Computational aspects of an extended EMQ model with variable production rate

Abstract

The paper considers a generalized economic manufacturing quantity (EMQ) model with stochastic machine breakdown and repair in which the time to machine failure, corrective and preventive repair times are all assumed to be random variables. The model is formulated under general failure and general repair time distributions, treating the machine production rate (speed) as a decision variable. As the stress condition of the machine changes with the production rate, the failure rate is assumed to be dependent on the production rate. The model is further extended to the case where certain safety stocks are hold in inventory to protect against possible stockout during machine repair. The solution procedure and computational algorithms of the associated constrained optimization problems are provided. Numerical examples are taken to determine the optimal production policies by the proposed algorithms and examine the sensitivity of the model parameters. Several economic manufacturing quantity (EMQ) models for unreliable manufacturing systems have been developed in the literature even for general failure and general repair (corrective) time distributions. In these studies, preventive repair has not been considered in a general way and efforts have been made to derive the production control and maintenance policy for inflexible manufacturing systems, where the machine capacity is pre-determined. The purpose of this article is to formulate a generalized EMQ model for a flexible unreliable manufacturing system in which (i) the time to machine failure and repair (corrective and preventive) times follow general probability distributions and (ii) the machine failure rate is dependent on the production rate. Consideration of a variable production rate makes the model hard to analyze completely. So, attempt has also been made to get into its computational aspects by developing solution algorithms.