An improved heuristic for the Capacitated Lot-Sizing problem

In this research, we present a heuristic for the Capacitated Lot-Sizing (CLS) problem without set-up time considerations and no backordering option. The CLS problem is formulated as a mixed integer-programming problem with an underlying fixed charge transportation problem structure. This formulation is flexible enough to handle different types of production capacity such as regular time capacity, overtime capacity and subcontracting. A heuristic that exploits the fixed charge transportation structure and trade-offs involved in lot-sizing decisions is developed for the problem. We also present a new Lower Bound Procedure for the multi-item CLS problems. We demonstrate the performance of the heuristic over a variety of test problems. The heuristic is evaluated by comparing the solution values to the lower bound values as well as to the solution values from another algorithm for similar problems.

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

[2]  Harish C. Bahl,et al.  A Lagrangean Relaxation Approach for Very-Large-Scale Capacitated Lot-Sizing , 1992 .

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

[4]  Yash P. Gupta,et al.  Solving the capacitated lot-sizing problem with backorder consideration , 2001, J. Oper. Res. Soc..

[5]  Zeger Degraeve,et al.  Modeling industrial lot sizing problems: a review , 2008 .

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

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

[8]  H. Romeijn,et al.  A Lagrangean heuristic for integrated production and transportation planning problems in a dynamic, multi-item, two-layer supply chain , 2007 .

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

[10]  Hartmut Stadtler,et al.  The Capacitated Lot-Sizing Problem with Linked Lot Sizes , 2003, Manag. Sci..

[11]  Albert P. M. Wagelmans,et al.  Integrated Lot Sizing in Serial Supply Chains with Production Capacities , 2005, Manag. Sci..

[12]  Stéphane Dauzère-Pérès,et al.  Capacitated Multi-Item Lot-Sizing Problems with Time Windows , 2006, Oper. Res..

[13]  Murali Sambasivan,et al.  A heuristic procedure for solving multi-plant, multi-item, multi-period capacitated lot-sizing problems , 2002 .

[14]  W. Walker.  A Heuristic Adjacent Extreme Point Algorithm for the Fixed Charge Problem , 1976 .

[15]  Moustapha Diaby.  Multi-item scheduling by lagrangean relaxation : capacitated lot-sizing , 1987 .

[16]  P. S. Eisenhut.  A Dynamic Lot Sizing Algorithm with Capacity Constraints , 1975 .

[17]  William W. Trigeiro,et al.  A Dual-Cost Heuristic For The Capacitated Lot Sizing Problem , 1987 .

[18]  Kenneth C. Gilbert,et al.  A Heuristic for a Class of Production Planning and Scheduling Problems , 1991 .

[19]  Wilbert E. Wilhelm,et al.  Scheduling and lot sizing with sequence-dependent setup: A literature review , 2006 .

[20]  Harvey H. Millar,et al.  An application of Lagrangean decomposition to the capacitated multi-item lot sizing proble , 1993, Comput. Oper. Res..

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

[22]  S. Graves.  Using Lagrangean Techniques to Solve Hierarchical Production Planning Problems , 1982 .