A polyhedral study of multiechelon lot sizing with intermediate demands
Author
Zhang, M.
Küçükyavuz, S.
Yaman, H.
Date
2012Source Title
Operations Research
Print ISSN
0030-364X
Electronic ISSN
1526-5463
Publisher
Institute for Operations Research and the Management Sciences (I N F O R M S)
Volume
60
Issue
4
Pages
918 - 935
Language
English
Type
ArticleItem Usage Stats
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Abstract
In this paper, we study a multiechelon uncapacitated lot-sizing problem in series (m-ULS), where the output of the intermediate echelons has its own external demand and is also an input to the next echelon. We propose a polynomial-time dynamic programming algorithm, which gives a tight, compact extended formulation for the two-echelon case (2-ULS). Next, we present a family of valid inequalities for m-ULS, show its strength, and give a polynomial-time separation algorithm. We establish a hierarchy between the alternative formulations for 2-ULS. In particular, we show that our valid inequalities can be obtained from the projection of the multicommodity formulation. Our computational results show that this extended formulation is very effective in solving our uncapacitated multi-item two-echelon test problems. In addition, for capacitated multi-item, multiechelon problems, we demonstrate the effectiveness of a branch-and-cut algorithm using the proposed inequalities.
Keywords
Branch-and-cut algorithmsComputational results
Extended formulations
Lot sizing
Lot sizing problems
Multi-commodity
Multi-item
Multiechelon
Polyhedral studies
Polynomial-time dynamic programming
Polynomial-time separation algorithms
Test problem
Valid inequality
Computer applications
Operations research
Algorithms