Coordination of a single-manufacturer multi-retailer supply chain with price and green sensitive demand under stochastic lead time

When dealing with uncertainties in the supply chain and ensuring customer satisfaction, efficient management of lead time plays a significant role. Likewise, besides managing inventory and pricing strategies adeptly in multi-retailer supply chains, it has become inevitable for firms to embrace green and sustainable business practices. In this context, this paper considers a two-level supply chain consisting of a single manufacturer and multiple retailers in which the manufacturer produces a single product and delivers it to the retailers in equal-sized batches. Each retailer faces a price and green-sensitive market demand. The lead time is assumed to be a random variable that follows a normal distribution. Shortages for retailer inventory are allowed to occur and are completely backlogged. The centralized model and a decentralized model based on the leader-follower Stackelberg gaming approach are developed. A price discount mechanism between the manufacturer and retailers is proposed. For the acceptance of this contract, the upper and lower limits of the price discount rate are established. Numerical outcomes exhibit that the price discount mechanism effectively coordinates the supply chain and enhances both environmental and economical performances. A sensitivity analysis with respect to some key parameters is performed, and certain managerial insights are emphasized.