Impact of uncertain demand and lead-time reduction on two-echelon supply chain

This paper develops a continuous-review vendor-buyer supply chain (SC) model wherein the lead-time (taken as replenished) is considered as a factor affected upon by the time stamp required for setup and production followed by transportation. Here, the production time indicates the interaction between the lot-size and lead-time. Assuming the existence of an opportunity with the buyer of reducing the replenishment lead-time. The buyer receives normally distributed stochastic lead-time demands from its customers. Due to the stochastic nature of lead-time demand, shortages may arise at the buyer’s side which is fully backlogged. We presume imperfection production at the vendor’s end, which leads to the generation of a certain ratio/percentage of defective products, which results in additional warranty costs for the vendor. This study intends to uncover the best policy that minimizes the system’s total expected cost. A solution algorithm with some lemmas is provided which helped in finding the optimal solution and to prove the uniqueness of the solutions. Findings demonstrate that a reduction in lead-time can effectively lower safety stock as well as the total cost.