A two-warehouse integrated inventory model with imperfect production process under stock-dependent demand and quantity discount offer

This paper presents a single-vendor single-buyer integrated inventory model with an imperfect production process of the vendor. The demand at the buyer is dependent on the on-hand stock (both at the own and rented warehouses) and the vendor offers a quantity discount to motivate the buyer to buy more quantities. The buyer's own warehouse has a limited capacity but, if needed, he can use rented warehouse of unlimited capacity. The vendor fulfils the buyer's order quantity in multiple equal-sized shipments. The objective is to determine the vendor's shipment scheme in response to the buyer's order quantity so that the average total cost of the integrated system is minimised. For a numerical example, the optimal solution of the integrated inventory model is obtained and effects of key model-parameters on the optimal solution are examined.