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

Bowen Zhang, C T Ng and T C E Cheng
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C T Ng: The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR, China
T C E Cheng: The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR, China

Journal of the Operational Research Society, 2014, vol. 65, issue 2, 302-319

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 (An), that is, importing empty containers up to An; exporting empty containers down to Sn; and doing nothing, otherwise. A polynomial-time algorithm is developed to determine the two thresholds, that is, An, 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.

Date: 2014
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