A new approach to deal with learning in inspection in an integrated vendor-buyer model with imperfect production process

This article considers learning in inspection in an integrated vendor-buyer model in which the vendor delivers the buyer's order quantity in a number of equal-sized shipments. The vendor's production process is imperfect and it produces a fraction of defective items. The buyer performs screening upon delivery of each batch but the screening process is erroneous and suffers from misclassification errors (Type I and Type II). As the buyer learns from the experience of screening, the probabilities of misclassification errors decrease with the increase in the cumulative number of batches inspected. The objective of this study is to incorporate the effect of learning in inspection when items are inspected in a batch-wise manner. The expected total cost per unit time of the integrated system is derived and a solution procedure is suggested to determine the optimal number of shipments and shipment size of the vendor. A numerical example is taken to illustrate the impact of learning through batch wise inspection in terms of cost reduction and provide some managerial insights.