Optimal single-cycle policies for the one-warehouse multi-retailer inventory/distribution system

This study investigates a multi-echelon inventory system with one warehouse and multiple retailers. The demand at each retailer is assumed to be known and satisfied by the warehouse. Shortages are not permitted and lead times are negligible. Additionally, order interval division (OID) and recursive tightening (RT) methods are developed to compute efficient and optimal single-cycle policies. Two theorems are proved to guarantee that the problem is solved optimally by using OID and RT methods. In other words, OID and RT methods theoretically reach the optimal solution in 100% of instances. The complexity of OID and RT methods is just O(N log N) where N denotes the number of retailers involved in the problem. Numerical examples are included to illustrate the algorithmic procedures.