Optimal vendor investment for reducing defect rate in a vendor-buyer integrated system with imperfect production process

This paper investigates a single-vendor single-buyer integrated production-inventory model with stochastic demand and imperfect production process. It is assumed that there is an inspection activity on the part of the buyer with a fixed screening rate greater than the demand rate. The vendor invests money in order to improve the production process quality and reduce the number of defectives. The expected annual integrated total cost is derived under the n-shipment policy and an iterative procedure is suggested to determine the optimal decisions. The benefit of investment in reducing the defect rate is illustrated by way of numerical examples. It is observed that, the higher the defect rate, the more beneficial the investment. Numerical studies further explore that an increased demand requires an increased investment to optimize the total cost.