This paper addresses a lot sizing and scheduling problem inspired from a real-world production environment apparent in food industry. Due to the scarcity of resources, only a subset of production lines can operate simultaneously, and those lines need to be assembled in each production period. In addition, the products are perishable, and there are often significant sequence-dependent setup times and costs. We first propose a standard mixed integer programming model for the problem, and then a reformulation of the standard model in order to allow us to define a branching rule to accelerate the performance of the branch-and-bound algorithm. We also propose an efficient relax-and-fix procedure that can provide high-quality feasible solutions and competitive dual bounds for the problem. Computational experiments indicate that our approaches provide superior results when benchmarked with a commercial solver and an established relax-and-fix heuristic from the literature.

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.

The purpose of this paper is to propose mathematical models to represent a lot sizing and scheduling problem on multiple production lines that share scarce resources and to investigate the computational performance of the proposed models. The main feature that differentiates this problem from others in the literature is that the decision on which lines to organize should be taken considering the availability of the necessary resources. The optimization criterion is the minimization of the costs incurred in the production process (inventory, backlogging, organization of production lines, and sequence-dependent setup costs). Nine mixed integer optimization models to represent the problem are given and, also, the results of an extensive computational study carried out using a set of instances from the literature. The computational study indicates that an efficient formulation, able to provide high quality solutions for large sized instances, can be obtained from a classical model by making the binary production variables explicit, using the facility location reformulation as well as the single commodity flow constraints to eliminate subsequences. Moreover, from the results, it is also clear that the consideration of scarce resources makes the problem significantly more difficult than the traditional one.

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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.