DOI: 10.3390/math12030376 ISSN: 2227-7390

An Energy-Efficient Unrelated Parallel Machine Scheduling Problem with Batch Processing and Time-of-Use Electricity Prices

Liman Feng, Guo Chen, Shengchao Zhou, Xiaojun Zhou, Mingzhou Jin
  • General Mathematics
  • Engineering (miscellaneous)
  • Computer Science (miscellaneous)

The extensive consumption of energy in manufacturing has led to a large amount of greenhouse gas emissions that have caused an enormous effect on the environment. Therefore, investigating how to reduce energy consumption in manufacturing is of great significance to cleaner production. This paper considers an energy-conscious unrelated parallel batch processing machine scheduling problem under time-of-use (TOU) electricity prices. Under TOU, electricity prices vary for different periods of a day. This problem is grouping jobs into batches, assigning the batches to machines and allocating time to the batches so as to minimize the total electricity cost. A mixed-integer linear programming model and two groups of heuristics are proposed to solve this problem. The first group of heuristics first forms batches, assigns the batches to machines and finally allocates time to the batches, while the second group of heuristics first assigns jobs to machines, batches the jobs on each machine and finally allocates time to each batch. The computational results show that the SPT-FBLPT-P1 heuristic in the second group can provide high-quality solutions for large-scaled instances in a short time, in which the jobs are assigned to the machines based on the shortest processing time rule, the jobs on each machine are batched following the full-batch longest processing time algorithm, and the time is allocated to each batch following an integer programming approach. The MDEC-FBLPT-P1 heuristic that uses the minimum difference of the power consumption algorithm to assign the jobs also performed well.

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