Batch Scheduling on a Single Machine with Maintenance Interval

Zhang Honglin; Bin Qian; Yaohua Wu

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preprints.org > engineering > control and systems engineering > 202007.0400.v2

Working Paper Article Version 2 This version is not peer-reviewed

Batch Scheduling on a Single Machine with Maintenance Interval

Zhang Honglin

^* ,

Bin Qian

Yaohua Wu

Version 1 : Received: 16 July 2020 / Approved: 17 July 2020 / Online: 17 July 2020 (16:11:57 CEST)
Version 2 : Received: 7 August 2020 / Approved: 7 August 2020 / Online: 7 August 2020 (09:48:54 CEST)

How to cite: Honglin, Z.; Qian, B.; Wu, Y. Batch Scheduling on a Single Machine with Maintenance Interval. Preprints 2020, 2020070400 Honglin, Z.; Qian, B.; Wu, Y. Batch Scheduling on a Single Machine with Maintenance Interval. Preprints 2020, 2020070400

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MDPI and ACS Style

Honglin, Z.; Qian, B.; Wu, Y. Batch Scheduling on a Single Machine with Maintenance Interval. Preprints 2020, 2020070400

APA Style

Honglin, Z., Qian, B., & Wu, Y. (2020). Batch Scheduling on a Single Machine with Maintenance Interval. Preprints. https://doi.org/

Chicago/Turabian Style

Honglin, Z., Bin Qian and Yaohua Wu. 2020 "Batch Scheduling on a Single Machine with Maintenance Interval" Preprints. https://doi.org/

Abstract

In the manufacturing industry, orders are typically scheduled and delivered through batches, and the probability of machine failure under high-load operation is high. On this basis, we focus on a single machine batch scheduling problem with a maintenance interval (SMBSP-MI). The studied problem is expressed by three-field representation as 1|B,MI|\sum{F_j+\mu}m, and the optimization objective is to minimize total flow time and delivery costs. Firstly, 1|B,MI|\sum{F_j+\mu}m is proved to be NP-hard by Turing reduction. Secondly, shortest processing time (SPT) order is shown the optimal scheduling of SMBSP-MI, and a dynamic programming algorithm based on SPT (DPA-SPT) with the time complexity of O(n^3T_1) is proposed. A small-scale example is designed to verify the feasibility of DPA-SPT. Finally, DPA-SPT is approximated to a fully-polynomial dynamic programming approximation algorithm based on SPT (FDPAA-SPT) by intervals partitioning technique. The proposed FDPAA-SPT runs in O(\frac{n^5}{\varepsilon^2})\ time with the approximation (1+\varepsilon).

Keywords

batch scheduling; single machine scheduling; maintenance interval; dynamic programming; approximation algorithm

Subject

Engineering, Control and Systems Engineering

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Comments (1)

Comment 1

Received: 7 August 2020
Commenter: HONGLIN ZHANG
Commenter's Conflict of Interests: Author

Comment: We are very sorry for submitting the wrong draft. In the submitted version, some equations, theorems, and abbreviations are not complete. At the same time, part of the format of the manuscript edited by the system was misplaced. In order not to cause unnecessary troubles to reviewers, we have updated a new version. Apologize again for our low-level mistakes.

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