Inventory Management for One Warehouse Multi-Port Systems with Free Storage Periods

Abstract

We consider a two-echelon supply chain network with one centralized warehouse and a set of ports, in which the sea cargo ports offer such kind of service that allows the in-transit inventory to stay in their ports for free for a certain time period. In the replenishment of the warehouse and ports, we take into account of the free storage period to minimize the two-echelon inventory cost. Focusing on stationary and integer-ratio policies, we formulate this problem as a mathematical model with a convex objective function and a set of integer-ratio constraints. We present an algorithm to solve the corresponding relaxed problem in () time, and prove that the objective function value of the relaxed problem (relaxing the integer-ratio constraints) is a lower bound on the average cost of all feasible policies (containing dynamic policies).Then we construct a stationary and integer-ratio inventory policy, i.e., the power-of-two policy, via the solution of the relaxed problem, and we also prove the optimality of the power-of-two policy.