A multi-constraint integrated vendor-buyer problem with beta distributed defective items under stochastic demand

This study develops a multi-constraint stochastic integrated system involving a buyer and a vendor with a service level constraint, defective items, the limited buyer's storage space, and the maximum permissible set-up cost for the vendor. The reorder point, set-up cost, lead time, shipment quantity, and the number of deliveries are decision variables. The vendor sells the items to the buyer in a certain number of lots. There are some imperfect quality (defective) items in the arrival lot, and the defective rate is viewed as a beta random variable. The demand has a normal distribution. The shortage is permitted and it is partially backlogged. The Karush-Kuhn-Tucker approach is implemented to solve the discussed model that minimise the joint cost. Sensitivity analyses are performed to provide managerial implications. Using a profit-sharing structure, although both the vendor and the buyer have some business constraints, we observe that they can benefit from the coordinated supply chain.