A vendor-buyer inventory model for defective items with errors in inspection, stochastic lead time and freight cost

Abstract

This study develops a mathematical model for an integrated vendor-buyer inventory with defective items and inspection error. We assume an imperfect production process with a known of defective probability. The buyer conducts a 100% quality check. However, due to an imperfect inspection process, the quality-controller may reject a good item as a defective item (Type I error), or accept a defective item as a non-defective item (Type II error). Different from existing research, we incorporate freight cost (a function of shipping weight and the distance between the vendor and the buyer) and stochastic lead time (a function of production and transportation times). The objective of the study is to minimize the joint total expected cost. This study indicates that Type I error is more significant when it is compared with Type II error. We also illustrate how the joint total expected cost and the lead time are significantly influenced by the distance of the buyer and the vendor. The results of our analysis also show that lead time can be shortened if the vendors speed up their shipment with smaller production lot sizes. Numerical examples and sensitivity analysis are given to illustrate the results.