The optimal number of distributor’s advertisements and distributor’s optimal cycle time by considering defective products, human errors during the inspection, two-level credit payment policy, and advertisement-dependent demand

This article has developed a three-level (single supplier-single distributor-single customer) inventory model with defective products in which the supplier delivers the distributor’s ordering quantity and the distributor inspects the finished products. In this inventory model in which order includes some imperfect products, it is assume that (a) Inspectors make mistakes during the inspection process. (b) Two-level credit payment is considered to the customers, in which customers are first divided into new and old categories. Accordingly, trade credit is assigned fully to old customers and partially to new customers. (c) New customers are also divided into well-accounted and bad accounted customers in which bad accounted customers are those who refuse to pay the price of purchased finished products after ending the credit payment period. (d) Demand is dependent on number of advertisements. In this research, five sub-case problems have been investigated based on the trade credit relation of supplier and distributor and for each case, the optimal number of promotional efforts and optimal length of the order cycle have been determined. In addition, the proposed model has numerically compared with the basic model and then solved with actual case study data. The results of sensitivity analysis of this real data set showed that the effect of the percentage of imperfect products and type one inspection error have a significant impact on the total profit function. Eventually, based on these results, managerial insights and some implications for future contributions are outlined.