Journal ArticleDOI
Capacitated lot sizing with setup times
TLDR
In this paper, a Lagrangian relaxation of the capacity constraints of CLSP allows it to be decomposed into a set of uncapacitated single product lot sizing problems, which are solved by dynamic programming.Abstract:
This research focuses on the effect of setup time on lot sizing. The setting is the Capacitated Lot Sizing Problem (the single-machine lot sizing problem) with nonstationary costs, demands, and setup times. A Lagrangian relaxation of the capacity constraints of CLSP allows it to be decomposed into a set of uncapacitated single product lot sizing problems. The Lagrangian dual costs are updated by subgradient optimization, and the single-item problems are solved by dynamic programming. A heuristic smoothing procedure constructs feasible solutions (production plans) which do not require overtime. The algorithm solves problems with setup time or setup cost. Problems with extremely tightly binding capacity constraints were much more difficult to solve than anticipated. Solutions without overtime could not always be found for them. The most significant results are that (1) the tightness of the capacity constraint is a good indicator of problem difficulty for problems with setup time; and (2) the algorithm solve...read more
Citations
More filters
Journal ArticleDOI
Variable neighborhood search
Nenad Mladenović,Pierre Hansen +1 more
TL;DR: This chapter presents the basic schemes of VNS and some of its extensions, and presents five families of applications in which VNS has proven to be very successful.
Journal ArticleDOI
The capacitated lot sizing problem: a review of models and algorithms
TL;DR: In this article, the authors consider single-level lot sizing problems, their variants and solution approaches, together with exact and heuristic approaches for their solution, and conclude with some suggestions for future research.
Journal ArticleDOI
Integrated production/distribution planning in supply chains: An invited review
TL;DR: Simpson and Vakharia as discussed by the authors proposed a method to identify the most important parts of the human brain in order to determine whether a person's brain is composed of neurons or not.
Journal ArticleDOI
Modeling Industrial Lot Sizing Problems: A Review
Raf Jans,Zeger Degraeve +1 more
TL;DR: In this article, the authors give an overview of recent developments in the field of modeling deterministic single-level dynamic lot sizing problems, focusing on the modeling of various industrial extensions and not on the solution approaches.
References
More filters
Journal ArticleDOI
Strong Formulations for Multi-Item Capacitated Lot Sizing
TL;DR: Multi-item capacitated lot-sizing problems are reformulated using a class of valid inequalities, which are facets for the single-item uncapacitated problem, and problems with up to 20 items and 13 periods have been solved to optimality using a commercial mixed integer code.
Journal ArticleDOI
An Efficient Algorithm for Multi-Item Scheduling
Leon S. Lasdon,R. C. Terjung +1 more
TL;DR: A number of resource-allocation problems, including that of multi-item scheduling, may be solved approximately as large linear programs, as in Manne, using the Dantzig-Wolfe decomposition principle.
Journal ArticleDOI
A heuristic solution procedure for the multi-item, single-level, limited capacity, lot-sizing problem
Paul S. Dixon,Edward A. Silver +1 more
TL;DR: In this paper, the problem of determining lot-sizes for a group of products which are produced at a single workcentre is considered, where the requirements for each product are known, period by period, out to the end of some common time horizon.
Journal ArticleDOI
Heuristic Procedures for the Single Operation, Multi-Item Loading Problem
Marc Lambrecht,H Vanderveken +1 more
TL;DR: In this article, the authors considered the planning of individual machine groups or work centers producing many different products such as components, subassemblies or assemblies and proposed an efficient heuristic which is an extension of the Eisenhut heuristic.
Journal ArticleDOI
Lagrangean Relaxation for the Multi-Item Capacitated Lot-Sizing Problem: A Heuristic Implementation
J. M. Thizy,L Van Wassenhove +1 more
TL;DR: In this paper, a primal partitioning scheme with a network flow subproblem is proposed to minimize the processing costs of a multi-item capacitated lot-sizing problem, based on a Lagrangean relaxation of the capacity constraints imposed on the resources.
Related Papers (5)
Solving multi-item capacitated lot-sizing problems using variable redefinition
Gary D. Eppen,R. Kipp Martin +1 more