The effect of human errors on an integrated stochastic supply chain model with setup cost reduction and backorder price discount

This study develops an integrated vendor–buyer inventory model for a supply chain where quality issues and human error affect its coordination. Each lot shipped to the buyer contains defective items, with a rate which randomly changes from a lot to the other. The buyer inspects every shipped lot to segregate defective items. However, the inspection process at the buyer's end goes wrong in the classification of defective and non-defective items. On the other hand, the buyer may run out of inventory, but in order to avoid lost sales, he/she offers a price discount on the backlogged items to his/her customers. Due to the vendor-buyer relationship, the buyer invests in reducing the setup cost of the vendor. Supply chain's lead-time is considered variable, and two models are developed based on the probability distribution of the lead-time demand. In the first model, it is assumed that lead-time demand follows a normal distribution, while in the latter one, it does not follow any certain distribution. Two models are developed to determine the joint optimal decision variables that minimize the total cost of the supply chain. Two iterative algorithms are developed to obtain the optimal solution for both models. A set of numerical analysis and sensitivity analysis are conducted to gain insights.