* Corresponding author. Tel.: #81-824-24-7697; fax: #81- 824-22-7025. E-mail address: dohi@gal.sys.hiroshima-u.ac.jp (T. Dohi). Int. J. Production Economics 74 (2001) 147}155 Optimal control of preventive maintenance schedule and safety stocks in an unreliable manufacturing environment Tadashi Dohi*, Hiroyuki Okamura, Shunji Osaki Department of Industrial and Systems Engineering, Hiroshima University, 4-1 Kagamiyama 1 Chome, Higashi-Hiroshima 739-8527, Japan Abstract This paper revisits the economic manufacturing quantity (EMQ) model by Cheung and Hausman (Nav. Res. Logist. 44 (1997) 257) from the theoretical point of view, and develops a new stochastic model under somewhat di!erent restrictive assumptions. The optimal policies, the order quantity and safety stock, are derived, respectively, so as to minimize the expected cost per unit time in the steady-state.  2001 Elsevier Science B.V. All rights reserved. Keywords: Economic manufacturing; Machine breakdown; Preventive maintenance; Safety stocks; Stochastic model 1. Introduction When dealing with stocked items, the question regarding how much to order is answered by the economic order quantity (EOQ). Similarly, the economic manufacturing quantity (EMQ) model, which is a natural extension of EOQ, provides the proper production lot size by minimizing the cost components involved, that is, the production cost, the inventory holding cost and the shortage cost if the stockout is permitted. When a machine break- down takes place in the production phase, however, the basic EMQ model loses its usefulness since the interruption by corrective maintenance operations is aborted. From a practical perspective, the manu- facturer should design the production lot from the standpoint of safety, and thus e!ects of machine breakdown and corrective maintenance in eco- nomic production lot sizing decisions should be examined exactly in uncertain environment with- out reliable manufacturing facilities. In this article, we consider an extended EMQ model with stochas- tic machine breakdown and repair. To motivate such a modeling, consider the just-in-time (JIT) philosophy. The JIT production whose lot size is required to be small or is ideally equivalent to one, has not been able to be achieved in many manufac- turing industries all over the world, since fairly high set-up and machine maintenance costs are needed in practice. In particular, one of the major impedi- ments for the successful operation of such a tightly coupled organization may be formed by break- downs in bottleneck resources. Numerous research e!orts have been undertaken to extend the manufacturing model subject to stochastic machine breakdowns. Lee and Rosen- blatt [1,2] focused on the imperfections in the pro- duction process and equipment, and determined the optimal EMQ policy and/or inspection sched- ule. Furthermore, Rosenblatt and Lee [3] analyzed a deteriorating system during the production 0925-5273/01/$-see front matter  2001 Elsevier Science B.V. All rights reserved. PII:S0925-5273(01)00121-9