A Lagrangean-based heuristic for dynamic multilevel multiitem constrained lotsizing with setup times

In this paper a heuristic approach for the dynamic multilevel multiitem lotsizing problem in general product structures with multiple constrained resources and setup times is proposed. With the help of Lagrangean relaxation the capacitated multilevel multiitem lotsizing problem is decomposed into several uncapacitated single-item lotsizing problems. From the solutions of these single-item problems lower bounds on the minimum objective function value are derived. Upper bounds are generated by means of a heuristic finite scheduling procedure. The quality of the approach is tested with reference to various problem groups of differing sizes.

[1]  N. Z. Shor.  The rate of convergence of the generalized gradient descent method , 1968 .

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

[3]  J. Shapiro.  A Survey of Lagrangian Techniques for Discrete Optimization. , 1979 .

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

[5]  Peter J. Billington,et al.  Multi-level lot-sizing with a bottleneck work center , 1983 .

[6]  L Van Wassenhove,et al.  Lagrangean Relaxation for the Multi-Item Capacitated Lot-Sizing Problem , 1985 .

[7]  Luk N. Van Wassenhove,et al.  A simple heuristic for the multi item single level capacitated lotsizing problem , 1986 .

[8]  L. J. Thomas,et al.  Heuristics for multilevel lot-sizing with a bottleneck , 1986 .

[9]  Claus E. Heinrich,et al.  Multi-Stage Lot-Sizing for General Production Systems , 1986 .

[10]  Jatinder N. D. Gupta,et al.  Determining lot sizes and resource requirements: A review , 1987 .

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

[12]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988 .

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

[14]  Wun-Hwa Chen,et al.  Analysis of relaxations for the multi-item capacitated lot-sizing problem , 1991 .

[15]  B. Fleischmann.  The discrete lot-sizing and scheduling problem , 1990 .

[16]  L. V. Wassenhove,et al.  Multilevel capacitated lotsizing complexity and LP-based heuristics , 1991 .

[17]  Luk N. Van Wassenhove,et al.  Capacitated dynamic lotsizing heuristics for serial systems , 1991 .

[18]  Sebastián Lozano,et al.  Primal-dual approach to the single level capacitated lot-sizing problem , 1991 .

[19]  Jean-Michel Thizy,et al.  Analysis Of Lagrangian Decomposition For The Multi-Item Capacitated Lot-Sizing Problem , 1991 .

[20]  Laurence A. Wolsey,et al.  Multi-item lot-sizing problems using strong cutting planes , 1991 .

[21]  E. J. Anderson,et al.  Deterministic Lotsizing Models for Production Planning , 1991 .

[22]  A. Federgruen,et al.  A Simple Forward Algorithm to Solve General Dynamic Lot Sizing Models with n Periods in 0n log n or 0n Time , 1991 .

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

[24]  Mahesh Gupta,et al.  Comparative analysis of lot-sizing models for multi-stage systems: a simulation study , 1992 .

[25]  Albert P. M. Wagelmans,et al.  Economic Lot Sizing: An O(n log n) Algorithm That Runs in Linear Time in the Wagner-Whitin Case , 1992, Oper. Res..

[26]  Horst Tempelmeier,et al.  A heuristic for dynamic multi-item multi-level capacitated lotsizing for general product structures , 1994 .

[27]  Marc Salomon,et al.  Batching decisions: structure and models , 1994 .

[28]  Stefan Helber,et al.  Lot sizing in capacitated production planning and control systems , 1995 .