Mixed batch scheduling on identical machines

  • Jun-Qiang WangEmail author
  • Guo-Qiang Fan
  • Zhixin Liu


This paper studies a new mixed batch scheduling problem that arises in vacuum heat treatment. A mixed batch machine can process at most a given number of jobs simultaneously. The processing time of a batch is the weighted sum of the maximum processing time and the total processing time of jobs in the batch. The objective is to minimize the makespan. We first prove that the problem on a single machine can be solved in polynomial time, while the problem on multiple identical machines is NP-hard. Then, we develop a pseudopolynomial time exact algorithm when the number of machines is fixed. Further, we analyze the worst-case performance ratio of a full batch longest processing time algorithm and design Algorithm LPT-Greedy with improved worst-case performance.


Scheduling Batch Algorithm Complexity Worst-case performance ratio 



We thank the Associate Editor and the two anonymous reviewers for their valuable comments and constructive suggestions, which helped us significantly improve the quality of our work. The work of the first two authors was partly supported by the National Natural Science Foundation of China (Grant Nos. 51675442 and 71931007) and the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University, China (Grant No. CX201808).


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Authors and Affiliations

  1. 1.Performance Analysis Center of Production and Operations Systems (PacPos)Northwestern Polytechnical UniversityXi’anPeople’s Republic of China
  2. 2.Department of Industrial Engineering, School of Mechanical EngineeringNorthwestern Polytechnical UniversityXi’anPeople’s Republic of China
  3. 3.Department of Management Studies, College of BusinessUniversity of Michigan-DearbornDearbornUSA

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