Machine scheduling with stochastic release and processing times

Abstract

Rapid development of technology provides the foundation for the fourth industrial revolution, namely Industry 4.0. The ability to cope with unpredictable and negative events is becoming increasingly important under Industry 4.0 settings. As scheduling plays an important role in the industry system, stochastic scheduling is therefore a rather hot and interesting research topic. Most existing works assume that the job processing times are stochastic, and rarely consider the release time uncertainty. However, in practice, job release times are usually stochastic as well, due to the various factors. This work considers a parallel machine scheduling problem, in which the processing times and release times are both uncertain. The objective is to minimize the expected total weighted earliness and tardiness in a Just-in-Time (JIT) mode. For the problem, a two-stage stochastic programming formulation is first proposed, and then a classic sample average approximation (SAA) and an improved SAA, combined with scenario reduction, are developed. A case study is conducted to illustrate the applicability of the proposed methods.