Engineering Costsand Production Economics, 9 (1985) 231-231 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands 231 zyxwvut SAFETY STOCK PLANNING IN A MULTI-STAGE PRODUCTION-INVENTORY SYSTEM Phter Kelle Computer and Automation Institute, Hungarian Academy of Sciences, P.O. Box 63, H-1502 Budapest (Hungary) ABSTRACT zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA The safety stocks of internal stores are analy sed in a production line. Production may often be disturbed by random factors such as machine failures, faulty products, breakdowns, etc. In this case both the demand and delivery process of each internal store have to be described by random pro- cesses, mostly by random step functions. If there is considerable random influence in the production process, a great difficulty for the production managers is to provide for continuous production with reasonable in-process inventories. Stochastic program- ming models have been formulated for the minimization of the total capital invested in safety stocks under prescribed probability constraints subject to the continuous supply of each stage of production. Based on the asymptotic distribution of the shortage prob- ability , simple deterministic methods have been derived for the approximate solution and they have been applied in practice. 1. MODELS FOR THE CUMULATIVE AMOUNT PROCESSED Consider a production line where the subsequent phases of processing form a multi- stage production-inventory system with inter- nal stocking. The serial system of the process- ing-inventory-processing is illustrated in Fig. 1. The processing at each stage (i.e. both delivery and demand of an internal store) may often be disturbed by random factors in production such as machine failures, faulty products, breakdowns, etc. For safety stock planning, delivery and demand have to be described by random processes. The processing is usually accomplished in different lot sizes which are often not exactly known at the time of safety stock planning. The setup times may also be disturbed by random factors of production. Thus, both demand and delivery can be described mostly by random step functions. In the most simple case the lots have uni- form size for a processing stage and the setup times are planned for n equidistant time points of the planning period [O,Tl . If the setup times are disturbed they can be con- sidered as random time points of the interval [O,T] . In many cases they are disturbed ac- cording to a uniform distribution on [ O ,T] , or in other cases according to another distribu- tion characterized by the distribution func- tion F(t). The cumulative processing of the 0167-188X/85/$03.30 0 1985 Elsevier Science Publishers B.V