The current context of World Globalization has raised many difficult problems regarding the transportation of goods. The products are hauled over large distances of land and water, and more often have to travel by more than one means of transport: by ships, planes, trucks (see Van Schijndel and Dinwoodie, 2000); all these lead to the Multimodal Transportation Systems (MMTS).

In contrast with classical, single mean transportation, multi-modal transportation has multiple constraints, for example, Litman (2017) names different optimization processes as parcel loading, and transfer between transports. In a context of today’s global warming and increased pollution, it is a necessity to also globally reduce gas emission. The environmental goal correlated with the economical performance could be reached through several ways including an optimized transport planning and using appropriate resources.

In the literature review on Multimodal freight transportation planning conducted by  SteadieSeifi et al. (2014), several strategic planning issues within multi-modal freight transportation and tactical planning problems are shown. Complex operational planning for real-time requirements of multimodal operators, carriers and shippers, not previously addressed at strategic and tactical levels, are described. The main models with related solvers and proposed future research are included. A detailed review, with an analysis of the optimization-based decision-making models for the problem of Disaster Recovery Planning of Transportation Networks (DRPTN), is provided by Zamanifar and Hartmann (2020). The authors described the phases of optimization-based decision-making models and investigate their methodologies. Nevertheless, the authors identified some challenges and opportunities, discussed research improvement and made suggestions for possible future research.

A recent systematic review about dynamic pricing techniques for Intelligent Transportation System (ITS) in smart cities was published by Saharan et al. (2020). The authors included existing ITS techniques with pertinent overviews and discussions about problems related to electric vehicles (EVs) used for reducing the peak loads and congestion, at the same time increasing the mobility.

The current work overviews the multimodal transport. Section 2 presents prerequisites related to the multimodal transport and the context around it. Section 3 follows presenting the characteristics and the challenges related to the transport. Further on, methods of planning (Section 4) and optimization (Section 5) in terms of time (Section 5.1), cost (Section 5.2) and network topology (Section 5.3) are presented. Existing unimodal transport models and solvers with possible future extension to multimodal features are included in Section 6. Section 7 draws the important conclusions about multimodal transport.

The multimodal transport is defined by the UN Convention on International Multimodal Transport of Goods as follows.

Definition 1

The multimodal transport is the transport of goods from one place to another, usually located in a different country, by at least two means of transportation.

Optimization. A classical transportation of goods implies direct links and one mode of transportation (Fig. 1 left), a shortest path route, from a sender to a receiver of goods, see Zografos and Androutsopoulos (2008); the multimodal transport (Fig. 1 right), implies complex links and more than one mode of transportation. Optimization of classical transportation routes is a fairly easy and intensely studied topic. There are already existing state-of-the-art algorithms, like Dijkstra’s Algorithm (see Jianya, 1999), or Clarke-Wright technique as in Golden et al. (1977). These approaches use a single mean of transport, a single warehouse and one or more clients (or receivers).

Real-life scenarios. In the complex reality, goods can be transported in any direction, for example, inside a country there are couriers delivering from any side of the country to another side; using just trucks to perform a complete task would be impossible, as the problem has O(n2) complexity for n cities to reach. Optimizing this case means designing a system with a central warehouse or hub, where all the goods are unloaded, sorted according to the destination and finally loaded on the respective trucks and dispatched towards the destination. This optimization alone reduces the required number of trucks (the same truck makes a round trip from each city to the central hub) (Zhang et al., 2013).

But what about the larger countries, or about international transport? The multimodal transportation has the advantage of moving a huge amount of goods, in the hundreds of thousands of tons at once, via large ships, over very large distances (Fig. 1).

This section focuses on the challenges of the multimodal transportation, both for passengers (Section 3.1) and freight (Section 3.2). The majority of received goods are moved by many transportation modes, e.g. ships, airplanes, trucks. In the first stages of the transport, the sorting hubs collect all the goods from different senders, establish their destination and assign them a way of dispatch. Routes may be calculated at this step to assess the most economical ones, both in cost and time. Goods with the same route are grouped and loaded on the same shipment mode.

Figure 2 shows the direct consequence: when reaching the end of a route, for each transportation mode there must be a sorting/dispatching hub. These operations of unloading, sorting, grouping and dispatching are repeated at every hub and with a highly time consuming action. As a consequence, the intermediate hubs have to be very organized so as to limit the time spent at that point, and also their number has to be kept low enough. As a disadvantage, the very large number of shipping hubs will dramatically increase the transport cost, due to the number of transport units used.

