Profit-driven stochastic scheduling considering discounted cash flows under Industry 4.0

Abstract Industry 4.0 introduces new paradigm change in manufacturing systems, i.e., a collective term of value chain organization, to cope with unforeseen and negative events more efficiently. Since scheduling is crucial in the manufacturing systems, stochastic scheduling is thus a hot and challenging research topic. Job processing times are usually assumed to be stochastic due to various factors. This work studies a parallel machine scheduling problem with uncertain processing times, in which the penalty cost incurred by job rejection arises at the beginning and the revenue of processing a job is received once the job is completed. Besides, based on the cooperation between production, marketing and finance, the capital time value is considered by discounting the cash flows. The pursued financial objective is to maximize the the net present value (NPV) of the total profit, including the negative penalty cost for rejecting jobs and the expected revenue for processing jobs. For the problem, a two-stage stochastic programming formulation with an exponential objective function is proposed. The second-order Taylor series expansion approximation for the objective function is first applied, and the classic sample average approximation (SAA) method is then developed. A case study is conducted to illustrate the applicability of the proposed method.