A Stochastic Programming Model for Production Scheduling Problems Considering Workstyles of Operators

In the field of production scheduling, there have been many reports of scheduling techniques based on evaluation indices from the manager's viewpoints, such as improving production efficiency and meeting deadlines. On the other hand, as companies are increasing their efforts to reform the way they work every year, attention is also being paid to scheduling that takes into account the perspective of the workers, such as minimizing excessive overtime. Uncertainty in the processing time of workers is thought to be one the cause of this overtime. In this paper, we propose an optimization technique for a scheduling problem in the machining processes where overtime is allowed and there is uncertainty about the processing time by human operators. In the proposed model, we regard a human operator as a processing machine as well as a machine tool, and show that overtime can be formulated as a stochastic programming model by considering it as a recourse in two-stage stochastic programming. Furthermore, by considering the probability distribution of the processing time that appears in this stochastic programming model as a discrete distribution, it is formulated as a mixed integer programming model, which enables optimization by mathematical programming. A hybrid solution method combining the simulated annealing and the mathematical programming is used from the viewpoint of reducing the amount of computation. The effectiveness of the proposed model is demonstrated through several numerical experiments on actual cases in textile processing.