DECOMPOSITION BASED HEURISTICS FOR A LOT SIZING AND SCHEDULING PROBLEM ON MULTIPLE HETEROGENEOUS PRODUCTION LINES WITH PERISHABLE PRODUCTS

This paper presents the synchronized and integrated two-level lot sizing and scheduling problem (SITLSP). This problem is found in beverage production, foundry, glass industry, and electrofused grains, where the production processes have usually two interdependent levels with sequence-dependent setups in each level. For instance, in the first level of soft drink production, raw materials are stored in tanks flowing to production lines in the second level. The amount and the time the raw materials and products have to be stored and produced should be determined. A synchronization problem occurs because the production in lines and the storage in tanks have to be compatible with each other throughout the time horizon. The SITLSP and its mathematical model are described in detail by this paper. The lack of similar models in the literature has led us to also propose a set of instances for the SITLSP, based on data provided by a soft drink company. Thus, a set of benchmark results for these problem instances are established using an exact method available in an optimization package. Moreover, results for two relaxations proved that the modeling methodology could be useful in real-world applications.

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Optimization models for a lot sizing and scheduling problem on parallel production lines that share scarce resources

RAIRO - Operations Research ◽

10.1051/ro/2021084 ◽

2021 ◽

Author(s):

Willy Alves de Oliveira Soler ◽

Maristela Oliveira Santos ◽

Maria do Socorro Nogueira Rangel

Keyword(s):

Lot Sizing ◽

Computational Study ◽

Mixed Integer ◽

Optimization Models ◽

Scheduling Problem ◽

Production Lines ◽

Commodity Flow ◽

Scarce Resources ◽

Computational Performance ◽

Lot Sizing And Scheduling

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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