A job shop scheduling problem with human operators in handicraft production

Abstract

This paper deals with complex job shop scheduling problems. A (typically large) number of elementary tasks has to be carried out, according to precedence constraints defined by a task graph. As typical of production environments such as handicraft production and task processing requires two different resources, i.e. machines and human operators. While for each operation a given machine is specified, there are in general more human operators capable of performing it. The problem is to assign the tasks to the operators, sequence them on each operator and sequence them on each machine so that the overall makespan is minimised. This scheduling problem is NP-hard even if the task graph consists of three chains (three-job job shop), and there are two fully skilled operators. We propose two heuristics for this scheduling problem, based on two different ways of decomposing the problem. An extensive computational experience allows a comparison between the heuristic solutions and the one obtained solving a mixed-integer programming formulation of the problem. The experiments show that close-to-optimal solutions can be obtained in reasonable time on a PC. Our model is applied to a case study from leather manufacturing, and we also show its use as a decision support tool in skill planning.

Keywords:

• handicraft production
• heuristics
• human operators
• job shop

Acknowledgements

The authors gratefully acknowledge Essetre Fashion Group s.r.l. for its availability and openness, crucial for the development of the case study. Riccardo Certosini has provided valuable contributions in an earlier study of leather production planning.

Notes

Details on the generated instances are provided in the supplementary material.

Details on each task, including a brief description and the processing time, are provided in the supplementary material.