Tingsong Wang

A chance constrained programming model for short-term liner ship fleet planning problems

This article deals with a short-term Liner Ship Fleet Planning (LSFP) problem with cargo shipment demand uncertainty for a single liner container shipping company. The cargo shipment demand uncertainty enables us to propose a chance constraint for each liner service route, which guarantees that the liner service route can satisfy the customers’ demand at least with a predetermined probability. Assuming that cargo shipment demand between any two ports on each liner service route is normally distributed, this article develops an integer linear programming model with chance constraints for the short-term LSFP problem. The proposed integer linear programming model can be efficiently solved by any optimization solver such as CPLEX. Finally, a numerical example is carried out to assess the model and analyze impact of the chance constraints and cargo shipment demand.

Short-term liner ship fleet planning with container transshipment and uncertain container shipment demand

This paper proposes a short-term liner ship fleet planning problem by taking into account container transshipment and uncertain container shipment demand. Given a liner shipping service network comprising a number of ship routes, the problem is to determine the numbers and types of ships required in the fleet and assign each of these ships to a particular ship route to maximize the expected value of the total profit over a short-term planning horizon. These decisions have to be made prior to knowing the exact container shipment demand, which is affected by some unpredictable and uncontrollable factors. This paper thus formulates this realistic short-term planning problem as a two-stage stochastic integer programming model. A solution algorithm, integrating the sample average approximation with a dual decomposition and Lagrangian relaxation approach, is then proposed. Finally, a numerical example is used to evaluate the performance of the proposed model and solution algorithm.

Multi-period liner ship fleet planning with dependent uncertain container shipment demand

This paper deals with a realistic multi-period liner ship fleet planning problem by incorporating stochastic dependency of the random and period-dependent container shipment demand. This problem is formulated as a multi-period stochastic programming model with a sequence of interrelated two-stage stochastic programming (2SSP) problems characterized ship fleet planning in each single period. A solution method integrating dual decomposition and Lagrangian relaxation method is designed for solving the developed model. Numerical experiments are carried out to assess applicability and performance of the proposed model and solution algorithm. The results further demonstrate importance of stochastic dependence of the uncertain container shipment demand.

Sample Average Approximation

In this chapter, we focus on the solution algorithm to solve the chance-constrained programming model introduced in Chapter 4 . The solution algorithm uses the average of the samples to approximate the chance-constrained programming problems in order to obtain good candidate solutions for the resulting problems. The convergence properties of the resulting problem will be discussed as well.

Robust optimization model for liner ship fleet planning with container transshipment and uncertain demand

This paper studies a problem of liner ship fleet planning with container transshipment under uncertain demand for container shipments. Generally, this problem can be solved with an optimization model to minimize or maximize the expected value of a key variable, such as cost or profit. However, such models do not consider the variance (namely, the risk), another issue of great concern to decision makers. Therefore, this paper aims to develop a robust optimization model in which both expected value and variance are considered simultaneously. By adjusting the penalty parameters of the robust optimization model, decision makers can determine an optimal plan for liner ship fleets (including decisions about fleet design and deployment) to maximize total profit under different container shipment demand scenarios while simultaneously controlling variance. The robustness and effectiveness of the developed model are demonstrated with numerical results.

Mixed-Integer Linear Programming Models for Teaching Assistant Assignment and Extensions

In this paper, we develop mixed-integer linear programming models for assigning the most appropriate teaching assistants to the tutorials in a department. The objective is to maximize the number of tutorials that are taught by the most suitable teaching assistants, accounting for the fact that different teaching assistants have different capabilities and each teaching assistantźs teaching load cannot exceed a maximum value. Moreover, with optimization models, the teaching load allocation, a time-consuming process, does not need to be carried out in a manual manner. We have further presented a number of extensions that capture more practical considerations. Extensive numerical experiments show that the optimization models can be solved by an off-the-shelf solver and used by departments in universities.

Optimal Container Routing in Liner Shipping Networks Considering Repacking 20 ft Containers into 40 ft Containers

The volume of a 40 ft container is twice as large as that of a 20 ft container. However, the handling cost (loading, unloading, and transshipment) of a 40 ft container is much lower than twice the corresponding handling cost of two 20 ft containers. Enlightened by this observation, we propose a novel container routing with repacking problem in liner shipping, where two 20 ft containers can be repacked to a 40 ft container in order to reduce the handling cost. We develop a mixed-integer linear programming model that formulates the routing decisions and the repacking decisions in a holistic manner. An illustrative example is reported to demonstrate the applicability of the model. Results show that the benefit of repacking is the most significant when containers are transshipped several times.

Liner ship fleet deployment with uncertain demand

This paper points out that the deployment problem of the liner ship fleet with uncertain demand is different from other logistics problems with uncertain demand (e.g., truck transport and airlines) because container ships operate 24 h a day and 7 days a week. This difference is largely ignored in the literature. To address this problem, a multilevel optimization model is developed. In addition to liner ship fleet deployment, the model is applicable to other liner shipping decision problems, such as network design with uncertain demand, and to port operations planning problems, such as berth planning with uncertain ship arrival times.

Multiperiod Liner Ship Fleet Planning

This chapter presents a long-term liner ship fleet planning problem with container shipment demand uncertainty. This problem is formulated as a multiperiod stochastic programming model with a sequence of interrelated, two-stage stochastic programming problems that characterize ship fleet planning in each period. A solution method that integrates a dual decomposition and Lagrangian relaxation method is designed for solving the developed model. Numerical experiments are carried out to assess applicability and performance of the proposed model and solution algorithm. The results further demonstrate the importance of the stochastic dependence of the uncertain container shipment demand.

Liner Ship Fleet Planning Problem With a Joint Chance-Constrained Service Level

This chapter presents a liner ship fleet planning problem with an individual chance-constrained service level. This chapter provides a tangible methodology to deal with the liner ship fleet deployment problem aimed at minimizing the total cost while maintaining a service level for the whole shipping network under an 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.