A two-echelon inventory system with transportation capacity constraint

Consider a one-warehouse multi-retailer system under constant and deterministic demand, which is subjected to transportation capacity for every delivery period. To search for the best stationary zero inventory ordering (ZIO) policy, or the best power-of-two policy, or the best nested policy, the problem is formulated as a 0-1 integer linear program in which the objective function comprises of a fixed transportation cost whenever a delivery is made and the inventory costs for both the warehouse and retailers. To overcome the transportation capacity limitation, we extend the policies to allow for staggering deliveries. It is shown that with transportation capacity constraint the non-staggering policy can have its effectiveness close to 0% from the best staggering policy and the power-of-two policy with staggering allowed can have its effectiveness close to 0% from the optimal policy. Nevertheless in general, the power-of-two policy fairs well on a number of randomly generated problems. To solve the large distribution network problem, an efficient heuristic based on the power-of-two policy with staggering of deliveries is suggested.