A dual ascent and column generation heuristic for the discrete lotsizing and scheduling problem with setup times

In this paper the Discrete Lotsizing and Scheduling Problem (DLSP) with setup times is considered. DLSP is the problem of determining the sequence and size of production batches for multiple items on a single machine. The objective is to find a minimal cost production schedule such that dynamic demand is fulfilled without backlogging. DLSP is formulated as a Set Partitioning Problem (SPP). We present a dual ascent and column generation heuristic to solve SPP. The quality of the solutions can be measured, since the heuristic generates lower and upper bounds. Computational results on a personal computer show that the heuristic is rather effective, both in terms of quality of the solutions as well as in terms of required memory and computation time.

[1]  M. Minoux,et al.  A new approach for crew pairing problems by column generation with an application to air transportation , 1988 .

[2]  William W. Trigeiro,et al.  Capacitated lot sizing with setup times , 1989 .

[3]  M. Rosenwein,et al.  An application-oriented guide for designing Lagrangean dual ascent algorithms , 1989 .

[4]  G. Bitran,et al.  Computational Complexity of the Capacitated Lot Size Problem , 1982 .

[5]  Thomas L. Magnanti,et al.  A Strong Cutting Plane Algorithm for Production Scheduling with Changeover Costs , 1990, Oper. Res..

[6]  Bezalel Gavish,et al.  A Fully Polynomial Approximation Scheme for Single-Product Scheduling in a Finite Capacity Facility , 1990, Oper. Res..

[7]  Jacques Desrosiers,et al.  Routing with time windows by column generation , 1983, Networks.

[8]  Leon S. Lasdon,et al.  Optimization Theory of Large Systems , 1970 .

[9]  Luk N. Van Wassenhove,et al.  Planning production in a bottleneck department , 1983 .

[10]  George L. Nemhauser,et al.  The Set-Partitioning Problem: Set Covering with Equality Constraints , 1969, Oper. Res..

[11]  D. Aucamp,et al.  The Computation of Shadow Prices in Linear Programming , 1982 .

[12]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[13]  Marc Salomon,et al.  The single item discrete lotsizing and scheduling problem : linear description and optimization , 1989 .

[14]  L. V. Wassenhove,et al.  Some extensions of the discrete lotsizing and scheduling problem , 1991 .

[15]  D. Ryan,et al.  On the integer properties of scheduling set partitioning models , 1988 .

[16]  L. V. Wassenhove,et al.  Set partitioning and column generation heuristics for capacitated dynamic lotsizing , 1990 .