Working Paper Article Version 2 This version is not peer-reviewed

Batch Scheduling on a Single Machine with Maintenance Interval

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


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).

Subject Areas

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

Comments (1)

Comment 1
Received: 7 August 2020
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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