Optimisation of flow-shop scheduling with batch processor and limited buffer

Abstract

This paper deals with a flow-shop scheduling problem with limited intermediate buffer. Jobs are grouped in incompatible job families. Each job has to be processed by a batch processor followed by a discrete processor in the same order. The batch processor can process several jobs simultaneously so that all jobs of the same batch start and complete together. We assume that the capacity of batch processor is bounded. The batch processing time is identical for batches of the same family. A batch which has completed processing on the batch processor may block the processor until there is a free unit in the buffer. The objective is to determine a batching and scheduling for all jobs so as to minimise mean completion time. A lower bound and two heuristics algorithm are developed. Moreover, a two-stage method embedded with a Differential Evolution (DE) algorithm is also developed. DE is one of the latest evolutionary computation algorithms, which implements mutation, crossover, and selection operators to improve the candidate solutions iteratively. Three variants of DE are first compared with a continuous Genetic Algorithm employing the random key representation. Then, one variant of the DE with the best convergence speed is selected. Numerical experiments are conducted to evaluate the performances of the selected two-stage meta-heuristic and two heuristics.

Keywords:

• flow-shop scheduling
• batch processor
• limited buffer
• differential evolution

Acknowledgements

The authors appreciate the constructive suggestions made by the referees. This work is supported by Nanyang Technological University Singapore–MIT Alliance and National Natural Science Foundation of China (No. 70972019).