Robust flow shop scheduling with random processing times for reduction of peak power consumption

Abstract

Recently, power shortages have become a major problem all over Japan, due to the Great East Japan Earthquake, which resulted in the shutdown of a nuclear power plant. As a consequence, production scheduling has become a problem for factories, due to considerations of the availability of electric power. For factories, the contract with the electric power company sets the maximum power demand for a unit period, and in order to minimize this, it is necessary to consider the peak power when scheduling production. There are conventional studies on flowshop scheduling with consideration of peak power. However, these studies did not consider fluctuations in the processing time. Because the actual processing time is not constant, there is an increase in the probability of simultaneous operations with multiple machines. If the probability of simultaneous operations is high, the probability of increasing the peak power is high. Thus, we consider inserting idle time (delay in inputting parts) into the schedule in order to reduce the likelihood of simultaneous operations. We consider a robust schedule that limits the peak power, in spite of an unexpected fluctuation in the processing time. However, when we insert idle time, the makespan gets longer, and the production efficiency decreases. Therefore, we performed simulations to investigate the optimal amount of idle time and the best point for inserting it. We propose a more robust production scheduling model that considers random processing times and the peak power consumption. The results of experiments show that the effectiveness of the schedule produced by the proposed method is superior to the initial schedule and to a schedule produced by another method. Thus, the use of random processing times can limit the peak power.