Optimal competitive freight network design as hierarchical variational inequalities programming problems

Freight networks are a case of systems that multiple participants are composing interrelations along the complete supply chain. Their interrelations correspond to alternative behavior, namely, cooperation, non-cooperation and competition, while they are large-scale spatially distributed systems combining multiple means of transportation and the infrastructure and equipment typically utilized for servicing demand, results to a complex system integration. In this paper, the case of the optimal design of freight networks is investigated, aiming to highlight the particularities emerging in this case of transportation facilities strategic and/or operational planning and the multiple game-theoretic and equilibrium problems that are structured in cascade and in hierarchies. The application that is investigated here focuses in the design of a significant ‘player’ of the freight supply chain, namely container terminals, while the proposed framework will aim on analyzing investment strategies built on integrated demand–supply models and the optimal network design format. The approach will build on the multilevel Mathematical Programming with Equilibrium Constraints (MPECs) formulation, but is further extended to cope with the properties introduced by the ‘designers’ (infrastructure authorities), shippers and carriers competition in all levels of MPECs. Since container terminals are typically competing each other, the nomenclature used here for formulating appropriate MPECs problems are based on hierarchies of Variational Inequalities (VI) problems, able to capture the alternative relationships emerging in realistic freight supply chains. The proposed formulations of the competitive network design case is addressed by a novel approach of co-evolutionary agents, which can be regarded as new in equilibrium estimation. Finally, the results are compared with alternative network design cases, namely the centralized cooperative and exchanging design. Under this analysis it is able to highlight the differences among alternative design cases, but moreover an estimation of the ‘price of anarchy’ in transportation systems design is offered, an element of both theoretical as well as practical relevance.     

Modeling dry-port-based freight distribution planning

In this paper we review the dry port concept and its outfalls in terms of optimal design and management of freight distribution. Some optimization challenges arising from the presence of dry ports in intermodal freight transport systems are presented and discussed. Then we consider the tactical planning problem of defining the optimal routes and schedules for the fleet of vehicles providing transportation services between the terminals of a dry-port-based intermodal system. An original service network design model based on a mixed integer programming mathematical formulation is proposed to solve the considered problem. An experimental framework built upon realistic instances inspired by regional cases is described and the computational results of the model are presented and discussed.     

Joint optimization of freight facility location and pavement infrastructure rehabilitation under network traffic equilibrium

Establishment of industry facilities often induces heavy vehicle traffic that exacerbates congestion and pavement deterioration in the neighboring highway network. While planning facility locations and land use developments, it is important to take into account the routing of freight vehicles, the impact on public traffic, as well as the planning of pavement rehabilitation. This paper presents an integrated facility location model that simultaneously considers traffic routing under congestion and pavement rehabilitation under deterioration. The objective is to minimize the total cost due to facility investment, transportation cost including traffic delay, and pavement life-cycle costs. Building upon analytical results on optimal pavement rehabilitation, the problem is formulated into a bi-level mixed-integer non-linear program (MINLP), with facility location, freight shipment routing and pavement rehabilitation decisions in the upper level and traffic equilibrium in the lower level. This problem is then reformulated into an equivalent single-level MINLP based on Karush–Kuhn–Tucker (KKT) conditions and approximation by piece-wise linear functions. Numerical experiments on hypothetical and empirical network examples are conducted to show performance of the proposed algorithm and to draw managerial insights.     

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.     

Modeling and solving discrete network design problem with stochastic user equilibrium

In this paper, we address the discrete network design problem, which determines the addition of new roads to existing transportation network to optimize the transportation system performance. Road users are assumed to follow the traffic assignment principle of stochastic user equilibrium. A mixed‐integer nonlinear nonconvex problem is developed to model this discrete network design problem with stochastic user equilibrium. The original problem is relaxed into a convex mixed‐integer nonlinear program, whose solution provides a lower bound of the original problem. The relaxed problem is then embedded into two proposed global optimization solution algorithms to obtain the global optimal solution of the problem. Copyright © 2016 John Wiley & Sons, Ltd.     

The impact of collaborative backhaul routing on carbon reduction in the freight industry

The study investigates a practical freight carrier collaboration problem in a carbon-constrained business context. It examines to see if collaboration between carriers can reduce the environmental issues of freight movement. The introduction of carbon credit systems will stimulate freight carriers to decide whether it should trade carbon credits with its collaborators. This issue is examined by formulating the problem as a two-stage stochastic program to minimize the joint emission of the carriers while meeting their service commitments. The collaborative model developed can reduce emissions across a freight network by 3–20%.     

Prediction of intercity freight flows,I: Theory

This paper presents the conceptual framework for a predictive network equilibrium model of a freight transportation system in which the generation, distribution, modal split and assignment of freight movements are performed simultaneously. A neoclassical profit maximization model is stated for the supply-side of the transportation market, the demand-side is represented by a spatial price equilibrium model, and the economic mechanism which integrates the supply and demand submodels is described. The theoretical limitations imposed on the model by the requirement that it be capable of solving large-scale problems are also addressed.     