Based on these features, several challenges arise: How can we make shipping from A to B cheaper, quicker, and with the least environmental impact? How can we calculate the optimum number of hubs with maximum benefits? What is the optimal way of transporting goods between hubs while avoiding their weaknesses?

> Real-life scenarios.

– HAZMAT: transport Security Vulnerability Assessment (SVA) by Reniers and Dullaert (2013). The hazardous materials HAZMAT transport SVA assesses the relative security risk levels of the different modes of hazardous freight transport models, e.g. road, inland waterways, pipelines or railway. The policymakers could use this tool to assess the user-friendly security in multi-modal transport. The HAZMAT model follows:

The intermodal risk is determined on the minimum security risk path, considering only the risks of the individual segments of a transport route and include also the number of intermodal transshipment.

The risk with the transshipment is defined as: Rt=Rnt(1+x(nts)) where Rt is the security with the transshipment, Rnt is the security risk without transshipment, x is the weight factor for importance of transshipment risks, compared with the transportation risks and nts is the number of transshipment. The model was implemented with CPLEX studio and OPL; it was successfully tested on two multimodal networks with highways and railways.

– New Delhi, Indian busy urban area MMTS by Kumar et al. (2013). In 2021 the Delhi population will be around 23 million, therefore public transit should be integrated. In Kumar et al. (2013) MMTS focuses on reducing congestion on roads and improving transfers and interchanges between modes. Delhi’s public transport will grow from a 60% of the total number of vehicular trips to at least at 80% in 2021; 15 million trips per day by 2021 in the Integrated Rail-cum-Bus Transit, plus 9 million by other modes are estimated. The Delhi public transport model is illustrated, evaluated and its performance is discussed in Kumar et al. (2013).

The performance of the MMTS is quantified using the following measures.

In particular, for the New Delhi case study: TTR=1.3 shows a competitive public transport; LS, the mean OVTT/IVTT>1 1$]]>, thus people spend more time out-of-vehicle than in-vehicle; IR∈[0.2,0.5] value shows that inter-connectivity between transportation modes should be improved; PWI=0.825 for the metro is recommended as the mean passenger waiting time is similar to metro’s frequency; RI=0.7681 , indicates that passenger satisfaction should be improved.

– ARKTRANS. The Norwegian MMTS framework architecture by Natvig et al. (2006) and Natvig and Vennesland (2010). The framework offers an overview of all the major systems running in Norway that will hopefully further contribute to new and improved solutions. The transport, whether sea, air or railway, have similar needs and challenges with respect to communication, information, management, planning and costs.

Figure 3 illustrates: a) specific multimodal components, b) an example of functionality between components, c) an example of the Transport Network Management, d) and how a transport process includes functionality from sub-domains and how processes are intertwined; thus transport services work together and efficiently exchange information. Furthermore, the main MMTS specifications of the ARKTRANS frameworks could serve as a guide for other similar frameworks.

The detailed technical aspects conclude this list. A beneficent interaction within all MMTS process leads to an efficient multimodal transport framework. Overall conclusions specify that MMTS is especially suited for long distances; a major MMTS feature is the total travel time; the access, egress and transfer times could be reduced if there is an integrated MMTS, e.g. park and bicycles facilities, and card access on transit systems.

Other Frameworks. Frameworks for multimodal transport security and various policy applications are described in detail in the book by Szyliowicz et al. (2016). Other related frameworks and security challenges, for both passengers and freight and security and policy applications around the world, are analysed in the book by Wiseman and Giat (2016).

Multiple facets of planning multimodal transport exist, making it more difficult. For example, in a large city, somebody might suddenly decide to engage in a long distance travel. This implies an ad-hoc computation of the route and means of transport to be used, according to the individual personal preferences, e.g. not using metro system due to motion-sickness. Planning such a transport means using any available means at the specific time; the factors to consider could include: time, cost, weather, waiting time in hubs, etc. What does planning a diverse transport system for a large city imply? The designer must compute the available resources, the requirements and even the schedules/working hours of different companies.

In the planning phase, the designer could suggest the transport means (buses, trams, etc.) in order to obtain an economic and eco-friendly system. An Introduction in Multimodal Transportation Planning book was published by Litman (2017) in which he summarizes the basic principles for multimodal transportation planning for people. He studies transport options for pedestrians, like sidewalk design, bicycles, ride-sharing and public transit systems. He also has very good explanations for multimodal transport planning process, impact to be considered that is often overlooked and different traffic models, like the Four-Step Traffic Model. The first stage of planning a multimodal transport system is to understand its complexities. A complete and accurate model has to be created and analysed.

