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Parallel-batching scheduling of deteriorating jobs with non-identical sizes and rejection on a single machine

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Abstract

This paper studies the bounded parallel-batching scheduling problem considering job rejection, deteriorating jobs, setup time, and non-identical job sizes. Each job will be either rejected with a certain penalty cost, or accepted and further processed in batches on a single machine. There is a setup time before processing each batch, and the objective is to minimize the sum of the makespan and the total penalty. Several useful preliminaries for arranging accepted job with identical size are proposed. Based on these preliminaries, we first investigate a special case where all the jobs are considered to have the identical size, and develop a dynamic programming algorithm to solve it. The preliminaries help to reduce the complexity of the dynamic programming algorithm from \( O\left( {n!n^{2} \sum\nolimits_{i = 1}^{n} {w_{j} } } \right) \) to \( O\left( {n^{2} \sum\nolimits_{i = 1}^{n} {w_{j} } } \right) \). For the general problem with non-identical job sizes, we propose a hybrid algorithm combining heuristic with dynamic programming algorithm (H-DP) to obtain satisfactory solutions within reasonable time. Finally, the effectiveness and efficiency of the H-DP algorithm are illustrated by a series of computational experiments.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. 71871080, 71231004, 71601065, 71690235, 71501058, 71601060), Innovative Research Groups of the National Natural Science Foundation of China (71521001), the Humanities and Social Sciences Foundation of the Chinese Ministry of Education (No. 15YJC630097), Base of Introducing Talents of Discipline to Universities for Optimization and Decision-making in the Manufacturing Process of Complex Product (111 project), the Project of Key Research Institute of Humanities and Social Science in University of Anhui Province, Open Research Fund Program of Key Laboratory of Process Optimization and Intelligent Decision-making (Hefei University of Technology), Ministry of Education.

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Authors and Affiliations

  1. School of Management, Hefei University of Technology, Hefei, 230009, People’s Republic of China

    Min Kong, Xinbao Liu, Jun Pei & Zhiping Zhou

  2. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611, USA

    Jun Pei, Zhiping Zhou & Panos M. Pardalos

  3. Key Laboratory of Process Optimization and Intelligent Decision-Making of Ministry of Education, Hefei, 230009, People’s Republic of China

    Min Kong, Xinbao Liu & Jun Pei

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  1. Min Kong
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  2. Xinbao Liu
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  3. Jun Pei
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  5. Panos M. Pardalos
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Correspondence to Min Kong or Jun Pei.

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Kong, M., Liu, X., Pei, J. et al. Parallel-batching scheduling of deteriorating jobs with non-identical sizes and rejection on a single machine. Optim Lett 14, 857–871 (2020). https://doi.org/10.1007/s11590-019-01389-x

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