Efficient methods for stochastic joint replenishment and delivery problem

In this paper, we consider the joint replenishment and delivery scheduling of the one‐warehouse, n$n$‐retailer system with stochastic demand. In this distribution system, items are first jointly replenished and therefore can share a major ordering cost. Then a coordinated delivery scheduling is adopted to arrange the delivery plan. The problem is formulated as a mixed integer nonlinear program. Subsequently, we introduce two algorithms to handle this complex problem: a Lipschitz optimization method and a modified RAND heuristic. Numerical experiments show that the proposed methods are quite efficient. Sensitivity analysis also shows some interesting findings in terms of management.