> Planning MMTS with uncertainties and limitations.

– Fuzzy cross-efficiency Data Envelopment Analysis by Dotoli et al. (2016). The planning of efficient multimodal transports using a fuzzy cross-efficiency Data Envelopment Analysis technique is presented by Dotoli et al. (2016). Other approaches like uncertainty conditions with complex traits and high discriminative power are described. They prove the effectiveness of their approach while studying the optimal transport planning and computing the boundaries of the multi-modal transport. In Sumalee et al. (2011) the multi-modal transport network with demand uncertainties and adverse weather conditions includes formulation of the fixed point problem; other future and existing related developments include works by Ticala (2017) and Xu and Gao (2009).

– Metaheuristics for real-time decisions by Mutlu et al. (2017). The planning part of multimodal transport with various limitations is reviewed by Mutlu et al. (2017). They discuss problems like real-time decisions in the context of short-term planning, restructuring and re-configuring logistic strategies, and collaborative planning (Fig. 5). Appropriate solution methods and intuitive meta-heuristic approaches to rapidly act upon changes are suggested.

> Passenger & freight flows Planning for Multimodal transport.

– Multi-Agents Systems for MMTS planning by Greulich et al. (2013). As the name suggests, the implementation uses intelligent agents representing various stakeholders and considers the effects of passenger behaviour.

– Genetic Local Search tested in the Java Island, Indonesia by Yamada et al. (2007). The research revealed that a procedure based on Genetic Local Search outperforms in order to find the best combination of alternatives.

> Multi-modal systems.

– A multimodal travel system by Bielli et al. (2006). The authors focused on the network object modelling (Fig.5). This enables to use the model for computing a shortest path while also integrating multimodal options. They also implement and test a solution for the problem of long-run planning in such systems.

– Syncromodal Transport Planning by Mes and Iacob (2016). It is a multimodal planning where the best possible combination of transport modes is selected for each package and is discussed in depth. The syncromodal algorithm is implemented in a 4PL service provider in the Netherlands and managed to obtain a 10.1% cost reduction and a 14.2% reduction in CO2 .

– A multimodal transport path sequence: AND/OR graphs facilitate planning by Wang et al. (2020b). It proposes a triple-phase generate route method for a feasible multimodal transport path sequence, based on AND/OR graphs. Energy consumption evaluates the multimodal transport energy efficiency. A biobjective optimization model for both energy consumption and route risk is solved with an ant-based technique. The research is limited by the graph complexity; the simulation shows valid and promising results.

> Traffic Flow Risk Analysis and Predictions.

– Fuzziness approach for risk analysis by Stanković et al. (2020). A fuzzy Measurement Alternatives and Ranking according to the Compromise Solution, fuzzy MARCOS for Road Traffic Risk Analysis was proposed. The method defines reference points, determined relationships between alternatives & fuzzy ideal/anti-ideal values and defined utility degree of alternatives in relation to the fuzzy ideal and fuzzy anti-ideal solutions. A case study on a road network of 7.4 km was made. The method supported multi-criteria decision-making, within uncertain environments and its results, in terms of risk, could be further used for improving road safety. Other similar efficient method used to cope with multi-criteria optimization is described in Dzemyda and Petkus (2001). As a plus, parallel processes, see e.g. Dzemyda (1996), are effective to optimize objective functions.

– A Best-worst method & triangular fuzzy sets by Moslem et al. (2020). It is used for ranking and prioritizing critical driver uncertain behaviour criteria for road safety. The case study uses data from Budapest city: on how drivers perceived road safety issues.

– Intelligent transportation system-Bird Swarm Optimizer by Zhang and Lin (2020). It includes an Improved Bird Swarm Optimizer used to predict traffic flows; the prediction results are evaluated and an accurate prediction is obtained; the model has positive significance to prevent urban traffic congestion.

A distributed approach for time-dependant transport networks integrated in the multimodal transport service of the European Carlink platform and validated in real scenarios, was proposed by Galvez-Fernandez et al. (2009) (Fig. 6). A real-life validation is included for a specific route from a Belgian city Arlon to Luxembourg.

In the related mobile application implementation within MTS of the Carlink Platform, the requests are sent to the MTS and the users get the shortest path between two selected locations. A framework for selecting an optimal multi-modal route was designed by Kengpol et al. (2014) based on a multimodal transport cost-model, CO₂ emissions and even the integrated quantitative risk assessment. This complex optimization targets to minimize transportation costs, transportation time, risk and CO₂ emission all at once. Multi-node, Multi-mode, Multi-path Integrated Optimization Problems using Hybrid heuristics in the work of Kai et al. (2010) are studied. They propose an integrated Particle Swarm Optimization (PSO)-Ant Colony Optimization (ACO) double-layer optimization algorithm.

