Abstract This paper considers a two‐echelon supply chain with single vendor single buyer for trading a single product. The buyer's demand has been assumed to be price‐sensitive. We have assumed three‐level inspection at the vendor's end in order to maintain good quality of the items delivered to the buyer. We have developed models for both decentralized and centralized scenarios and have determined the optimal solution using the basic concepts of analytic geometry and algebra. In addition, we have proposed a price discount mechanism, where the vendor has provided discounts on the purchase cost to the buyer against the buyer's (increased) order quantity. Finally, in order to illustrate and validate the proposed model, a numerical example and sensitivity analysis is carried out, which has provided some important managerial implications. It has been observed from the numerical study that the proposed price discount policy coordinates the supply chain and has improved the profitability of the supply chain and its members.
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