Improving the energy efficiency of freight in the United States through commodity-based analysis: justification and implementation

Efforts to reduce energy use in freight transportation usually center around “mode-based” approaches, namely improving the energy efficiency of energy intensive modes, such as truck, and shifting more freight to energy efficient modes, such as rail. In the first part of this paper we review the recent trends and future prospects for these mode-based approaches, finding that despite substantial improvement in the technological efficiency of freight modes and robust growth in the use of intermodal rail since 1980, total freight energy use across all modes in the US has grown by approximately 33%, with proportional growth in carbon emissions. In the second part of the paper we propose use of a “commodity-based” approach, in which freight energy use is disaggregated by contribution of major commodity groups, in order to support efficiency improvement at the commodity level. Two potential applications of the commodity based approach, namely (1) life cycle analysis of energy use for major commodity groups and (2) spatial analysis of freight patterns, are demonstrated using the 1993 US Commodity Flow Survey data. Results of these preliminary findings suggest that commodity groups vary widely in the ratio of energy use in production to energy use in transport, and that for many commodity groups, there may be substantial opportunities for saving energy by redistributing flow patterns. Through development of the commodity-based approach, we also identify the collaborative involvement of shippers and carriers as a key point in improving energy efficiency, since it can be used to both make the mode-based approach more effective and address new issues such as the underlying growth in tonne-km. Benefits for air quality and other transportation issues are also discussed.     

Price and frequency competition in freight transportation

This paper develops a simple analytical model of price and frequency competition among freight carriers. In the model, the full price faced by a shipper (a goods producer) includes the actual shipping price plus an inventory holding cost, which is inversely proportional to the frequency of shipments offered by the freight carrier. Taking brand loyalty on the part of shippers into account, competing freight carriers maximize profit by setting prices, frequencies and vehicle carrying capacities. Assuming tractable functional forms, long- and short-run comparative-static results are derived to show how the choice variables are affected by the model’s parameters. The paper also provides an efficiency analysis, comparing the equilibrium to the social optimum, and it attempts to explain the phenomenon of excess capacity in the freight industry.     

Intermodal and international freight network modeling

The authors describe the development and application of a single, integrated digital representation of a multimodal and transcontinental freight transportation network. The network was constructed to support the simulation of some five million origin to destination freight shipments reported as part of the 1997 United States Commodity Flow Survey. The paper focuses on the routing of the tens of thousands of intermodal freight movements reported in this survey. Routings involve different combinations of truck, rail and water transportation. Geographic information systems (GIS) technology was invaluable in the cost-effective construction and maintenance of this network and in the subsequent validation of mode sequences and route selections. However, computationally efficient routing of intermodal freight shipments was found to be most efficiently accomplished outside the GIS. Selection of appropriate intermodal routes required procedures for linking freight origins and destinations to the transportation network, procedures for modeling intermodal terminal transfers and inter-carrier interlining practices, and a procedure for generating multimodal impedance functions to reflect the relative costs of alternative, survey reported mode sequences.     

A green intermodal service network design problem with travel time uncertainty

In a more and more competitive and global world, freight transports have to overcome increasingly long distances while at the same time becoming more reliable. In addition, a raising awareness of the need for environmentally friendly solutions increases the importance of transportation modes other than road. Intermodal transportation, in that regard, allows for the combination of different modes in order to exploit their individual advantages. Intermodal transportation networks offer flexible, robust and environmentally friendly alternatives to transport high volumes of goods over long distances. In order to reflect these advantages, it is the challenge to develop models which both represent multiple modes and their characteristics (e.g., fixed-time schedules and routes) as well as the transhipment between these transportation modes. In this paper, we introduce a Green Intermodal Service Network Design Problem with Travel Time Uncertainty (GISND-TTU) for combined offline intermodal routing decisions of multiple commodities. The proposed stochastic approach allows for the generation of robust transportation plans according to different objectives (i.e., cost, time and greenhouse gas (GHG) emissions) by considering uncertainties in travel times as well as demands with the help of the sample average approximation method. The proposed methodology is applied to a real-world network, which shows the advantages of stochasticity in achieving robust transportation plans.     

Service network design with asset management: Formulations and comparative analyses

In this paper, we address the service network design with asset management problem, which integrates asset management considerations into service network design models for consolidation-based freight carriers. We propose model formulations based on arc variables for both flow and design, as well as formulations with path flow variables and new cycle design variables. Problem instances reflecting actual planning problems are used in the computational study to analyze the strengths and weaknesses of the various model formulations and the impact of asset management considerations on the transportation plan and the computational effort. Experimental results indicate that formulations based on cycle variables outperform traditional arc-based formulations, and that considering asset management issues may significantly impact the outcome of service planning models.     

