A heuristic for the dynamic multi-level capacitated lotsizing problem with linked lotsizes for general product structures

In this paper, a new model formulation for the dynamic multi-level capacitated lotsizing problem with linked lotsizes is introduced. Linked lotsizes means that the model formulation correctly accounts for setup carryovers between adjacent periods if production of a product is continued in the next period. This model formulation is a good compromise between the big-bucket and small-bucket model formulation in that it inherits the stability of a big-bucket model and at least partially includes the precise description of setup operations provided by a small-bucket model. A Lagrangean heuristic is developed and tested in a numerical experiment with a set of invented data and a data set taken from industry. The solutions found show a good quality.

[1]  Herbert Meyr.  Simultane Losgrößen- und Reihenfolgeplanung für kontinuierliche Produktionslinien , 1999 .

[2]  C. R. Sox,et al.  The capacitated lot sizing problem with setup carry-over , 1999 .

[3]  C. Suerie.  Time Continuity in Discrete Time Models , 2005 .

[4]  K. Haase.  Lotsizing and Scheduling for Production Planning , 1994 .

[5]  John M. Wilson,et al.  The capacitated lot sizing problem: a review of models and algorithms , 2003 .

[6]  John O. McClain,et al.  Mathematical Programming Approaches to Capacity-Constrained MRP Systems: Review, Formulation and Problem Reduction , 1983 .

[7]  H. Tempelmeier,et al.  A Lagrangean-based heuristic for dynamic multilevel multiitem constrained lotsizing with setup times , 1996 .

[8]  Alf Kimms,et al.  Beyond Manufacturing Resource Planning (MRP II): Advanced Models and Methods for Production Planning , 2010 .

[9]  Zeger Degraeve,et al.  Meta-heuristics for dynamic lot sizing: A review and comparison of solution approaches , 2004, Eur. J. Oper. Res..

[10]  Andrea T.. Staggemeier,et al.  A survey of lot-sizing and scheduling models , 2001 .

[11]  L. J. Thomas,et al.  Heuristics for multilevel lot-sizing with a bottleneck , 1986 .

[12]  H. Günther,et al.  Produktion Und Logistik , 1994 .

[13]  Harvey M. Wagner,et al.  Dynamic Version of the Economic Lot Size Model , 2004, Manag. Sci..

[14]  Alf Kimms,et al.  Lot sizing and scheduling -- Survey and extensions , 1997 .

[15]  Matthias Carl Derstroff.  Mehrstufige Losgrößenplanung mit Kapazitätsbeschränkungen , 1995 .

[16]  Dirk Briskorn,et al.  A note on capacitated lot sizing with setup carry over , 2006 .

[17]  Knut Haase.  Capacitated Lot-Sizing with Linked Production Quantities of Adjacent Periods , 1998 .