A tight approximation algorithm for problem P2→D|v=1,c=1|Cmax

This paper focuses on the scheduling problem on two parallel machines with delivery coordination. In particular, given a set of n jobs, we aim to find a schedule with a minimal makespan such that all jobs are first executed on two parallel machines then delivered at the destination with a transporte...

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Bibliographic Details
Published inJournal of combinatorial optimization Vol. 44; no. 4; pp. 2195 - 2206
Main Authors Wang, Yinling, Lan, Yan, Chen, Xin, Han, Xin, Piao, Yong
Format Journal Article
LanguageEnglish
Published New York Springer US 01.11.2022
Springer Nature B.V
Subjects
Algorithms
Approximation
Combinatorics
Convex and Discrete Geometry
Mathematical analysis
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Polynomials
Scheduling
Theory of Computation
Bin packing
Approximation algorithm
Scheduling with transportation
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ISSN1382-6905
1573-2886
DOI10.1007/s10878-020-00593-1

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Summary:This paper focuses on the scheduling problem on two parallel machines with delivery coordination. In particular, given a set of n jobs, we aim to find a schedule with a minimal makespan such that all jobs are first executed on two parallel machines then delivered at the destination with a transporter. This problem is known to be NP-hard Chang and Lee (Eur J Oper Res 158(2):470–487, 2004), cannot be solved with an approximation ratio strictly less than 3/2 unless P=NP. We close the gap by proposing a polynomial time algorithm whose approximation ratio is 3 / 2 + ε with ε > 0 , improve the previous best ratio 14 / 9 + ϵ .
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ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-020-00593-1