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Title: Two-agent single-machine scheduling to minimize the batch delivery cost
Authors: Yin, Y
Wang, Y
Cheng, TCE 
Wang, DJ
Wu, CC
Keywords: Batch delivery
Fully polynomial-time approximation scheme
Two agents
Issue Date: 2016
Publisher: Pergamon Press
Source: Computers and industrial engineering, 2016, v. 92, p. 16-30 How to cite?
Journal: Computers and industrial engineering 
Abstract: We consider integrated production and batch delivery scheduling in a make-to-order production system involving two competing agents, each of which having its own job set competes to process its jobs on a shared single machine. To save the delivery cost, the jobs of the same agent can be processed and delivered together batches. The completion time of each job in the same batch coincides with the batch completion time. A batch setup time is incurred before the processing of the first job in each batch. Each of the agents wants to minimize an objective function depending on the completion times of its own jobs. The goal is to determine a schedule for all the jobs of the two agents that minimizes the objective function of one agent, while keeping the objective function value of the other agent below or at a given value. For each of the problems under consideration, we either provide a polynomial-time algorithm to solve it or show that it is NP-hard. In addition, for each of the NP-hard problems, we present a mixed integer linear programming (MILP) formulation and provide a pseudo-polynomial dynamic programming algorithm, establishing that it is NP-hard in the ordinary sense only, and show that it admits an efficient fully polynomial-time approximation scheme, if viable. Finally, we compare the performance of the pseudo-polynomial dynamic programming algorithms against the corresponding MILP formulations with randomly generated instances.
ISSN: 0360-8352
EISSN: 1879-0550
DOI: 10.1016/j.cie.2015.12.003
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