A Production/Inventory Policy for an Unreliable Machine

Abstract

In this paper, the economic lot-sizing problem for an unreliable production facility is considered. As in the standard Economic Manufacturing Quantity (EMQ) model, the demand and production rates are assumed to be constant. Unlike the EMQmodel, the facility is assumed to deteriorate while it is in operation, with an increasing failure rate. However, a preventive maintenance overhaul of the facility is assumed to restore the facility to its original condition.

A production run is initiated as soon as the inventory level drops down to zero, and it continues until the inverntory reaches a predetermined level S.It the facility fails during the production run, it is minimally repaired and put back into commission. The facility is set aside for preventive maintenance every Nproduction runs. The preventive maintenance activity takes a random amount of time; if the inventory level drops to zero during this activity, then production resumes as soon as the activity is completed. Any deman that arrives during a stock-out period is assumed to be lost.

The control policy is thus the pair (S, N). Under a cost structure that includes a preventive maintenance cost, a minimal repair cost, a setup cost, a holding cost and a penalty cost due to lost sales, an expression for the expected cos per unit time is obtained for a given policy. Following that, some properties of the cost function are developed to characterize the optimal policy. Based on these properties, an efficient search procedure to find the optimal policy is presented.