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Parallel machine scheduling with linearly increasing energy consumption cost

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Abstract

This paper deals with a parallel machine scheduling problem with linearly increasing energy consumption cost. Maintenance activities are considered in the problem. After maintenance, the machine energy consumption cost returns to the normal level. Thus, an important decision is how to determine a reasonable number of maintenance activities to enable a significant tradeoff between the maintenance cost and the energy consumption cost. We define the jobs processed between two adjacent maintenance activities as a batch since the job processing cannot be interrupted. A further decision is how to batch the jobs. To solve the investigated problem, we first study a special case where there is only one single machine. A heuristic approach is proposed to solve the single machine scheduling problem. Then, we present a variable neighborhood search (VNS) algorithm for general cases, where the heuristic approach for the single machine case is intergrated. Extensive computational experiments are conducted and the results show that the proposed VNS algorithm is superior to artificial bee colony (ABC) algorithm, genetic algorithm (GA), ant colony optimization (ACO) algorithm, Tabu search (TS)algorithm, and greedy randomized adaptive search procedure (GRASP) algorithm.

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Acknowledgements

This work is supported by the National Key Research and Development Program of China (2019YFB1705300), the National Natural Science Foundation of China (Nos. 72101071, 72071056, 71690235, 71601060), the Fundamental Research Funds for the Central Universities (Nos. JZ2020HGTB0035, JZ2021HGTA0134, JZ2021HGQA0200), the Anhui Province Natural Science Foundation (No. 1908085MG223), Natural Science Foundation of Anhui Province (2108085QG287), Key Research and Development Project of Anhui Province (2022a05020023), and the Base of Introducing Talents of Discipline to Universities for Optimization and Decision-making in the Manufacturing Process of Complex Product (111 projects).

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Authors and Affiliations

  1. School of Management, Hefei University of Technology, Hefei, Anhui, People’s Republic of China

    Chaoming Hu, Shaojun Lu & Xinbao Liu

  2. Key Laboratory of Process Optimization and Intelligent Decision-Making of the Ministry of Education, Hefei, Anhui, People’s Republic of China

    Chaoming Hu, Shaojun Lu & Xinbao Liu

  3. School of Economics and Management, Anhui Normal University, Wuhu, People’s Republic of China

    Min Kong

  4. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

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  1. Chaoming Hu
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  2. Shaojun Lu
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  3. Min Kong
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  4. Xinbao Liu
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Correspondence to Shaojun Lu, Min Kong or Xinbao Liu.

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Hu, C., Lu, S., Kong, M. et al. Parallel machine scheduling with linearly increasing energy consumption cost. Ann Math Artif Intell 91, 239–258 (2023). https://doi.org/10.1007/s10472-022-09810-5

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