Production run time problem with machine breakdowns under AR control policy and rework

Abstract

This paper examines the production run time problem with random machine breakdowns under abort/ resume (AR) policy and reworking of defective items produced. Under AR policy, production of interrupted lot will be immediately resumed when breakdown is fixed and machine is restored. Mathematical modeling and derivation of the production- inventory cost functions for both systems with/without breakdowns are presented. These cost functions are integrated and long-run average cost per unit time is obtained. Theorems on convexity and on bounds of run time are proposed and proved. A recursive searching algorithm is developed for locating optimal run time within the bounds. Numerical example with sensitivity analysis is provided to assist in optimal operational control of such an unreliable system.