Solving the CLSP by a Tabu Search Heuristic

The multi-item, single-level, capacitated, dynamic lot-sizing problem, commonly abbreviated as CLSP, is considered. The problem is cast in a tight mixed-integer programming model (MIP); tight in the sense that the gap between the optimal value of MIP and that of its linear programming relaxation (LP) is small. The LP relaxation of MIP is then solved by column generation. The resulting feasible solution is further improved by adopting the corresponding set-up schedule and re-optimizing variable costs by solving a minimum-cost network flow (trans-shipment) problem. Subsequently, the improved solution is used as a starting solution for a tabu search procedure, with the worth of moves assessed using the same trans-shipment problem. Results of computational testing of benchmark problem instances are presented. They show that the heuristic solutions obtained are effective, in that they are extremely close to the best known solutions. The computational efficiency makes it possible to solve realistically large problem instances routinely on a personal computer; in particular, the solution procedure is most effective, in terms of solution quality, for larger problem instances.

[1]  G. D. Eppen,et al.  Solving Multi-Item Capacitated Lot-Sizing Problems Using Variable Redefinition , 1987, Oper. Res..

[2]  N. Adam,et al.  The Dynamic Lot-Sizing Problem for Multiple Items Under Limited Capacity , 1981 .

[3]  Ludo Gelders,et al.  A Branch and Bound Algorithm for the Multi Item Single Level Capacitated Dynamic Lotsizing Problem , 1986 .

[4]  E. Newson.  Multi-Item Lot Size Scheduling by Heuristic Part I: With Fixed Resources , 1975 .

[5]  E. H. Bowman.  Production Scheduling by the Transportation Method of Linear Programming , 1956 .

[6]  M. D. Grigoriadis,et al.  An efficient implementation of the network simplex method , 1986 .

[7]  Fred Glover,et al.  Tabu Search - Part II , 1989, INFORMS J. Comput..

[8]  Colin R. Reeves,et al.  Improving the Efficiency of Tabu Search for Machine Sequencing Problems , 1993 .

[9]  Leon S. Lasdon,et al.  An Efficient Algorithm for Multi-Item Scheduling , 1971, Oper. Res..

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

[11]  Rema Padman,et al.  Dual Algorithms for Pure Network Problems , 1989, Oper. Res..

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

[13]  B. P. Dzielinski,et al.  Optimal Programming of Lot Sizes, Inventory and Labor Allocations , 1965 .

[14]  L. Ritzman,et al.  A cyclical scheduling heuristic for lot sizing with capacity constraints , 1984 .

[15]  Gabriel R. Bitran,et al.  The Multi-Item Capacitated Lot Size Problem: Error Bounds of Manne's Formulations , 1986 .

[16]  Luk N. Van Wassenhove,et al.  Multi-Item Single-Level Capacitated Dynamic Lot-Sizing Heuristics: A General Review , 1988 .

[17]  E. Silver,et al.  A heuristic solution procedure for the multi-item, single-level, limited capacity, lot-sizing problem , 1981 .

[18]  Paul Tseng,et al.  Relaxation Methods for Minimum Cost Ordinary and Generalized Network Flow Problems , 1988, Oper. Res..

[19]  Alan S. Manne,et al.  Programming of Economic Lot Sizes , 1958 .

[20]  M. Lambrecht,et al.  Heuristic Procedures for the Single Operation, Multi-Item Loading Problem , 1979 .

[21]  E. Newson.  Multi-Item Lot Size Scheduling by Heuristic Part II: With Variable Resources , 1975 .

[22]  R. Kipp Martin,et al.  Generating Alternative Mixed-Integer Programming Models Using Variable Redefinition , 1987, Oper. Res..

[23]  Harish C. Bahl.  Column Generation Based Heuristic Algorithm for Multi-Item Scheduling , 1983 .

[24]  Y. Roll,et al.  A Heuristic Algorithm for the Multi-Item Lot-Sizing Problem with Capacity Constraints , 1982 .

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

[26]  J. K. Lenstra,et al.  Deterministic Production Planning: Algorithms and Complexity , 1980 .