A genetic algorithm to solve the general multi-level lot-sizing problem with time-varying costs

The multi-level lot-sizing (MLLS) problem in material requirements planning (MRP) systems belongs to those problems that industry manufacturers daily face in organizing their overall production plans. However, this combinatorial optimization problem can be solved optimally in a reasonable CPU only when very small instances are considered. This legitimates the search for heuristic techniques that achieve a satisfactory balance between computational demands and cost effectiveness. In this paper, we propose a solution method that exploits the virtues and relative simplicity of genetic algorithms to address combinatorial problems. The MLLS problem that is examined here is the most general version in which the possibility of time-varying costs is allowed. We develop a binary encoding genetic algorithm and design five specific genetic operators to ensure that exploration takes place within the set of feasible solutions. An experimental framework is set up to test the efficiency of the proposed method, which turns out to rate high both in terms of cost effectiveness and execution speed.

[1]  Bezalel Gavish,et al.  Optimal Lot-Sizing Algorithms for Complex Product Structures , 1986, Oper. Res..

[2]  Anders Segerstedt.  A capacity-constrained multi-level inventory and production control problem , 1996 .

[3]  M. H. Wagner,et al.  Dynamic Lot Size Models for Multi-Stage Assembly Systems , 1973 .

[4]  H. Albert Napier,et al.  Optimal Multi-Level Lot Sizing for Requirements Planning Systems , 1980 .

[5]  Kenneth Alan De Jong,et al.  An analysis of the behavior of a class of genetic adaptive systems. , 1975 .

[6]  David A. Collier,et al.  THE MEASUREMENT AND OPERATING BENEFITS OF COMPONENT PART COMMONALITY , 1981 .

[7]  James H. Bookbinder,et al.  Production planning for mixed assembly/arborescent systems , 1990 .

[8]  Mark A. McKnew,et al.  An Improved Heuristic for Multilevel Lot Sizing in Material Requirements Planning , 1991 .

[9]  A. Kimms.  Multi-Level Lot Sizing and Scheduling: Methods for Capacitated, Dynamic, and Deterministic Models , 1996 .

[10]  Louis E. Yelle.  Materials requirements lot sizing: a multi-level approach , 1979 .

[11]  Arthur F. Veinott,et al.  Minimum Concave-Cost Solution of Leontief Substitution Models of Multi-Facility Inventory Systems , 1969, Oper. Res..

[12]  Joseph D. Blackburn,et al.  Improved heuristics for multistage requirements planning systems , 1982 .

[13]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1992, Artificial Intelligence.

[14]  Jully Jeunet,et al.  Randomized cost-modification procedures for multilevel lot sizing heuristics , 1999 .

[15]  U. Karmarkar,et al.  Computationally Efficient Optimal Solutions to the Lot-Sizing Problem in Multistage Assembly Systems , 1984 .

[16]  תמר אליאב.  גמלאות אמהות 1995-1992 , 1996 .

[17]  אסתר טולדנו,et al.  מקבלי דמי אבטלה בשנת 1996 , 1997 .

[18]  K. Dejong,et al.  An analysis of the behavior of a class of genetic adaptive systems , 1975 .

[19]  Emre A. Veral,et al.  THE PERFORMANCE OF A SIMPLE INCREMENTAL LOT‐SIZING RULE IN A MULTILEVEL INVENTORY ENVIRONMENT , 1985 .

[20]  W. Zangwill.  A Backlogging Model and a Multi-Echelon Model of a Dynamic Economic Lot Size Production System---A Network Approach , 1969 .

[21]  W. Zangwill.  Minimum Concave Cost Flows in Certain Networks , 1968 .

[22]  אסתר טולידנו.  מקבלי דמי אבטלה בשנת 1995 , 1996 .