Two‐agent scheduling on a single sequential and compatible batching machine

We study two‐agent scheduling on a single sequential and compatible batching machine in which jobs in each batch are processed sequentially and compatibility means that jobs of distinct agents can be processed in a common batch. A fixed setup time is required before each batch is started. Each agent...

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Bibliographic Details
Published in:Naval research logistics Vol. 64; no. 8; pp. 628 - 641
Main Authors: Li, Shisheng, Cheng, T.C.E., Ng, C.T., Yuan, Jinjiang
Format: Journal Article
Language:English
Published: New York Wiley Subscription Services, Inc 01.12.2017
Subjects:
Approximation
Batch processing
Compatibility
Completion time
Criteria
dynamic programming
FPTAS
Lateness
Mathematical models
Optimization
Polynomials
Production scheduling
Scheduling
sequential and compatible batch
single‐machine scheduling
two agents
Upper bounds
ISSN:0894-069X, 1520-6750
Online Access:Get full text
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Summary:We study two‐agent scheduling on a single sequential and compatible batching machine in which jobs in each batch are processed sequentially and compatibility means that jobs of distinct agents can be processed in a common batch. A fixed setup time is required before each batch is started. Each agent seeks to optimize some scheduling criterion that depends on the completion times of its own jobs only. We consider several scheduling problems arising from different combinations of some regular scheduling criteria, including the maximum cost (embracing lateness and makespan as its special cases), the total completion time, and the (weighted) number of tardy jobs. Our goal is to find an optimal schedule that minimizes the objective value of one agent, subject to an upper bound on the objective value of the other agent. For each problem under consideration, we provide either a polynomial‐time or a pseudo‐polynomial‐time algorithm to solve it. We also devise a fully polynomial‐time approximation scheme when both agents’ scheduling criteria are the weighted number of tardy jobs.
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ISSN:0894-069X
1520-6750
DOI:10.1002/nav.21779