A Mathematical Model for the Synchronized and Integrated Two-Level Lot Sizing and Scheduling Problem Claudio Fabiano Motta Toledo Universidade Estadual de Campinas (UNICAMP) Faculdade de Engenharia El´ etrica e de Computa¸c˜ ao (FEEC) Departamento de Engenharia de Sistemas (DENSIS) Rua Albert Einstein, 400 ·Caixa Postal 6101 ·Cep 13083–970, Campinas, SP ·Brazil email: claudio@densis.fee.unicamp.br Alf Kimms Chair of Logistics and Traffic Mgmt. Dept. of Technology and Operations Mgmt. Mercator School of Management University of Duisburg–Essen, Campus Duisburg 47048 Duisburg · Germany email: alf.kimms@uni–duisburg–essen.de Paulo Morelato Fran¸ ca Universidade Estadual de Campinas (UNICAMP) Faculdade de Engenharia El´ etrica e de Computa¸c˜ ao (FEEC) Departamento de Engenharia de Sistemas (DENSIS) Rua Albert Einstein, 400 ·Caixa Postal 6101 ·Cep 13083–970, Campinas, SP ·Brazil email: franca@densis.fee.unicamp.br Reinaldo Morabito Universidade Federal de So Carlos (USFCar) Departamento de Engenharia de Produo (DEP) Via Washington Luiz, km.235 ·Caixa Postal 676 ·Cep 13.565-905, So Carlos, SP ·Brazil email: morabito@power.ufscar.br Abstract The present paper proposes a multi–level lot sizing and schedul- ing problem with parallel machines, capacity constraints and sequence- dependent setup costs and times. This problem was motivated by a real situation found in some industrial settings, mainly soft drink companies. In this kind of industrial process, the production involves two interde- pendent levels with decisions about raw material storage and soft drink bottling. The various raw materials are stored in tanks, from which they flow to bottling production lines. The challenge is to simultaneously determine the lot sizing and scheduling of raw materials in tanks and also in the bottling lines, where setup costs and times depend on the previous items stored and bottled. We call this problem a Synchronized and Integrated Two-Level Lot Sizing and Scheduling Problem (SITLSP). A mixed-integer linear model is proposed with various combined con- straints that are not usually dealt with in the literature. This complex model was solved by the GAMS/CPLEX software. The lack of similar 1