An optimization problem of manufacturing systems with stochastic machine breakdown and rework process

This paper is concerned with optimization of production run time that takes stochastic breakdown and the reworking of defective items into consideration. In a real‐life manufacturing process, production of imperfect quality items as well as random breakdowns of production equipment is inevitable. All defective items produced are assumed to be repairable through a rework process right after the regular production stops in each cycle. This research starts with derivations of the cost functions for production systems with breakdown (no‐resumption policy is considered) and without breakdown taking place, respectively. Then cost functions of both cases are integrated. Theorems on conditional convexity of the overall cost function and bounds for optimal production run time are proposed and proved. This study concludes that although the optimal run time cannot be expressed in a closed form, it falls within the range of bounds. Hence, it can be pinpointed by the use of the bisection method based on the intermediate value theorem. A numerical example is provided to demonstrate its practical usages. Copyright © 2007 John Wiley & Sons, Ltd.