Lagrangean Relaxation for the Multi-Item Capacitated Lot-Sizing Problem

Abstract The multi-item capacitated lot-sizing problem consists of determining the magnitude and the timing of some operations of durable results for several items in a finite number of processing periods so as to satisfy a known demand in each period. The subgradient algorithm implemented to minimize the processing costs is based on a Lagrangean relaxation of the capacity constraints imposed on the resources. The method incorporates a primal partitioning scheme—with a network flow subproblem—to obtain good feasible solutions.

[1]  Philip Wolfe,et al.  Validation of subgradient optimization , 1974, Math. Program..

[2]  F. L. Hitchcock.  The Distribution of a Product from Several Sources to Numerous Localities , 1941 .

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

[4]  Uday S. Karmarkar,et al.  The Deterministic Dynamic Product Cycling Problem , 1985, Oper. Res..

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

[6]  Gerald L. Thompson,et al.  Benefit-Cost Analysis of Coding Techniques for the Primal Transportation Algorithm , 1973, JACM.

[7]  P. R. Kleindorfer,et al.  A Lower Bounding Structure for Lot-Size Scheduling Problems , 1975, Oper. Res..

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

[9]  J. Krarup,et al.  Plant location, Set Covering and Economic Lot Size: An 0 (mn)-Algorithm for Structured Problems , 1977 .

[10]  Bezalel Gavish,et al.  Formulations and Algorithms for the Capacitated Minimal Directed Tree Problem , 1983, JACM.

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

[12]  Abraham Charnes,et al.  Management Models and Industrial Applications of Linear Programming , 1961 .

[13]  J Jaap Wessels,et al.  Multi item lot size determination and scheduling under capacity constraints , 1976 .

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

[15]  J. F. Benders.  Partitioning procedures for solving mixed-variables programming problems , 1962 .

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

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

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

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

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

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

[22]  Fred Glover,et al.  Generalized Networks: A Fundamental Computer-Based Planning Tool , 1978 .

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