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• Proposed a reliable liner shipping planning problem under uncertainties. • The correlation between freight rates and demand can be captured by extended model. • Designed a column-and-constraint generation algorithm enables faster model tackling. This paper investigates a reliable ship fleet planning problem with the uncertainties of container shipping demand, transport costs and freight rates in liner shipping services, and this problem is formulated as a two-stage robust optimization model. In our model, the first-stage decision is to determine the types and quantities of ships, as well as their allocation to different routes, and the second-stage is to fulfill container shipping demand after uncertain information is revealed. Compared to the models proposed in existing researches, our model involves multiple uncertainties aforementioned, and it can also capture the correlation between demand and freight rates. Due to the difficulty of directly solving the two-stage robust optimization model, the column-and-constraint generation algorithm and the benders-dual cutting plane algorithm are developed to address this model. Based on a real shipping network case, extensive computational experiments are conducted to test the practical significance of the presented model and the applicability of our algorithm. The computational results indicate that considering multiple uncertainties simultaneously can significantly save the worst-case costs, demonstrating that the developed two-stage robust optimization model provides a valuable decision-making reference for liner companies seeking to enhance the reliability of ship fleet planning. [ABSTRACT FROM AUTHOR]

• E-service quality positively impacts shippers' e-satisfaction and e-loyalty. • Trust positively moderates the relationship between shippers' e-satisfaction and e-loyalty. • We converted a structural equation modeling model to a network data envelopment analysis model. • Small-scale shippers exhibit minimal slack in e-service quality and e-loyalty, increasing with their scale. • Liner carriers should pay more attention to shippers' e-service quality and e-loyalty as they grow in scale. Focusing on the e-commerce platforms provided by major global liner shipping companies (LSCs), this study explores how e-service quality (e-SQ) influences e-loyalty (e-LY) and establish benchmarks for individual customers. We initially employed structural equation modeling to develop a research framework, and then we transformed this framework into a network data envelopment analysis model. Our findings revealed that the e-SQ of LSCs has a significant positive impact on the e-satisfaction (e-SA) and e-LY of their customers. Additionally, we observed that trust plays a significant moderating role in the relationship between e-SA and e-LY. Through benchmark analysis, we found that for small-scale shippers, virtually no slack exists between their benchmark and actual perception. However, the slack increased as the scale of the shipper increased, implying that LSCs have provided an e-SQ that exceeds the expectations of their large-scale customers. Meanwhile, it's crucial for LSCs to pay attention to specific aspects such as the architecture of e-commerce platforms and privacy protection because the slacks of these e-SQ items are relatively small. Furthermore, the large slacks in e-LY for large-scale shippers imply that their e-LY leaves much room for improvement compared with that of small-scale shippers. Overall, our study underscores the importance of maintaining or elevating e-SQ standards to reinforce e-LY while considering the mediating and moderating effects of e-SA and trust in the context of the e-commerce platforms provided by major LSCs. [ABSTRACT FROM AUTHOR]

• Propose a hub location problem considering canal effects. • Present several binary linear programming models. • Ship capacity limitation has a bigger impact on hub location around a canal. The Panama Canal and the Suez Canal are two key canals around the world, both of which have a great number of connections with other ports because of various liner shipping service routes. Liner carriers can facilitate container transshipment operations by opening hub ports around the canal. This paper aims to investigate canal effects on hub location in liner shipping. Different from the conventional hub location problem with fixed costs, our hub location problem with fixed costs can be reduced to a p-median problem, while addressing the research issue considered in the conventional hub location problem with fixed costs. In order to describe canal effects, besides its geographic location, this paper mainly considers three aspects: canal toll, canal congestion, and ship capacity limitation when passing through a canal. Several binary linear programming models are mainly developed for our hub location problem considering canal effects. Moreover, a theoretical analysis is also developed for simplified hub location around a canal. Numerical results show that ship capacity limitation has a bigger impact on hub location around a canal, as compared with canal toll and canal congestion. Such phenomenon can be partly supported by the theoretical analysis. This insight to some extent justifies the recent canal expansion projects to widen or add a new lane waterway for the Panama Canal and the Suez Canal, respectively. [ABSTRACT FROM AUTHOR]

Highlights • Uncertain demands and bookings in liner shipping call for stochastic approaches. • Novel multistage stochastic formulation for the Liner shipping cargo-mix problem. • Efficient & effective two-phase matheuristic based on a rolling horizon approach. • Realistic size instances with over 32,000 scenarios can be solved within minutes. Abstract This paper presents the stochastic cargo-mix problem, which aims at analysing the cargo composition needed for a liner vessel to maximise its revenue on a given service. The unreliability with respect to the demand forecast is included by considering the cargo-flows as being stochastic instead of deterministic. We also take into account accepted bookings, draft, stability and capacity constraints. A compact formulation of the problem is shown to be too complex to solve industrially sized instances. Instead, a rolling horizon matheuristic is presented, and the computational results show that it can achieve high-quality results in reasonable time. [ABSTRACT FROM AUTHOR]

• Investigate the maximal detour liner shipping hub location problem; • Improve the applicability of the p -hub center problem; • Devise an improved Benders decomposition algorithm. This paper investigates a novel maximal detour hub location problem arising in liner shipping, referred to as a maximal detour liner shipping hub location problem, which can be regarded as a novel p -hub center problem. Different from conventional formulations of the p -hub center problem, both cost and service can be kept at a good level based on our investigated problem, although economic objectives are not considered in our problem. By considering origin–destination (OD) path based detour and sub-path based detours, we propose three mixed-integer linear programming models for our problem. The proposed formulations with sub-path based detours can be efficiently solved by CPLEX. To efficiently solve our formulation with OD path based detour, we propose an improved Benders decomposition algorithm, where the inspection strategy, the heuristic strategy and the multi-cut strategy are developed for improving algorithm efficiency. Finally, we provide numerical experiments to account for the effectiveness and efficiency of the proposed formulations and algorithm. [ABSTRACT FROM AUTHOR]

Highlights • Propose a global hub location problem in liner shipping. • Community structure is properly used to split our problem into some subproblems. • Present a two-stage optimization method to efficiently solve our problem. Abstract This paper proposes a global hub location problem (GHLP) in liner shipping considering community structure. A two-stage optimization method is developed to solve the proposed problem. In the first stage, ports are partitioned into different communities by using a community detection algorithm. In the second stage, we determine the location of hub ports for various communities, respectively. The optimal hub location solution for each considered community can be independently determined. Then the problem size can be sharply decreased. More importantly, we find that it forms a community structure based optimal solution of the GHLP by combining the optimal hub location solutions for all considered communities. Numerical experiments are carried out to account for the effectiveness of our two-stage optimization method. [ABSTRACT FROM AUTHOR]

This paper examines the liner fleet deployment problem when only conditional shipping demand information is known. For such a case, it is generally not possible to determine the exact optimal solution. A set of complementary upper and lower bounds on the optimal cost are derived by exploiting the problem structure. These bounds are explicitly shown to converge to the optimal cost when a sufficiently refined partition is available. A numerical example illustrates the model. [ABSTRACT FROM AUTHOR]

In recent years, the Northern Sea Route (NSR) has attracted significant attention with respect to liner shipping. In this research, we propose a general time-space network-based mathematical formulation to analyze the ship routing and freight assignment problem in liner shipping and apply it to NSR planning problem. To solve the resulting program, we propose a Lagrangian relaxation-based decomposition algorithm that facilitates the network features. Empirical results show that navigation skill, bunker price, delay penalty and service commitment are the primary factors that affect the NSR’s commercial practicability. [ABSTRACT FROM AUTHOR]

This paper studies the Feeder Network Design Problem (FNDP), which considers the design of a minimum cost liner shipping network for the transportation of cargo (containers) between a given hub port and a set of feeder ports. In addition to determining the services to operate (i.e., the routes), the FNDP deals with deciding the fleet of vessels to deploy on these services. In contrast to most FNDPs previously studied in the literature, the feeder network can, if found beneficial, be a hub-and-spoke system where cargo can be transshipped at any feeder ports. Thus, we denote our problem as the Feeder Network Design with Optional Transshipment (FND-OT). To solve the FND-OT, we propose a novel adaptive Heuristic with a special data structure for solution representation, which gives significant speed-ups. Furthermore, a new escape algorithm is used to escape from local optima. We show that the adaptive heuristic outperforms an existing solution algorithm in the literature on a set of realistic test instances. We also present results for a new set of instances adapted from a previously published benchmark suite (LINER-LIB) and show that including the possibility of having cargo transshipment in the FNDP can give significant benefits and reduced costs. • A Feeder Network Design is extended to include transshipment at any feeder port. • An adaptive heuristic uses a simple, efficient representation for solutions. • The heuristic is tested on realistic data and adapted instances from the LINER-LIB. • Computational study shows the benefits from allowing optional transshipments. [ABSTRACT FROM AUTHOR]

We present an integrated modelling framework for the joint problems of network design, fleet deployment and empty repositioning in liner shipping. In our problem the number of service routes and their design are an endogenous part of the problem. The cost of a route is a set function mapping a subset of edges, vessel types and quantities to deploy to the set of non-negative real numbers. Since such cost structures cannot be accommodated in a compact formulation, our modelling framework, which is based on the paradigm of the Benders reformulation, integrates separate problems aiming to obtain a solution to the integrated problem. In this work we look at the Benders approach as a tool for integrating separate optimization problems rather than decomposing an integrated holistic optimization problem. Our numerical experiments show that the method is very efficient in solving instances of this problem with respect to both the problem size and the computational time. [ABSTRACT FROM AUTHOR]

We present a mathematical model and a solution method for the liner shipping network design problem. The model takes into account coordination between vessels and transit time restrictions on the cargo flow. The solution method is an improvement heuristic, where an integer program is solved iteratively to perform moves in a large neighborhood search. Our improvement heuristic is applicable as a real-time decision support tool for a liner shipping company. It can be used to find improvements to the network when evaluating changes in operating conditions or testing different scenarios. Computational results on the benchmark suite LINER-LIB are reported. [ABSTRACT FROM AUTHOR]

This study investigates an optimal control policy for a liner ship to decide at which ports and how much fuel the liner ship should be refueled under stochastic fuel consumption in each leg and stochastic fuel price at each port. Based on some properties proved in this study, a dynamic programming algorithm is then designed to obtain some important threshold values, which are used in the optimal control policy for ship refueling decision. Extensive experiments show that the proposed method can obtain the optimal decision within a reasonable time (about 170 s) for various scales of problem instances (up to 30 ports) as well as various settings of probability distributions. In addition, some comparative experiments also show that the proposed optimal decision policy can save at least 8% fuel consumption cost by comparing with some relatively simple rules and save about 1% cost on average by comparing with some brilliantly-designed rules. [ABSTRACT FROM AUTHOR]

The cargo-mix problem aims at selecting the amount of containers of a given type to load on a vessel. In this article we present an extended definition that includes the analysis of a circular route with draft restrictions, limitations on expected cargo and the use of a block stowage strategy. A compact formulation of the problem based on the state-of-the-art heuristic decomposition is shown not to be able to solve the extended problem, thus a matheuristic approach is presented that can achieve high quality results in a matter of seconds. [ABSTRACT FROM AUTHOR]

In maritime transportation of automobiles, roll-on/roll-off (ro–ro) shipping companies operate liner shipping services across major trade routes. Large ro–ro shipping companies are well placed to offer end-to-end integrated logistics services to auto manufacturers engaged in international trade of vehicles. Therefore, we present a new mixed integer programming model for fleet deployment including inventory management at the ports along each trade route. Due to the complexity of the problem, a rolling horizon heuristic (RHH) is proposed. The RHH solves the problem by iteratively solving sub-problems with shorter planning horizon. Computational results based on real instances are presented. [ABSTRACT FROM AUTHOR]

In this paper speed optimization of an existing liner shipping network is solved by adjusting the port berth times. The objective is to minimize fuel consumption while retaining the customer transit times including the transhipment times. To avoid too many changes to the time table, changes of port berth times are only accepted if they lead to savings above a threshold value. Since the fuel consumption of a vessel is a non-linear convex function of the speed, it is approximated by a piecewise linear function. The developed model is solved using exact methods in less than two minutes for large instances. Computational experiments on real-size liner shipping networks are presented showing that fuels savings in the magnitude 2–10% can be obtained. The work has been carried out in collaboration with Maersk Line and the tests instances are confirmed to be representative of real-life networks. [ABSTRACT FROM AUTHOR]

The cargo allocation problem is a key strategic problem that determines the profitability of a liner shipping network. We present a novel mixed-integer programming model for this problem that introduces service levels for transit time requirements and optimizes the vessel speed on each leg of a service. These extensions to the cargo allocation problem greatly increase its realism and value for carriers. We evaluate our model on realistic data from the LINER-LIB and perform a sensitivity analysis of transit times versus bunker costs. Furthermore, we show how carriers can use our model to make data driven decisions in their operations. [ABSTRACT FROM AUTHOR]

This work expounds on implementing an effective dynamic ( s , S ) policy to solve a liner shipping refueling and speed determination problem under both bunker prices and consumption uncertainties. While solving an optimization model which incorporates a continuous distribution is extremely challenging, we use sample average approximation method to solve it. However, the resulting problem is still a very large-scaled problem. Therefore, we propose two variations of the progressive hedging algorithm to tackle it. Numerical results show that our solution method is efficient and, in addition, our dynamic ( s , S ) policy model has significant cost reduction potential compared to stationary models. [ABSTRACT FROM AUTHOR]

• A two-stage stochastic programming model adopts the Conditional-Value-at-Risk to measure profit variations. • A risk-averse Benders decomposition method for the model is proposed for the model. • The model significantly reduces the profit variations with little profit loss. Liner shipping companies need to satisfy the shipping demand from both the long-term contracts and the spot market. In general, the container shipping demand of the long-term contract has more stable volumes but lower freight rates compared with the spot market demand. It is thus a critical problem for the shipping companies how to provide discriminative shipping services to these two types of shipping demand through contract selection and container slot allocation to simultaneously increase the shipping profit and control its variations resulting from the demand variations. To handle this problem, a two-stage stochastic programming model is constructed in this paper which adopts the Conditional-Value-at-Risk (CVaR) to measure the profit variations. In the first stage, the shipping company selects the long-term contracts from a candidate contract set to sign with customers under the uncertainties in the show-up rates of containers in long-term contracts, and the volumes and the freight rates of the spot market demands. In the second stage, after all uncertainties have been realized, the shipping company determines the slot allocation for both the contract and spot demands. With the introduction of the CVaR, classical Benders decomposition cannot be directly applied to solve the risk-averse model. This paper thus develops a risk-averse Benders decomposition method tailored for the model. Numerical experiments are also conducted to verify the effectiveness of the solution method and provide some meaningful managerial insights. [ABSTRACT FROM AUTHOR]

We present an integer programming based heuristic, a matheuristic , for the liner shipping network design problem. This problem consists of finding a set of container shipping routes defining a capacitated network for cargo transport. The objective is to maximize the revenue of cargo transport, while minimizing the cost of operating the network. Liner shipping companies publish a set of routes with a time schedule, and it is an industry standard to have a weekly departure at each port call on a route. A weekly frequency is achieved by deploying several vessels to a single route, respecting the available fleet of container vessels. The matheuristic is composed of four main algorithmic components: a construction heuristic, an improvement heuristic, a reinsertion heuristic, and a perturbation heuristic. The improvement heuristic uses an integer program to select a set of improving port insertions and removals on each service. Computational results are reported for the benchmark suite LINER-LIB 2012 following the industry standard of weekly departures on every schedule. The heuristic shows overall good performance and is able to find high quality solutions within competitive execution times. The matheuristic can also be applied as a decision support tool to improve an existing network by optimizing on a designated subset of the routes. A case study is presented for this approach with very promising results. [ABSTRACT FROM AUTHOR]

Highlights: [•] A combination of origins and destinations in the formulation. [•] A general and compact hybrid-link-based model. [•] The choice of origins and destinations has the totally unimodular property. [•] New formulation for the multi-commodity flow problems. [ABSTRACT FROM AUTHOR]

Abstract: Container paths play an important role in liner shipping services with container transshipment operations. In the literature, link-based multi-commodity flow formulations are widely used for container routing. However, they have two deficiencies: the level of service in terms of the origin-to-destination transit time is not incorporated and maritime cabotage may be violated. To overcome these deficiencies, we first present an operational network representation of a liner shipping network. Based on the network, an integer linear programming model is formulated to obtain container paths with minimum cost. Finally, we add constraints to the integer linear programming model, excluding those paths already obtained, so as to find all the container paths. [Copyright &y& Elsevier]

Abstract: This paper examines the design of liner ship route schedules that can hedge against the uncertainties in port operations, which include the uncertain wait time due to port congestion and uncertain container handling time. The designed schedule is robust in that uncertainties in port operations and schedule recovery by fast steaming are captured endogenously. This problem is formulated as a mixed-integer nonlinear stochastic programming model. A solution algorithm which incorporates a sample average approximation method, linearization techniques, and a decomposition scheme, is proposed. Extensive numerical experiments demonstrate that the algorithm obtains near-optimal solutions with the stochastic optimality gap less 1.5% within reasonable time. [Copyright &y& Elsevier]

Abstract: We consider the problem of designing an optimal vessel schedule in the liner shipping route to minimize the total expected fuel consumption (and emissions) considering uncertain port times and frequency requirements on the liner schedule. The general optimal scheduling problem is formulated and tackled by simulation-based stochastic approximation methods. For special cases subject to the constraint of 100% service level, we prove the convexity and continuous differentiability of the objective function. Structural properties of the optimal schedule under certain conditions are obtained with useful managerial insights regarding the impact of port uncertainties. Case studies are given to illustrate the results. [Copyright &y& Elsevier]

Abstract: This paper proposes a liner ship fleet deployment (LSFD) problem with container transshipment operations. The proposed problem is formulated as a mixed-integer linear programming model which allows container transshipment operations at any port, any number of times, without explicitly defining the container transshipment variables. Experiments on the Asia–Europe–Oceania shipping network of a global liner shipping company show that more than one third (17–22 ports) of the total of 46 ports have transshipment throughputs. Computational studies based on randomly generated large-scale shipping networks demonstrate that the proposed model can be solved efficiently by CPLEX. [Copyright &y& Elsevier]

Abstract: A mixed integer linear programming formulation is proposed for the simultaneous design of network and fleet deployment of a deep-sea liner service provider. The underlying network design problem is based on a 4-index (5-index by considering capacity type) formulation of the hub location problem which are known for their tightness. The demand is elastic in the sense that the service provider can accept any fraction of the origin–destination demand. We then propose a primal decomposition method to solve instances of the problem to optimality. Numerical results confirm superiority of our approach in comparison with a general-purpose mixed integer programming solver. [Copyright &y& Elsevier]

Abstract: In this paper we propose a 4-index formulation for the uncapacitated multiple allocation hub location problem tailored for urban transport and liner shipping network design. This formulation is very tight and most of the tractable instances for MIP solvers are optimally solvable at the root node. While the existing state-of-the-art MIP solvers fail to solve even small size instances of problem, our accelerated and efficient primal (Benders) decomposition solves larger ones. In addition, a very efficient greedy heuristic, proven to be capable of obtaining high quality solutions, is proposed. We also introduce fixed cost values for Australian Post (AP) dataset. [Copyright &y& Elsevier]

Abstract: A mixed integer programming formulation is proposed for hub-and-spoke network design in a competitive environment. It addresses the competition between a newcomer liner service provider and an existing dominating operator, both operating on hub-and-spoke networks. The newcomer company maximizes its market share—which depends on the service time and transportation cost—by locating a predefined number of hubs at candidate ports and designing its network. While general-purpose solvers do not solve instances of even small size, an accelerated Lagrangian method combined with a primal heuristic obtains promising bounds. Our computational experiments on real instances of practical size indicate superiority of our approach. [Copyright &y& Elsevier]

Abstract: This paper is concerned with model development for a short-term fleet deployment problem of liner shipping operations. We first present a mixed integer nonlinear programming model in which the optimal vessel speeds for different vessel types on different routes are interpreted as their realistic optimal travel times. We then linearize the proposed nonlinear model and obtain a mixed integer linear programming (MILP) model that can be efficiently solved by a standard mixed integer programming solver such as CPLEX. The MILP model determines the optimal route service frequency pattern and take into account the time window constraints of shipping services. Finally, we report our numerical results and performance of CPLEX on randomly generated instances. [Copyright &y& Elsevier]

Abstract: This study empirically identifies crucial knowledge management enablers and examines their impacts on organizational performance using survey data collected from liner shipping firms include shipping companies and agencies. Results indicated that knowledge management enablers such as organizational structure and knowledge management culture are found to have significantly positive effects on the organizational performance aspects of innovativeness, financial performance, and customer service, whereas information technology support is a positive effect on organizational performance aspect of innovativeness. Theoretical and managerial implications of the research findings on knowledge management for liner shipping companies are discussed. [Copyright &y& Elsevier]

The multi-commodity network flow problem (MCNF) consists in routing a set of commodities through a capacitated network at minimum cost and is relevant for routing containers in liner shipping networks. As commodity transit times are often a critical factor, the literature has introduced hard limits on commodity transit times. In practical contexts, however, these hard limits may fail to provide sufficient flexibility since routes with even tiny delays would be discarded. Motivated by a major liner shipping operator, we study an MCNF generalization where transit time restrictions are modeled as soft constraints, in which delays are discouraged using penalty functions of transit time. Similarly, early commodity arrivals can receive a discount in cost. We derive properties that distinguish this model from other MCNF variants and adapt a column generation procedure to efficiently solve it. Extensive numerical experiments conducted on realistic liner shipping instances reveal that the explicit consideration of penalty functions can lead to significant cost reductions compared to hard transit time deadlines. Moreover, the penalties can be used to steer the flow towards slower or faster configurations, resulting in a potential increase in operational costs, which generates a trade-off that we quantify under varying penalty functions. • We study a generalization of the multi-commodity network flow problem. • Longer commodity routes are discouraged using a penalty function of transit time. • We propose a path formulation that is solved using a column generation method. • Numerical experiments are conducted using realistic liner shipping instances. • We discuss economic implications on costs and delays at varying penalty functions. [ABSTRACT FROM AUTHOR]

• Set up a model for carrier-shipper structures versus market demand and spot rate. • Reveal different roles of the long-term contract and the spot freight rate. • Study the impact of risk-aversion of shipper on performances. • Fluctuations of market demand and spot rate have different impacts. • Design coordination solutions initiated by the carrier for the shipper. The spot freight market in the liner shipping industry has developed significantly in recent years and interplays with the long-term contract between carriers and shippers. Under this background, this paper presents a Stackelberg games model by taking into account both the carrier's long-term decision (on freight rate) as well as the shipper's long-term decision (on shipment capacity procurement amount) and spot market supplementary procurement decision. The shipper is risk-averse facing market uncertainty. Three basic shipping structures are considered: procuring only from carrier with long-term contract, only from spot market, and from both of these channels. We show that dual channels play different roles for the shipper. Although the spot market is not favourable for the carrier, it increases both the shipper's utility and the carrier-shipper's overall performance. Risk-aversion reduces the shipment capacity procurement amount, which protects the shipper but jeopardizes the carrier's and the carrier-shipper's overall performance. Fluctuations of market demand and spot freight rate have different (sometimes even opposite) impacts on the carrier and the shipper. Correlation of market demand and spot freight rate brings more uncertainty for the shipper but grants more leverage for the carrier. Coordination initiated by the carrier improves the carrier-shipper's overall performance substantially, but full coordination is not feasible owing to the shipper's aversion to risk. Quantity-discount rather than two-part tariff contract works. [ABSTRACT FROM AUTHOR]

Liner carriers must regularly adjust their shipping networks to respond to competitors and changing seasonal customer demands. They do this by selecting and moving ships between routes. State-of-the-art approaches decompose this into two separate problems. We propose an integrated mathematical model and matheuristic for the liner shipping fleet deployment and repositioning problem that jointly optimizes the choice of vessels for routes and the cost of moving vessels to their assignments. We use real-world data to show that simultaneously optimizing deployment and repositioning can result in significant cost reduction over solving the problems independently. • A math model and matheuristic to integrate vessel deployment and repositioning. • Combines fleet deployment and fleet repositioning to improve liner networks. • Outperforms state-of-the-art methods on real-world sized instances. • Provides managerial insights found due to the integrated model. [ABSTRACT FROM AUTHOR]

• We examine the volatility spillover and connectedness. • We employ dynamic conditional equicorrelations and spillover index. • Volatility comovement between oil and liner shipping increased during crisis period. • We estimate portfolio diversification strategies and utility gains. Given the importance of the relationship between oil and liner shipping markets, this paper examines the volatility spillover and connectedness between oil and liner shipping markets. We employ dynamic conditional equicorrelations and spillover index approach to know volatility co-movement and spillover between oil prices and returns of liner shipping stocks, respectively. The volatility co-movement between oil and liner shipping companies' stock returns increased during the 2007–09 global financial crisis, and 2010–12 Eurozone debt crisis. We extend our analysis by considering portfolio diversification strategies and utility gains across pre-crisis, crisis, and post-crisis periods. Our findings are useful to policymakers and investors. [ABSTRACT FROM AUTHOR]