A -approximation algorithm for scheduling on two parallel machines with job delivery coordination

Integration of production and distribution operations at the scheduling level is one of the most important issues concerned in recent years in supply chain management. We investigate the scheduling problem with job delivery coordination. Concretely, we are given a set of jobs with non-identical proc...

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Bibliographic Details
Published in:The Journal of the Operational Research Society Vol. 72; no. 9; pp. 1929 - 1942
Main Authors: Chen, Yong, Zhang, An, Tan, Zhiyi, Xue, Ying, Chen, Guangting
Format: Journal Article
Language:English
Published: Taylor & Francis 02.09.2021
Subjects:
approximation algorithms
job delivery
Scheduling
worst-case ratio
ISSN:0160-5682, 1476-9360
Online Access:Get full text
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Summary:Integration of production and distribution operations at the scheduling level is one of the most important issues concerned in recent years in supply chain management. We investigate the scheduling problem with job delivery coordination. Concretely, we are given a set of jobs with non-identical processing times and non-identical sizes to be first processed by two parallel-identical machines and then delivered to a common customer by a single vehicle, which has a limited capacity that can carry up to a fixed total size of jobs in one batch. The objective is to minimize the makespan, ie, the time when all the jobs have reached the customer and the delivery vehicle has returned to the machine. The problem does not admit a polynomial time approximation algorithm with worst-case ratio smaller than unless P = NP. By introducing some novel ideas and new methods, including algorithms solving multiple knapsack problem as subprocedures and the rediscovery of the profound nature of the bin-packing algorithm, we propose a polynomial time approximation algorithm with worst-case ratio arbitrary close to . The algorithm, acquired after long-term research containing many earlier related works, is the first algorithm for this kind of problems and its theoretical performance is nearly best.
ISSN:0160-5682
1476-9360
DOI:10.1080/01605682.2019.1655204