Design of mathematical models for the integration of purchase and production lot-sizing and scheduling problems under demand uncertainty |
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| Affiliation: | 1. Department of Production Engineering, Federal University of São Carlos. Rodovia Washington Luís - Km 235, São Carlos-SP, CEP: 13565-905, Brazil;2. HEC Montréal and GERAD. 3000, Chemin de la Côte-Sainte-Catherine, Montréal, H3T 2A7, Canada;3. Department of Production Engineering, Federal University of São Carlos. Rodovia João Leme dos Santos - Km 110, Sorocaba-SP, CEP: 18052-780, Brazil;1. Federal University of São Carlos, Rodovia João Leme dos Santos (SP-264), Km 110 Bairro do Itinga, Sorocaba, Brazil;2. INESC TEC, Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal;1. Instituto de Ciências Matemticas e de Computação, Universidade de São Paulo, São Carlos, SP CEP 13560-970, Brazil;2. Departamento de Engenharia de Produção, Universidade Federal de São Carlos, São Carlos, SP CEP 13565-905, Brazil;3. Centro de Estudos de Gestão, Instituto Superior Técnico, Universidade Técnica de Lisboa, Lisboa 1049-101, Portugal;1. Escuela de Ingeniería y Ciencias, Tecnológico de Monterrey, México;2. Research Center of Physics and Mathematics, Universidad Autónomo de Nuevo Léon, México;3. Department of Mathematics, ITAM - Instituto Tecnológico Autónomo de México, México |
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| Abstract: | This study addresses the multi-level lot-sizing and scheduling problem with complex setups and considers supplier selection with quantity discounts and multiple modes of transportation. The present research proposes a mixed-integer linear programming (MILP) model in which the purchase lot-sizing from multiple suppliers, production lot-sizing with multiple machines and scheduling of various products of different families are accomplished at the same time. However, these decisions are not integrated in traditional environments and are taken separately. In this study, two different types of lot-sizing models called aggregated and disaggregated are developed for the problem to evaluate and compare the computational efficiency of them under deterministic and stochastic demands and provide some managerial insights. To deal with the stochastic demands, Chance-Constrained Programming (CCP) approach is applied. Based on the results of this study, the average profit of the separated (purchase from production) lot-sizing model under demand choice flexibility and stochastic demand is 24% and 22% less than the integrated model, respectively. Moreover, the results also confirm the effect of discount structure on the amount of purchases, productions, revenues and costs. |
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