Costing-based coordination between mt-iPSS customer and providers for job shop production using game theory

The industrial product-service system for Computer Numerical Control machine tool (mt-iPSS) has drawn much interest. Under the new paradigm of functional result-oriented mt-iPSS, mt-iPSS customer (i.e. owner of the workshop) pays for time or results of mt-iPSS providers. The present problem for mt-iPSS customer is how to timely identify the optimal machine tools, sequence and cutting parameters of operation to finish the jobs while mt-iPSS providers try to maximise their benefit in a non-cooperative game structure. In this paper, a Stackelberg game model is put forward to solve the coordination problem based on the costing of different job shop scheduling solutions under the result-oriented mt-iPSS paradigm. Then, to solve the established bi-level programming model of the Stackelberg game, a solution procedure based on hierarchical particle swarm optimisation is proposed. Finally, a case from a printing machinery enterprise is analysed to validate the proposed model. This research is expected to improve the quality and effectiveness of coordination for scheduling and process planning decision between mt-iPSS customer and multi-providers.