An integrated vendor–buyer model with stochastic demand, lot‑size dependent lead‑time and learning in production

In this article, an imperfect vendor–buyer inventory system with stochastic demand, process quality control and learning in production is investigated. It is assumed that there are learning in production and investment for process quality improvement at the vendor’s end, and lot-size dependent lead-time at the buyer’s end. The lead-time for the first batch and those for the rest of the batches are different. Under n-shipment policy, the annual expected total cost of the system is derived. An algorithm is suggested to derive the optimal values of the number of shipments, the lot-size, the percentage of defective produced per batch and the safety stock factor so as to minimize the annual expected total cost of the system. The solution procedure is illustrated through numerical examples. The benefit of investment for reducing the defect rate is shown numerically. It is also observed that learning in production has significant effect on the annual expected total cost of the integrated system.