Abstract
This paper studies a two-level supply chain consisting of a manufacturer and a retailer. The manufacturer's production output follows a random process due to the presence of defective goods. The retailer faces random price dependent customer demand. We propose that the manufacturer can reduce the number of defective items manufactured by performing inspection and rework. We first consider both decentralised and centralised supply chain models to determine the manufacturer's production size, the retailer's order quantity, the manufacturer's rework cost, and the retailer's sales price, as well as the retailer's and the manufacturer's expected profit. We then propose a buy-back contract to coordinate the supply chain. We also use numerical examples to illustrate our findings and perform sensitivity analysis on the price elasticity of the demand and tensile coefficient of rework cost.