Risk cost estimation of job shop scheduling with random machine breakdowns

Abstract

Scheduling has been playing an important role in the manufacturing phase of product life cycle. In this paper, we focus on the estimation of risk cost for the job shop scheduling under random machine breakdowns, in which all jobs should be delivered together at a given due date. The risk cost measures the sum of expected earliness and tardiness costs. Considering that the risk cost in the form of expectation does not allow analytical calculation for the job shop scheduling, we will try to build a computable analytical approximation to replace the commonly used but time-consuming Monte Carlo simulation. However, the manual design of an effective analytical approximation is generally very complicated. To address it, we will develop a learning method based on the symbolic regression to extract an analytical approximation of risk cost from experimental data automatically. For this purpose, we first list all the features which may be related to the risk cost by analyzing deeply the job shop scheduling under random machine breakdowns. Then, a learning algorithm based on the genetic programming is proposed to extract an analytical approximation of risk cost. Finally, extensive experiments have shown that the accuracy of the generated analytical approximation in evaluating the risk cost is close to that of the Monte Carlo simulation, while it can significantly improve the efficiency of estimation.