Coordinated order scheduling and outsourcing on dedicated parallel machines

In this paper we investigate two order scheduling problems with bundled operations on m dedicated parallel machines when outsourcing is allowed. In the first problem, the objective is to minimize the makespan of the accepted jobs (orders) subject to the constraint that the total rejection (outsourci...

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Bibliographic Details
Published in:European journal of operational research
Main Authors: Ou, Jinwen, Li, Weidong, Zhong, Xueling
Format: Journal Article
Language:English
Published: Elsevier B.V 01.09.2025
Subjects:
Approximation algorithm
Bundled operation
Dedicated machines
FPTAS
Order scheduling
Bundled operation
Dedicated machines
Approximation algorithm
FPTAS
Order scheduling
ISSN:0377-2217
Online Access:Get full text
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Summary:In this paper we investigate two order scheduling problems with bundled operations on m dedicated parallel machines when outsourcing is allowed. In the first problem, the objective is to minimize the makespan of the accepted jobs (orders) subject to the constraint that the total rejection (outsourcing) cost is no more than a budget. In the second problem, the objective is to minimize the makespan of accepted jobs plus the total rejection cost of rejected jobs. We show that the first problem cannot be approximated within a factor less than 2 in polynomial time, unless P = NP. For each of the two problems when m is fixed, we present a quasi-linear-time FPTAS (fully polynomial time approximation scheme). For the second problem when m=2, we develop a faster FPTAS by an interesting problem transformation and advanced rounding method. •Coordinated order scheduling and outsourcing on dedicated machines in parallel.•No polynomial-time (2-ϵ)-approximation algorithm for the bounded problem.•Quasi-linear-time FPTASes when the number of machines is fixed.•Faster FPTAS for the unbounded problem with two machines.•Interesting problem transformation and advanced rounding method.
ISSN:0377-2217
DOI:10.1016/j.ejor.2025.08.035