Hierarchical network structures of transport networks and how the main mechanisms lead to these network structures are the main interests of van Nes (2002). Optimizing Containerized Transport across multiple choice Multimodal Networks using Dynamic Programming was proposed and successfully tested on a real problem by Hao and Yue (2016). Route Optimisation Problem using Genetic Algorithms (GA) was proposed by Jing et al. (2012); the same technique was used to solve a Multi-Objective Transport System by Khan et al. (2019) and could be further extended for the multimodal transport. GA was also used by Kozan and Preston (1999) to optimize the time for container handling/transfer, and, respectively, the time at the port, by speeding up the handling of operations.

As transportation quickly expands worldwide, some existing unimodal transport problems and their solvers could be furthermore extended while including specific requirements to solve multimodal transport problems. Some of these problems are further described briefly.

A. Supply Chain Networks. One of the two-stage supply chain network is considered here to optimize the cost from a manufacturer, to a given number of customers while using a set of distribution centres (Fig. 8).

Models & Solvers: Supply chain for further Multimodal extension.

–

Multi-Objective Goal Programming by Roy et al. (2017). The mathematical model of Two-Stage Multi-Objective Transportation Problem (MOTP) with the use of a utility function for selecting the goals of the objective functions and numeric tests are included; real-world uncertainty with the use of grey parameters (reduced to numbers) are also involved. As for the metrics within objective functions, usually Euclidean distances are used, but today, for urban related ITS, for example, it could be a plus to use city-block distances as in Redondo et al. (2012), where an evolutionary multimodal optimization technique with suitable parameters obtains better results than existing techniques.

Due to its effectiveness many variations of the VRP were built on the basic VRP with extra features, e.g. the Generalized VRP (GVRP), Fig. 8. VRP with time windows and VRP pick-up and delivery problems, e.g. solved by Vaira and Kurasova (2014) with GA insertion operators, can be further extended to related complex problem.

A version of GVRP includes designing optimal delivery or collection routes, subject to capacity restrictions, from a given depot to a number of locations organized in clusters, with exactly one node visited from each cluster. See Ghiani and Improta (2000), Pop et al. (2013) for more details.

Models & Solvers: (G)VRP for further Multimodal extension. –

Capacitated VRP implies that the vehicles have fixed capacities and the locations have fixed demands in time, see Toth and Vigo (2002);

Models & Solvers (G)TSP for further Multimodal extension.

An abstract Formalization of Multimodal Transportation, as a concept, is presented by Ayed et al. (2008). ITS could be expanded by using multi-objective facility location problem models and solvers including heuristics, e.g. Lancinskas et al. (2016).

The graph theory is applied within an algorithm in order to optimize routes and route guidance. The authors try to insert their approach into the Carlink project in order to assess its performance. Cosma et al. (2018) propose an efficient Hybrid Iterated local Search heuristic procedure to obtain high-quality solutions in a reasonable running-time.

The current selective survey presents a review of real-world problems, applications and optimization in the integrative multimodal transportation. Transportation is a key element of today’s society and a very important engine for economic growth. Some areas (like food, medical supplies) raise transportation to strategic importance, and thus indispensable.

The multimodal transport comes with diverse challenges, e.g. related to security, resource saving and reduction of emissions. In the context of today’s accelerated global warming, it is more important than ever to do everything to reduce pollution as much as possible. An example is the green multi-modal transport organization approach presented by Wang et al. (2020a), where the China-Europe railway network is validated, reducing the transportation time, increasing energy conservation and lowering carbon emissions by 40%, when compared with the classical unimodal water transport.

Uncertainties will coexist with the multimodal transportation problem, and as recent (Sharma et al., 2020) research shows, while using road, rail and air transportation, soft sets, for example, could be used to model these uncertainties related to the transportation attributes (cost, distance and duration of transport). Multi-criteria shortest path optimization, including time, travel cost and route length, for the NP-complete bus routing problem as in Widuch (2013) could be further extended for complex ITS problems.

Multimodal transportation research nowadays is a challenge that is being continued, on both theory (e.g. solving complex vehicle routing problem) and applicability, in order to obtain feasible models and solvers for various transportation means on complex conditions, with general and specific attributes.