This paper provides a tangible methodology to deal with the liner ship fleet deployment problem aiming at minimizing the total cost while maintaining a service level under uncertain container demand. The problem is first formulated as a joint chance constrained programming model, and the sample average approximation method and mixed-integer programming are used to deal with it. Finally, a numerical example of a liner shipping network is carried out to verify the applicability of the proposed model and solution algorithm. It is found that the service level has significant effect on the total cost.
AbstractThe liner ship fleet deployment problem with uncertain container demand is one of the risk management issues in liner shipping industry. This paper provides a methodology to deal with this problem, which ensures that the deployed liner ship fleet satisfy the shipping requirement of shippers at least with a predetermined probability. The problem is formulated as a joint chance constrained programming (JCCP) model to minimize the total expected cost incurred in container shipment. As the critical issue of the JCCP model is that the closed forms of the joint chance constraints are analytically intractable, the sample average approximation (SAA) method is used to deal with this issue and a SAA model is then proposed to approximate the JCCP model. Further, the SAA model is equivalently transformed into a mixed-integer linear programming (MIP) model which can be efficiently solved by an optimization solver CPLEX. Finally, a sensitivity analysis is conducted to evaluate the performance of SAA method and a numerical example of a real world liner shipping network provided by a liner shipping company is carried out to show the risk analysis based on the proposed model.
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