International Journal of Production Economics, 26 ( 1992) 3 19-326 Elsevier 319 Extension of a reliability-type inventory model to Just-in-Time systems Peter Kelle and Helmut Schneider Quantitative Business Analysis Department, Louisiana State University, Baton Rouge, LA, USA Abstract Reliability-type inventory models are formulated to determine the minimal safety stock that will provide a prescribed service level for satisfying demand. We give an extension of such a model as an approximation for handling the specific features of Just-in-Time (JIT) production and service systems. Introduction Just-in-Time (JIT) production systems have gained increased importance in manufacturing, pro- cessing and service industries. The inventory reduction achieved in these systems lead to cost reduc- tions, and higher efficiency. However, in certain cases, it can cause supply delays and productivity reduction. A critical issue in avoiding these negative effects is appropriate inventory control. In practice, very simple rules are used to control Work-in-Process (WIP) inventories. The manual kanban system fails to work properly in several applications where significant demand changes are frequent. Simple mathematical models applied in computerized control systems are based on assump- tions that are not valid under JIT circumstances. In this paper, we give an extension of a reliability-type inventory model, as an approximation for modeling JIT production. Component availability times and quantities are characterized, considering random effects such as breakdowns and quality problems. The final issue, as in known reliability-type inventory models, is to find the minimal safety stock or safety lead time that will provide the appropri- ate service level to maintain an effective and smooth JIT production. First, we describe the production environment, followed by a discussion on the assumptions and the model. Then, the mathematical properties are detailed. Simple, approximate solutions are presented for practical applications. These approximate solutions are compared with exact analytic solutions and simulation results. Production environment We consider multi-stage JIT production systems. A WIP inventory is built between the subsequent stages of the production process. It should be noted that a very low level of WIP inventory is desired. This is possible because of the production and delivery coordination through kanban or MRP-type control. In practice, the level of safety stocks is determined by simple heuristic safety factors used to fix the number of kanban cards, or applied to safety stock calculations in MRP. Production is in very small batches. The release times and sizes of the batches are coordinated throughout the production stages including raw material delivery and customer demand. Ideally, al- most zero WIP inventories are sufficient. But, in practice, large demand fluctuations, capacity con- straints, breakdowns, and quality problems necessitate some WIP safety stocks, in order to maintain 09255273/92/$05.00 0 1992 Elsevier Science Publishers B.V. All rights reserved.