Trade credit financing in the vendor–buyer inventory system with ordering cost reduction, transportation cost and backorder price discount when the received quantity is uncertain

• We proposed an integrated inventory model with variable ordering cost, backorder price and transportation cost discount.
• We include the cases where the received quantity is uncertain and the vendor offers a certain credit period to the buyer.
• The transportation cost as a function of the shipment lot-size and it is taken to be in an allunit-discount cost format.
• We incorporate transportation cost explicitly into the model and develop solution procedures for solving the proposed problem.
• Numerical and sensitivity analyses are given to demonstrate the applications and performance of the proposed methodology.

Previous ordering cost reduction vendor–buyer inventory models with backorder price discount usually assumed that the buyer must pay to the vendor for the ordered items as soon as the items are received, the received quantity is same as the ordered quantity and the transportation cost is independent of the shipment lot-size. In practice, however, the vendor is willing to offer the buyer a certain credit period without interest to promote market competition as well as the buyer's quantity received may not match with the ordered quantity due to unavailability of the raw material, worker's strike, human errors in counting, transcribing, etc. Furthermore, the discounts are offered for the transportation cost of large ordered quantities. This paper derives a single-vendor single-buyer supply chain model for the ordering cost reduction inventory system with backorder price discount, taking into consideration the effect of transportation cost discount and the condition of permissible delay in payments include the case where the buyer's received quantity does not necessarily match the quantity requisitioned. We take the transportation cost as a function of the shipment lot-size and it is taken to be in an all-unit-discount cost format. Thus we incorporate transportation cost explicitly into the model and develop optimal solution procedures for solving the proposed inventory problem. Numerical example and sensitivity analyses are given to demonstrate the applications and performance of the proposed methodology.