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

Abstract

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 (A_n, S_n), that is, importing empty containers up to A_n when the number of empty containers in the port is fewer than A_n; exporting empty containers down to S_n when the number of empty containers in the port is more than S_n; and doing nothing, otherwise. A polynomial-time algorithm is developed to determine the two thresholds, that is, A_n and S_n, 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.

Keywords:

• empty container repositioning
• heuristic algorithm
• lost sales
• multi-periods
• stochastic demand
• threshold-type optimal policy

Acknowledgements

This research was supported in part by The Hong Kong Polytechnic University under a research studentship for MPhil study to Zhang. It was also supported in part by grant J-BB7J.