Optimal utilization of ports' free-of-charge times in one distribution center and multiple ports inventory systems (Q2325145)

Summary: In this paper, we consider a distribution system consisting of one distribution center (DC), a set of ports, and a set of retailers, in which the product is distributed to the retailers from the DC through the ports by the water transport, and study inventory management for the distribution system with considering the effect of the free storage periods provided by the ports. Inventory management for the distribution system is to determine the order intervals of the DC and the retailers while minimizing the inventory ordering and holding costs. Focusing on stationary and integer-ratio policies, we formulate this inventory management problem as an optimization problem with a convex objective function and a set of integer-ratio constraints and present \(O(N \log N)\) time algorithm to solve the relaxed problem (relaxing the integer-ratio constraints) to optimality, where \(N\) is the number of the retailers. We prove that the relaxed problem provides a lower bound on average cost for all the feasible policies (containing dynamic policies) for this inventory management problem. By using the optimal solution of the relaxed problem, we build a stationary integer-ratio policy (a power-of-two policy) for this inventory management problem and prove that the power-of-two policy can approximate the optimal inventory policy to 83\% accuracy.