An integrated single vendor–buyer inventory model for imperfect production process with stochastic demand in controllable lead time

An integrated single vendor, single buyer inventory policy is incorporated in a continuous review model with stochastic demand. The production process is assumed to involve deterioration process and produces a certain number of defective items. In the real life production environment, it can often be observed that defective items are produced due to imperfect production processes. A situation in which the vendor invests money to improve the quality of the production process and thereby reduce the defective percentage is considered. 100% error-free screening process adopted by the buyer to separate the defective and non defective items is incorporated to focus on the varying inventory holding costs. Shortages are allowed and completely backlogged. In realistic circumstance, when an order is placed, the products will be delivered only after a certain period of time (lead time). But, owing to tough competition, the buyer may pay an extra amount in order to reduce the lead time. This realistic assumption is incorporated in this model. The model is formulated by allowing the lead time demand to be distributions free and follow a normal distribution. The prime motive is to determine the optimal policies regarding optimal order quantity, reorder point, lead time and the number of lots delivered in a production run by minimizing the expected total cost of the system considered. © 2017, The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden.