Container Shipment Demand Research Articles

Container Shipment Demand Forecasting in the Australian Shipping Industry: A Case Study of Asia–Oceania Trade Lane

Demand forecasting has a pivotal role in making informed business decisions by predicting future sales using historical data. Traditionally, demand forecasting has been widely used in the management of production, staffing and warehousing for sales and marketing data. However, the use of demand forecasting has little been studied in the container shipping industry. Improved visibility into the demand for container shipments has been a long-held objective of industry stakeholders. This paper addresses the shortcomings of both short-term and long-term shipment demand forecasting for the Australian container shipping industry. In this study, we compare three forecasting models, namely, the seasonal auto-regressive integrated moving average (SARIMA), Holt–Winters’ seasonal method and Facebook’s Prophet, to find the best fitting model for short-term and long-term import demand forecasting in the Australian shipping industry. Demand data from three years, i.e., 2016–2018, is used for the Asia–Oceania trade lane. The mean absolute percentage error (MAPE), root mean squared error (RMSE) and 2-fold walk-forward cross-validation are used for the model evaluation. The experiment results observed from the selected metrics suggest that Prophet outperforms the other models in its comparison for container shipment demand forecasting.

Analysis of three container routing strategies

As containers need several weeks to be delivered to their destinations and the future container shipment demand is uncertain, a myopic strategy for container routing that maximizes the immediate profit may lead to insufficient remaining capacity for transporting more profitable containers in the future. This study conducts a theoretical analysis to compare three container routing strategies, i.e., (i) a widely used myopic strategy, (ii) a non-myopic heuristic routing strategy that incorporates information about the future demand distribution, and (iii) a strategy that assumes future demand is known. Then a practical non-myopic heuristic container routing strategy is developed for practical purposes to increase the profit of liner shipping companies. Extensive numerical experiments show that the proposed non-myopic heuristic container routing strategy brings in an extra of 2%–3% profit over the myopic strategy.

Optimal reefer slot conversion for container freight transportation

ABSTRACTGiven a fleet of container ships of varying capacity, a cost-efficient approach for improving fleet utilization and reducing the number of delayed containers is to optimize the sequence of container ships in a given string, a problem which belongs to the large ship-deployment class. A string sequence with ‘uniformly’ distributed ship capacity is more likely to accommodate a random container shipment demand. The number of one’s total ship slots acts as a gauge of the capacity of the container ships. Meanwhile, there are two types of ship slots: dry slots and reefer slots. A dry slot only accommodates a dry container, while a reefer slot can accommodate either a dry or a reefer container. The numbers of dry and reefer slots for ships in a string are different. Therefore, in this study, we propose a model that considers both dry and reefer slots and use it to elucidate the optimal ship-deployment sequence. The objective is to minimize the delay of dry and reefer containers when the demand is uncertain. Furthermore, based on the optimal sequence deduced, the study also investigates the need to convert some dry slots to reefer slots for the container ships.

Liner container assignment model with transit-time-sensitive container shipment demand and its applications

This paper proposes a practical tactical-level liner container assignment model for liner shipping companies, in which the container shipment demand is a non-increasing function of the transit time. Given the transit-time-sensitive demand, the model aims to determine which proportion of the demand to fulfill and how to transport these containers in a liner shipping network to maximize the total profit. Although the proposed model is similar to multi-commodity network-flow (MCNF) with side constraints, unlike the MCNF with time delay constraints or reliability constraints that is NP-hard, we show that the liner container assignment model is polynomially solvable due to its weekly schedule characteristics by developing two link-based linear programing formulations. A number of practical extensions and applications are analyzed and managerial insights are discussed. The polynomially solvable liner container assignment model is then applied to address several important decision problems proposed by a global liner shipping company.

Liner shipping fleet deployment considering decision makers’ psychological behavior

Decision makers in liner shipping (i.e., liner shipping planners) are risk-averse in that they aim to minimize the adverse effect under the least desirable scenario. To take this behavior into account, we propose a minimax regret model for fleet deployment with uncertain container shipment demand. The minimax regret model reflects how in reality network planners are evaluated. A dynamic scenario inclusion method is proposed to solve the model to optimality using a limited number of demand scenarios. A case study based on a real liner shipping network is carried out to demonstrate the applicability of the proposed model.

Profit-based maritime container assignment models for liner shipping networks

We propose the problem of profit-based container assignment (P-CA), in which the container shipment demand is dependent on the freight rate, similar to the “elastic demand” in the literature on urban transportation networks. The problem involves determining the optimal freight rates, the number of containers to transport and how to transport the containers in a liner shipping network to maximize the total profit. We first consider a tactical-level P-CA with known demand functions that are estimated based on historical data and formulate it as a nonlinear optimization model. The tactical-level P-CA can be used for evaluating and improving the container liner shipping network. We then address the operational-level P-CA with unknown demand functions, which aims to design a mechanism that adjusts the freight rates to maximize the profit. A theoretically convergent trial-and-error approach, and a practical trial-and-error approach, are developed. A numerical example is reported to illustrate the application of the models and approaches.

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.

Containership scheduling with transit-time-sensitive container shipment demand

This paper examines the optimal containership schedule with transit-time-sensitive demand that is assumed to be a decreasing continuous function of transit time. A mixed-integer nonlinear non-convex optimization model is first formulated to maximize the total profit of a ship route. In view of the problem structure, a branch-and-bound based holistic solution method is developed. It is rigorously demonstrated that this solution method can obtain an ε-optimal solution in a finite number of iterations for general forms of transit-time-sensitive demand. Computational results based on a trans-Pacific liner ship route demonstrate the applicability and efficiency of the solution method.

Liner ship route capacity utilization estimation with a bounded polyhedral container shipment demand pattern

This paper aims to estimate capacity utilization of a liner ship route with a bounded polyhedral container shipment demand pattern, arising in the liner container shipping industry. The proposed maximum and minimum liner ship route capacity utilization problems are formulated as a linear programming model and a min–max model, respectively. We examine two fundamental properties of the min–max model. These two nice properties enable us to develop two ε-optimal global optimization algorithms for solving the min–max model, which find a globally ε-optimal solution by iteratively cutting off the bounded polyhedral container shipment demand set with a cut. The latter algorithm overcomes non-convexity of the remaining feasible demand set generated by the former algorithm via a novel hyperplane cut. Each hyperplane cut can assure that the current vertex of the polyhedral demand set is cut off, whereas solutions that may improve the current one by more than a factor of ε are retained. Extensive numerical experiments for problems larger than those encountered in real applications demonstrate the computational efficacy of the latter algorithm.

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.

Liner ship fleet deployment with week-dependent container shipment demand

This paper addresses a practical liner ship fleet deployment problem with week-dependent container shipment demand and transit time constraint, namely, maximum allowable transit time in container routing between a pair of ports. It first uses the space–time network approach to generate practical container routes subject to the transit time constraints. This paper proceeds to formulate the fleet deployment problem based on the practical container routes generated. In view of the intractability of the formulation, two relaxation models providing lower bounds are built: one requires known container shipment demand at the fleet deployment stage, and the other assumes constant container shipment demand over the planning horizon. An efficient global optimization algorithm is subsequently proposed. Extensive numerical experiments on the shipping data of a global liner shipping company demonstrate the applicability of the proposed model and algorithm.

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.