Integrated vendor-buyer model with defective items, inspection error and stochastic demand

Abstract

This paper proposes a vendor-buyer integrated production-inventory model with defective items, inspection error and stochastic demand. The lot transferred from vendor to buyer contains some defective items. The buyer conducts an inspection process to classify the quality of the items. The inspection process is imperfect. The inspector may incorrectly classify non-defective item as defective or incorrectly classify a defective item as non-defective. The lead time is assumed to be variable and consists of the sum of production time and non-productive time. In addition, transportation cost incurred by the buyer is modelled by using a tapering rate function. An iterative procedure is used to determine simultaneously shipment lot, safety factor and number of deliveries for each production run. The impact of key parameters on the proposed model is illustrated in numerical examples. The result shows that the probability of inspection error affects vendor cost, buyer cost and total cost. The probability of type I inspection error has a greater impact on total cost than that of probability of type II inspection error. In addition, the increases in both defective rate and the probability of type I inspection error lead to the increases in shipment lot and reorder point.