Zusammenfassung
Es wird ein heuristisches Verfahren zur Lösung des mehrstufigen Mehrprodukt-Losgrößenproblems für generelle Erzeugnis- und Prozeßstrukturen unter Beachtung multipler Ressourcen bei deterministisch schwankenden, dynamischen Bedarfen vorgestellt. Dabei werden auch Rüstzeiten berücksichtigt. Das mehrstufige Mehrprodukt-Losgrößenproblem wird mit Hilfe der Lagrange-Relaxation in mehrere unkapazitierte Einprodukt-Losgrößenprobleme überführt, aus deren Lösungen eine untere Schranke des optimalen Zielfunktionswerts abgeleitet wird. Zur Bestimmung einer oberen Schranke wird ein heuristisches Verfahren eingesetzt. Die Güte des Verfahrens wird anhand mehrerer Problemgruppen mit unterschiedlichen Größenordnungen überprüft.
Summary
In this paper a heuristic approach for the dynamic multi-level multi-item lotsizing problem in general product structures with multiple constrained resources and setup times is proposed. With the help of Lagrangean relaxation the capacitated multi-level lotsizing problem is decomposed into several uncapacitated single-item lotsizing problems. From the solutions of these single-item problems lower bounds on the minimal objective value are derived. Upper bounds are generated by means of a heuristic finite scheduling procedure. The quality of the approach is tested with reference to various problem groups of differing sizes.
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Literatur
Bahl HC, Ritzman LP, Gupta JND (1987) Determining lot sizes and resource requirements: A review. Oper Res 35:329–345
Billington PJ (1983) Multi-level lot-sizing with a bottleneck work center. Ph.D. Dissertation. Cornell University, Ithaca, New York
Chen W-H, Thizy J-M (1990) Analysis of relaxations for the multi-item capacitated lot-sizing problem. Ann Oper Res 26:29–72
Crowder H (1976) Computational improvements for subgradient optimization. Symposia Mathematica 19:357–372
Diaby M, Bahl HC, Karwan MH, Zionts S (1992) A lagrangean relaxation approach for very-large-scale capacitated lot-sizing. Manag Sci 38:1329–1340
Dixon PS, Silver EA (1981) A heuristic solution procedure for multi-item, single-level, limited capacity lot-sizing problem. J Oper Manag 2:22–39
Federgruen A, Tzur M (1991) A simple forward algorithm to solve general dynamic lot sizing models withn periods inO(n logn) orO(n) time. Manag Sci 37:909–925
Fisher ML (1981) The lagrangian relaxation method for solving integer programming problems. Manag Sci 27:1–18
Fleischmann B (1990) The discrete lot-sizing and scheduling problem. Eur J Oper Res 44:337–348
Gupta YP, Keung YK, Gupta MC (1992) Comparative analysis of lot-sizing models for multi-stage systems: A simulation study. Int J Prod Res 30:695–716
Heinrich CE (1987) Mehrstufige Losgrößenplanung in hierarchisch strukturierten Produktionsplanungssystemen. Springer, Berlin Heidelberg New York
Held M, Wolfe P, Crowder HP (1974) Validation of subgradient optimization. Math Prog 6:62–88
Lozano S, Larraneta J, Onieva L (1991) Primal-dual approach to the single level capacitated lot-sizing problem. Eur J Oper Res 51:354–366
Maes J (1987) Capacitated lotsizing techniques in manufacturing resource planning. Ph.D. Dissertation, Katholieke Universiteit Leuven, Fakulteit der Toegepaste Wetenschappen, Leuven
Maes J, Van Wassenhove LN (1986) A simple heuristic for the multi-item single level capacitated lotsizing problem. OR Lett 4:265–273
Maes J, Van Wassenhove LN (1991) Capacitated dynamic lotsizing heuristics for serial systems. Int J Prod Res 29:1235–1249
Maes J, McClain JO, Van Wassenhove LN (1991) Multilevel capacitated lotsizing complexity and LP-based heuristics. Eur J Oper Res 53:131–148
Nemhauser GL, Wolsey LA (1988) Integer and combinatorial optimization. Wiley, New York
Salomon M (1991) Deterministic lotsizing models for production planning. Springer, Berlin Heidelberg New York
Shapiro JF (1979) A survey of lagrangean techniques for discrete optimization. Ann Discr Math 5:113–138
Tempelmeier H (1992) Material-Logistik. Grundlagen der Bedarfs- und Losgrößenplanung in PPS-Systemen. 2. Aufl. Springer, Berlin Heidelberg New York
Tempelmeier H, Helber S (1993) A heuristic for dynamic multiitem multi-level capacitated lotsizing for general product structures. Eur J Oper Res (forthcoming)
Thizy J-M (1991) Analysis of lagrangian decomposition for the multi-item capacitated lot-sizing problem. INFOR 29:271–283
Thizy J-M, Van Wassenhove LN (1985) Lagrangean relaxation for multi-item capacitated lot-sizing problem: A heuristic implementation. IIE Trans 17:308–313
Trigeiro WW (1987) A dual-cost heuristic for the capacitated lot sizing problem. IIE Trans 19:67–72
Trigeiro WW, Thomas LJ, McClain JO (1989) Capacitated lot sizing with setup times. Manag Sci 35:353–366
Wagelmans A, Van Hoesel S, Kolen A (1992) Economic lot sizing: AnO(n logn) algorithm that runs in linear time in the Wagner-Whitin case. Oper Res 40:145–155
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Tempelmeier, H., Derstroff, M. Mehrstufige Mehrprodukt-Losgrößenplanung bei beschränkten Ressourcen und genereller Erzeugnisstruktur. OR Spektrum 15, 63–73 (1993). https://doi.org/10.1007/BF01720518
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DOI: https://doi.org/10.1007/BF01720518