction, deterministic improvement and stochastic improvement phases) and combines relax-and-fix, fix-and-optimize, and iterative MIP based neighborhood search procedures. Computational tests are presented in order to study the efficiency of the proposed approaches.