Coordinated production, ordering, shipment and pricing model for supplier-retailer inventory system under trade credit

The objective of this article is to maximize the joint profit for supplier and retailer by constructing a combined supplier–retailer inventory model wherein supplier and retailer both have implemented trade credit policies, and some defective items are received by the retailer. The customer’s demand is expressed as a function of time, price and credit period, which is appropriate for the products for which demand increases initially and after some time it starts to decrease. Production, directly proportional to the customer’s demand rate, is considered as one of the decision variables for the purpose of reducing the holding cost of the supplier. The article estimates the optimum replenishment cycle, customer’s credit period, retail selling price by a classical optimization technique. For validation of the derived model, various numerical examples are demonstrated. Finally, implementing sensitivity analysis on the decision variables by varying the inventory parameters, effective managerial insights are generated which is beneficial for the players of supply chain by practically gaining the maximum joint profit through advising to opt for the case ,N M T i.e., when the customer’s trade credit period offered by the retailer is lesser than the retailer’s trade credit period offered by the supplier and which is lesser than the replenishment cycle length.