<p>The emergence of Buy-Now-Pay-Later (BNPL) services has significantly boosted consumers’ willingness to make purchases in recent years. This paper explores the impact of BNPL installment payments on retailer replenishment decisions in a multi-retailer inventory replenishment model, and studies the problem of cost allocation among retailers from a cooperative game perspective. We first explore the optimal ordering policy to minimize the total cost in both independent and joint replenishment scenarios. We find that joint replenishment can reduce the total cost for retailers and shorten their optimal ordering cycle compared to individual ordering. Then, to allocate the cooperative costs among retailers participating in the joint replenishment, we introduce a joint replenishment game with BNPL installment payments and show that this game is concave. Based on this, we propose an easy-to-compute proportional allocation rule which is stable (in the sense of core) and consistent (can be reached through population monotonic allocation scheme). Finally, we use a numerical example to compare our proposed allocation rule with the classical Shapley value. The results indicate that the proposed rule is more favorable to retailers with smaller annual demands for the product, whereas the Shapley value favors retailers with larger demands.</p>