A Genetic Algorithm for the Integrated Scheduling of Production and Transport Systems
The integrated scheduling of production and transport systems is a NP-hard mixed-integer problem. This paper introduces a genetic algorithm (GA) that addresses this problem by decomposing it into combinatorial and continuous subproblems. The binary variab
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1 Introduction The scheduling of production and transport processes in manufacturing supply chains is currently done separately. Thus, these schedules might lead to a local optimum of an objective pursued by the supply chain. Improvements of the operational supply chain performance might be achieved by an integrated consideration of operations [1]. The integrated production and transport scheduling problem (PTSP) can be formulated as a mixed-integer program (MIP) [3, 6]. The MIP comprises binary optimization variables that represent assignments, e.g. jobs to machines or transport devices, as well as continuous optimization variables like time and costs [2]. Since it belongs to the class of NP-hard problems, exact solutions are limited to small problem instances [7]. In particular, the considered production scheduling is based on a heterogeneous open flow-shop with several consecutive production levels [5]. Each production level n consists of several machines r , which feature a job-class specific processing time and cost. All jobs j have to be processed on one machine at each production level, which is denoted by X j,n,r . The processing sequence of assigned jobs is given by Y j, j ,n,r . The jobs can be stored before the first production level, between production levels and before the assigned tour A j,v departs. Furthermore, jobs can be processed J. Hartmann (B) · T. Makuschewitz · B. Scholz-Reiter BIBA - Bremer Institut für Produktion und Logistik GmbH at the University of Bremen, Hochschulring 20,28359 Bremen, Germany e-mail: [email protected] T. Makuschewitz e-mail: [email protected] B. Scholz-Reiter e-mail: [email protected] Enzo M. Frazzon Industrial and Systems Engineering Department,Federal University of Santa Catarina (UFSC), Campus Universitário Trindade, Florianópolis-SC 88040-970, Brazil e-mail: [email protected] S. Helber et al. (eds.), Operations Research Proceedings 2012, Operations Research Proceedings, DOI: 10.1007/978-3-319-00795-3_80, © Springer International Publishing Switzerland 2014
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externally (E j ) in a very short time, but causing a comparatively high cost. The transport of jobs from the production facility to their destination is performed by a homogeneous fleet of vehicles v, featuring a limited transport capacity. All considered tours start and terminate at the production facility. If at least one job is assigned to a tour, this tour is conducted (Ov ). The tour can depart as soon as the processing of all assigned jobs is finalized. The routing of a tour v between the locations i is given by Z v,i,i . A performed tour involves fixed and variable costs. The variable costs depend on the duration of the tour. In addition, costs for an unpunctual delivery of orders occur. Furthermore, jobs can be shipped directly to their destination in time by a costly third party logistics provider (3PL), denoted by L j . External processing and 3PL transport ensure the feasibility of the problem. Genetic algorithms (GA) are efficient to explore a large
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