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

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Journal of the Operational Research Society

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.

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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.

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Authors and Affiliations

  1. The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR, China

    B Zhang, C T Ng & T C E Cheng

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  1. B Zhang
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  2. C T Ng
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  3. T C E Cheng
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Correspondence to C T Ng.

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Zhang, B., Ng, C. & Cheng, T. Multi-period empty container repositioning with stochastic demand and lost sales. J Oper Res Soc 65, 302–319 (2014). https://doi.org/10.1057/jors.2012.187

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  • DOI: https://doi.org/10.1057/jors.2012.187

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