Robust planning in optimization for production system subject to random machine breakdown and failure in rework

This study is concerned with robust planning in optimization, specifically in determining the optimal run time for production system that is subject to random breakdowns under abort/resume (AR) control policy and failure in rework. In most real-life production processes, generation of defective items and breakdowns of manufacturing equipment are inevitable. In this study, random defective rate is assumed and all manufactured items are screened. The perfect quality, reworkable and scrap items are identified and separated; failure-in-rework is assumed. The system is also subject to random machine breakdown; and when it occurs, the AR policy is adopted. Under such policy, the production of the interrupted lot will be immediately resumed when the machine is restored. Mathematical modeling and derivation of the production-inventory cost functions for both systems with/without breakdowns are presented. The renewal reward theorem is used to cope with the variable cycle length when integrating cost functions. The long-run average cost per unit time is obtained. Theorems on convexity and on bounds of production run time are proposed and proved. A recursive searching algorithm is developed for locating the optimal run time that minimizes the expected production-inventory costs. A numerical example with sensitivity analysis is provided to give insight into the optimal operational control of such an unreliable system.