Positioning empty containers under dependent demand

Owing to trade imbalance, shipping companies position empty containers between ports or depots periodically. The most difficult problem for positioning is that it is not easy to know the exact amounts of empty containers required in the future. The paper deals with the problem of positioning empty containers in a port area with multiple depots. Customer demands and returning containers in depots per unit time period are assumed to be serially-correlated and dependent random variables. Three options are considered to prepare the required extent of positioning: positioning from other overseas ports, inland positioning between depots, and leasing. The policies for empty-container management consist of three parts as follows: a coordinated, (S, s) inventory policy for positioning from other ports, (R_i, r_i) policy for inland positioning between depots; and a simple leasing policy with zero lead-time. The objective is to minimize the expected total costs including inventory holding, overseas positioning, inland positioning and leasing costs. The optimal results are then compared with those in case that customer demands and returning containers are independent and identically distributed random variables. A genetic-based optimization procedure is developed to find the optimal parameters (S, s) and (R_i, r_i). Some numerical examples are given to demonstrate the results.