This article studies a problem of optimal scheduling and lot sizing a number of products on m unrelated parallel machines to satisfy given demands. A sequence-dependent setup time is required between lots of different products. The products are assumed to be all continuously divisible or all discrete. The criterion is to minimize the time at which all the demands are satisfied, Cmax, or the maximum lateness of the product completion times from the given due dates, Lmax. The problem is motivated by the real-life scheduling applications in multi-product plants. The properties of optimal solutions, NP-hardness proofs, enumeration, and dynamic programming algorithms for various special cases of the problem are presented. A greedy-type heuristic is proposed and experimentally tested. The major contributions are an NP-hardness proof, pseudo-polynomial algorithms linear in m for the case, in which the number of products is a given constant and the heuristic. The results can be adapted for solving a production line design problem.
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production line design
Document Type: Research Article
Industrial Engineering and Computer Science Research Center, Ecole des Mines de Saint-Etienne, Saint-Etienne, Cedex 2, France
Omsk Branch of Sobolev Institute of Mathematics SB RAS, Omsk, Russia
United Institute of Informatics Problems, National Academy of Sciences of Belarus, Minsk, Belarus
Institute of Mathematics and Information Technologies, Omsk State University, Omsk, Russia
Publication date: 2010-07-01