A Primal-Dual Approach to Analyzing ATO Systems

We study assemble-to-order (ATO) problems from the literature. ATO problems with general structure and integrality constraints are well known to be difficult to solve, and we provide new insight into these issues by establishing worst-case approximation guarantees through primal-dual analyses and li...

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Vydané v:Management science Ročník 66; číslo 11; s. 5389 - 5407
Hlavní autori: DeValve, Levi, Pekeč, Saša, Wei, Yehua
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Linthicum INFORMS 01.11.2020
Institute for Operations Research and the Management Sciences
Predmet:
Algorithms
Approximation
approximations-heuristics
assemble-to-order system
Asymptotic methods
Integer programming
Inventory control
Linear programming
Mathematical optimization
Methods
Numerical analysis
primal-dual analysis
Relaxation
Warehousing
Iran
United States
ISSN:0025-1909, 1526-5501
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Popis
Shrnutí:We study assemble-to-order (ATO) problems from the literature. ATO problems with general structure and integrality constraints are well known to be difficult to solve, and we provide new insight into these issues by establishing worst-case approximation guarantees through primal-dual analyses and linear programming (LP) rounding. First, we relax the one-period ATO problem using a natural newsvendor decomposition and use the dual solution for the relaxation to derive a lower bound on optimal cost, providing a tight approximation guarantee that grows with the maximum product size in the system. Then, we present an LP rounding algorithm that achieves both asymptotic optimality as demand grows large, and a 1.8 approximation factor for any problem instance. In addition to theoretical guarantees, we perform comprehensive numerical simulations and find that our rounding algorithm outperforms existing techniques and is close to optimal. Finally, we demonstrate that our one-period LP rounding results can be used to develop an asymptotically optimal integral policy for dynamic ATO problems with backlogging and identical component lead-times. This paper was accepted by Yinyu Ye, optimization.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0025-1909
1526-5501
DOI:10.1287/mnsc.2019.3486