Adjustable Robust Optimization for multi-tasking scheduling with reprocessing due to imperfect tasks

Abstract

This work contemplates the optimal scheduling of multi-tasking production environments where the processing tasks are subject to uncertain success rates. Such problems arise in many industrial applications that have the potential to yield non compliant products, which must then be reprocessed. We address this problem by mapping the multi-tasking sequential recipe into a State-Task Network representation that includes suitably defined recycle streams to accommodate the option for reprocessing. This allows us to utilize a variant of an established global-event continuous time scheduling formulation to model the overall problem, as well as to employ an Adjustable Robust Optimization framework to account for the uncertainty in the production yields associated with each processing task. We assess the computational performance of the proposed approach via a comprehensive study that involves a large database of multi-tasking scheduling benchmark problems, and we demonstrate that instances involving more than 100 uncertain parameters can be addressed within reasonable computational times. Our results also help elucidate the expected amount of cost premium to insure against various levels of uncertainty in the production success rates.