NP-hardness proof for the assembly problem with stationary setup and additive holding costs

Retsef Levi; Liron Yedidsion

doi:10.1016/j.orl.2012.12.004

NP-hardness proof for the assembly problem with stationary setup and additive holding costs

Retsef Levi, Liron Yedidsion

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In this paper we answer a long-standing open question regarding the computational complexity of one of the core problems in inventory management, the assembly problem. In spite of effort on part of many researchers over the years to design efficient optimization algorithms for the problem, or alternatively prove that it is NP-hard, this fundamental question was left unanswered. In this paper, we provide a proof that the problem is indeed NP-hard, so it is not likely that there exists an efficient algorithm that solves the problem optimally.

Original language	English
Pages (from-to)	134-137
Number of pages	4
Journal	Operations Research Letters
Volume	41
Issue number	2
DOIs	https://doi.org/10.1016/j.orl.2012.12.004
State	Published - 1 Mar 2013
Externally published	Yes

Keywords

Assembly line
Computational complexity
Inventory management

ASJC Scopus subject areas

Software
Management Science and Operations Research
Industrial and Manufacturing Engineering
Applied Mathematics

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10.1016/j.orl.2012.12.004

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title = "NP-hardness proof for the assembly problem with stationary setup and additive holding costs",

abstract = "In this paper we answer a long-standing open question regarding the computational complexity of one of the core problems in inventory management, the assembly problem. In spite of effort on part of many researchers over the years to design efficient optimization algorithms for the problem, or alternatively prove that it is NP-hard, this fundamental question was left unanswered. In this paper, we provide a proof that the problem is indeed NP-hard, so it is not likely that there exists an efficient algorithm that solves the problem optimally.",

keywords = "Assembly line, Computational complexity, Inventory management",

author = "Retsef Levi and Liron Yedidsion",

note = "Funding Information: The research of the first author is partially supported by NSF grant CMMI-0846554 (CAREER Award), an Air Force Office of Scientific Research (AFOSR) awards FA9550-11-1-0150 and FA9550-08-1-0369 , and the Buschbaum Research Fund of MIT .",

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AU - Yedidsion, Liron

N1 - Funding Information: The research of the first author is partially supported by NSF grant CMMI-0846554 (CAREER Award), an Air Force Office of Scientific Research (AFOSR) awards FA9550-11-1-0150 and FA9550-08-1-0369 , and the Buschbaum Research Fund of MIT .

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N2 - In this paper we answer a long-standing open question regarding the computational complexity of one of the core problems in inventory management, the assembly problem. In spite of effort on part of many researchers over the years to design efficient optimization algorithms for the problem, or alternatively prove that it is NP-hard, this fundamental question was left unanswered. In this paper, we provide a proof that the problem is indeed NP-hard, so it is not likely that there exists an efficient algorithm that solves the problem optimally.

AB - In this paper we answer a long-standing open question regarding the computational complexity of one of the core problems in inventory management, the assembly problem. In spite of effort on part of many researchers over the years to design efficient optimization algorithms for the problem, or alternatively prove that it is NP-hard, this fundamental question was left unanswered. In this paper, we provide a proof that the problem is indeed NP-hard, so it is not likely that there exists an efficient algorithm that solves the problem optimally.

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KW - Inventory management

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JO - Operations Research Letters

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ER -

NP-hardness proof for the assembly problem with stationary setup and additive holding costs

Abstract

Keywords

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