Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed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 (doi: 10.20944/preprints202007.0400.v1). Honglin, Z.; Qian, B.; Wu, Y. Batch Scheduling on a Single Machine with Maintenance Interval. Preprints 2020, 2020070400 (doi: 10.20944/preprints202007.0400.v1).

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).

Subject Areas

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

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