A complexity analysis and algorithms for two-machine shop scheduling problems under linear constraints

We study several two-machine shop scheduling problems, namely flow shop, job shop and open shop scheduling problems under linear constraints. In these problems, the processing times of two stages of jobs are also decision variables and satisfy a system of linear constraints. The goal of each problem...

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Vydáno v:Journal of scheduling Ročník 26; číslo 6; s. 543 - 558
Hlavní autoři: Nip, Kameng, Wang, Zhenbo
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.12.2023
Springer Nature B.V
Témata:
Algorithms
Approximation
Artificial Intelligence
Business and Management
Calculus of Variations and Optimal Control; Optimization
Completion time
Complexity
Job shop scheduling
Job shops
Machine shops
Operations Research/Decision Theory
Optimization
Polynomials
Production scheduling
Scheduling
Supply Chain Management
Open shop scheduling
Linear programming
Job shop scheduling
Computational complexity
Flow shop scheduling
ISSN:1094-6136, 1099-1425
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Shrnutí:We study several two-machine shop scheduling problems, namely flow shop, job shop and open shop scheduling problems under linear constraints. In these problems, the processing times of two stages of jobs are also decision variables and satisfy a system of linear constraints. The goal of each problem is to determine the processing time of each job, and to schedule the jobs to the shop machine such that the makespan, i.e., the completion time of all jobs, is minimized. These problems can find application in various areas, such as industrial production, advertising and automotive maintenance. We study the computational complexity and propose polynomial-time optimal or approximation algorithms for them. In particular, we show that although a two-machine flow shop scheduling problem and a two-machine job shop scheduling problem without recirculation can be solved in polynomial time, the problems where processing times satisfy linear constraints are generally NP-hard in the strong sense. Then, we design algorithms for various settings of these problems. We design polynomial-time algorithms for them when there are a fixed number of constraints. For the general case, we first propose a simple 2-approximation algorithm, and then design a polynomial-time approximation schemes. In contrast to the previous two problems, we show that the two-machine open shop scheduling problem under linear constraints can be solved in polynomial time.
Bibliografie:ObjectType-Article-1
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ISSN:1094-6136
1099-1425
DOI:10.1007/s10951-021-00677-8