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A Lagrangean decomposition solution to a single line multiproduct scheduling problem. (English) Zbl 0812.90058

Summary: One of the major concerns in manufacturing is the cost and/or time of product changeovers on a production line. A changeover involves setting up the line to produce a different product. The problem of finding the schedule for producing products on a single level, capacitated line such that the best trade-offs between changeover and inventory carrying costs is obtained can be complex. We solve a mixed integer programming formulation of that problem utilizing Lagrangean decomposition for finding lower bounds, and a primal heuristic for generating feasible schedules from Lagrangean solutions. Compared to existing approaches, our procedure yields near optimum solutions to large problems faster.

MSC:

90B30 Production models
90B35 Deterministic scheduling theory in operations research
90C11 Mixed integer programming
Full Text: DOI

References:

[1] De Matta, R.; Guignard, M., Dynamic production scheduling in a process industry, (Working Paper in Decision Sciences (1990), Wharton School, University of Pennsylvania) · Zbl 0809.90066
[2] Elmaghraby, S. E., The Economic Lot Scheduling Problem (ELSP): Review and extensions, Management Science, 24, 587-598 (1978) · Zbl 0376.90051
[3] Gascon, A.; Leachman, R. C., A dynamic programming solution of the dynamic, multi-item single machine scheduling problem, Operations Research, 36, 50-56 (1988) · Zbl 0657.90045
[4] Glassey, C. R., Minimum change-over scheduling of several products on one machine, Operations Research, 16, 342-352 (1968) · Zbl 0186.24902
[5] Glover, F.; Mulvey, J., The equivalence of the 0-1 integer programming problem to discrete generalized and pure network models, Operations Research, 28, 829-933 (1980) · Zbl 0443.90064
[6] Guignard, M.; Kim, S., Lagrangean decomposition for integer programming: Theory and application, RAIRO Operations Research, 21/4, 307-323 (1987) · Zbl 0638.90075
[7] Guignard, M.; Kim, S., Lagrangean decomposition: A model yielding stronger Lagrangean bounds, Mathematical Programming, 39, 215-228 (1987) · Zbl 0638.90074
[8] Guignard, M.; Kim, S.; Rosenwein, M.; Spielberg, K., A survey of Lagrangean decomposition and its application (1989), Dept. of Decision Sciences, University of Pennsylvania
[9] Held, M.; Wolfe, P.; Crowder, H. P., Validation of subgradient optimization, Mathematical Programming, 6, 62-88 (1974) · Zbl 0284.90057
[10] Karmarkar, U. S.; Schrage, L., The deterministic dynamic product cyclic problem, Operations Research, 33, 326-345 (1985) · Zbl 0571.90038
[11] Magnanti, T. L.; Vachani, R., A strong cutting plane algorithm for production scheduling with changeover costs, Operations Research, 38, 456-473 (1990) · Zbl 0707.90047
[12] Mitsumori, S., Optimum production scheduling of multicommodity in flow line, IEEE Transactions on Systems, Man, and Cybernetics, 2, 486-493 (1972) · Zbl 0241.90028
[13] Pape, U., Algorithm 562: Shortest path lengths, ACM Transactions on Mathematical Software, 5, 450-455 (1980) · Zbl 0442.68063
[14] Shepardson, F.; Marsten, R., A Lagrangean relaxation algorithm for the two-duty period scheduling problem, Management Science, 26, 274-281 (1980) · Zbl 0448.90042
[15] Wolsey, L. A., Uncapacitated lot-sizing problems with start-up costs, Operations Research, 37, 741-747 (1989) · Zbl 0696.90021
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