Intl. Trans. in Op. Res. 00 (2019) 1–25 DOI: 10.1111/itor.12678 INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH Channel coordination with price discount mechanism under price-sensitive market demand Sumon Sarkar a , Sunil Tiwari b , Hui-Ming Wee c and B.C. Giri a a Department of Mathematics, Jadavpur University, Kolkata 700032, West Bengal, India b The Logistics Institute – Asia Pacific, National University of Singapore, 21 Heng Mui Keng Terrace, Singapore 119613, Singapore c Department of Industrial and Systems Engineering, Chung Yuan Christian University, 200 Chung-Pei Rd., 32023, Chung-li, Taiwan E-mail: ss.sumonsarkar@gmail.com [Sarkar]; sunil.tiwari04@gmail.com [Tiwari]; weehm@cycu.edu.tw [Wee]; bibhas_pnu@yahoo.com [Giri] Received 8 May 2018; received in revised form 23 February 2019; accepted 26 April 2019 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. Keywords: supply chain; coordination; price discount; price-sensitive demand; variable back-order 1. Introduction A supply chain (SC) is a combination of collection of raw materials, converting it into the final product by manufacturers, movements of the product through distributors, sold by retailers to end- customers. It can be categorized into centralized and decentralized. In a centralized supply chain, all the decisions on behalf of the supply chain members are taken by one decision maker, whereas in a decentralized supply chain, the objective of every member is to optimize its profit without considering the entire supply chain’s profit. However, it seems hypothetical that only a single decision C  2019 The Authors. International Transactions in Operational Research C  2019 International Federation of Operational Research Societies Published by John Wiley & Sons Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main St, Malden, MA02148, USA.