Multi‐period empty container repositioning with stochastic demand and lost sales

This paper considers repositioning empty containers between multi‐ports over multi‐periods with stochastic demand and lost sales. The objective is to minimize the total operating cost including container‐holding cost, stockout cost, importing cost and exporting cost. First, we formulate the single‐port case as an inventory problem over a finite horizon with stochastic import and export of empty containers. The optimal policy for period n is characterized by a pair of critical points (An, Sn), that is, importing empty containers up to An when the number of empty containers in the port is fewer than An; exporting empty containers down to Sn when the number of empty containers in the port is more than Sn; and doing nothing, otherwise. A polynomial‐time algorithm is developed to determine the two thresholds, that is, An and Sn, for each period. Next, we formulate the multi‐port problem and determine a tight lower bound on the cost function. On the basis of the two‐threshold optimal policy for a single port, a polynomial‐time algorithm is developed to find an approximate repositioning policy for multi‐ports. Simulation results show that the proposed approximate repositioning algorithm performs very effectively and efficiently.