Joint Optimization of Jobs Sequence and Inspection Policy for a Single System With Two-Stage Failure Process

We will discuss the joint optimization of the jobs sequence as well as inspection policy for a single system expected to process n jobs with different processing times. The system has a two-stage failures process, i.e., first a defect arises in the system, and if the defect is not detected, the system eventually fails. The interrupted job due to failure should be restarted after corrective replacement of the system. The possibility of inspecting the system before starting a job is considered to detect a potential defect. We develop two models to find the optimal policy based on either total expected makespan, or total expected cost. In the cost optimization model, we assume a common due date for all jobs and incur a penalty cost per unit time that the makespan exceeds the due date. We develop a recursive formula to obtain the expected makespan, and the number of failures and preventive replacements and present the application of our proposed models to a system, which is supposed to process four jobs. We compare the results of the direct calculation (recursive formula) with a Monte Carlo simulation model, and discuss how changing the models' parameters can impact the optimal policy.