Lot-sizing with production and delivery time windows

We study two different lot-sizing problems with time windows that have been proposed recently. For the case of production time windows, in which each client specific order must be produced within a given time interval, we derive tight extended formulations for both the constant capacity and uncapaci...

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Bibliographic Details
Published in:Mathematical programming Vol. 107; no. 3; pp. 471 - 489
Main Author: Wolsey, Laurence A.
Format: Journal Article
Language:English
Published: Heidelberg Springer 01.07.2006
Springer Nature B.V
Subjects:
Algorithms
Applied sciences
Costs
Digital Object Identifier
Dynamic programming
Equivalence
Exact sciences and technology
Integer programming
Linear programming
Lot sizing
Mathematical models
Mathematical programming
Operational research and scientific management
Operational research. Management science
Optimization algorithms
Polynomials
Scheduling, sequencing
Studies
Upper bounds
Windows (intervals)
Convex hull
Lot-sizing
Time window
Production time windows
Mixed integer programming
Time interval
Lot sizing
Dynamic programming
Delivery lead time
Mathematical programming
ISSN:0025-5610, 1436-4646
Online Access:Get full text
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Summary:We study two different lot-sizing problems with time windows that have been proposed recently. For the case of production time windows, in which each client specific order must be produced within a given time interval, we derive tight extended formulations for both the constant capacity and uncapacitated problems with Wagner-Whitin (non-speculative) costs. For the variant with nonspecific orders, known to be equivalent to the problem in which the time windows can be ordered by time, we also show equivalence to the basic lot-sizing problem with upper bounds on the stocks. Here we derive polynomial time dynamic programming algorithms and tight extended formulations for the uncapacitated and constant capacity problems with general costs. For the problem with delivery time windows, we use a similar approach to derive tight extended formulations for both the constant capacity and uncapacitated problems with Wagner-Whitin (non-speculative) costs. [PUBLICATION ABSTRACT]
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-005-0675-3