An intermodal freight transport system for optimal supply chain logistics

Complexity in transport networks evokes the need for instant response to the changing dynamics and uncertainties in the upstream operations, where multiple modes of transport are often available, but rarely used in conjunction. This paper proposes a model for strategic transport planning involving a network wide intermodal transport system. The system determines the spatio-temporal states of road based freight networks (unimodal) and future traffic flow in definite time intervals. This information is processed to devise efficient scheduling plans by coordinating and connecting existing rail transport schedules to road based freight systems (intermodal). The traffic flow estimation is performed by kernel based support vector mechanisms while mixed integer programming (MIP) is used to optimize schedules for intermodal transport network by considering various costs and additional capacity constraints. The model has been successfully applied to an existing Fast Moving Consumer Goods (FMCG) distribution network in India with encouraging results.     

Private road competition and equilibrium with traffic equilibrium constraints

Toll road competition is one of the important issues under a build-operate-transfer (BOT) scheme, which is being encountered nowadays in many cities. When there are two or more competing firms and each firm operates a competitive toll road, their profits are interrelated due to the competitors' choices and demand inter-dependence in the network. In this paper we develop game-theoretic approaches to the study of the road network, on which multiple toll roads are operated by competitive private firms. The strategic interactions and market equilibria among the private firms are analyzed both in determining their supply (road capacity) and price (toll level) over the network. The toll road competition problems in general traffic equilibrium networks are formulated as an equilibrium program with equilibrium constraints or bi-level variational inequalities. Heuristic solution methods are proposed and their convergences are demonstrated with simple network examples. It is shown that private pricing and competition can be both profitable and welfare-improving.     

An agent-based framework for cooperative planning of intermodal freight transport chains

The recent development of Intelligent Transportation Systems offers the possibility of cooperative planning of multi-actor systems in a distributed framework, by enabling prompt exchange of information among actors. This paper proposes a modeling framework for cooperation in intermodal freight transport chains as multi-actor systems. In this framework, the problem of optimizing freight transportation is decomposed into a suitable set of sub-problems, each representing the operations of an actor which are connected using a negotiation scheme. A Discrete Event model is developed which optimizes the system on a rolling horizon basis to account for the dynamics of intermodal freight transport operations. This framework allows for an event driven short/medium term planning of intermodal freight transport chains. The proposed methodology is evaluated using a realistic case study, and the results are compared against the First-Come-First-Served strategy, highlighting the significance of cooperation in systems operating close to capacity.     

A continuous approximation model for time definite many-to-many transportation

Time definite freight transportation carriers provide very reliable scheduled services between origin and destination terminals. They seek to reduce transportation costs through consolidation of shipments at hubs, but are restricted by the high levels of service to provide less circuitous routings. This paper develops a continuous approximation model for time definite transportation from many origins to many destinations. We consider a transportation carrier serving a fixed geographic region in which demand is modeled as a continuous distribution and time definite service levels are imposed by limiting the maximum travel distance via the hub network. Analytical expressions are developed for the optimal number of hubs, hub locations, and transportation costs. Computational results for an analogous discrete demand model are presented to illustrate the behavior observed with the continuous approximation models.     

Intermodal freight transport planning – A receding horizon control approach

This paper investigates intermodal freight transport planning problems among deep-sea terminals and inland terminals in hinterland haulage for a horizontally fully integrated intermodal freight transport operator at the tactical container flow level. An intermodal freight transport network (IFTN) model is first developed to capture the key characteristics of intermodal freight transport such as the modality change phenomena at intermodal terminals, physical capacity constraints of the network, time-dependent transport times on freeways, and time schedules for trains and barges. After that, the intermodal freight transport planning problem is formulated as an optimal intermodal container flow control problem from a system and control perspective with the use of the proposed IFTN model. To deal with the dynamic transport demands and dynamic traffic conditions in the IFTN, a receding horizon intermodal container flow control (RIFC) approach is proposed to control and to reassign intermodal container flows in a receding horizon way. This container flow control approach involves solving linear programming problems and is suited for transport planning on large-sized networks. Both an all-or-nothing approach and the proposed RIFC approach are evaluated through simulation studies. Simulation results show the potential of the proposed RIFC approach.     

Decisionmaking in the motor carrier industry

Distinct discrete decisions made by the same economic actor are likely to be correlated, particularly those decisions involved in transportation demand. These correlations may be due to economic interactions among the decisions, or to heterogeneity, or both. This paper develops an econometric method that can distinguish among these possibilities and applies this method to analyzing motor carrier deregulation. One overall goal of the Motor Carrier Act of 1980, which substantially reduced federal regulation, was to promote greater competition in the industry. Other things equal, the more competition in an industry, the less concentration. However, concentration has been increasing among general freight carriers since deregulation. The positive correlations found between the decisions to acquire broker authority and to be a general freight carrier could be due to joint economies between broker authority and general freight carriage, in which case the two interact as economic complements, or to heterogeneity among motor carrier licensees. In the first case, but not the second, deregulation of broker authority could lead to increased concentration in the general freight sector. Empirically, we find that the decisions are correlated due to heterogeneity, but do not interact. Thus, increased concentration in the general freight sector must be attributed to other causes.     

Transportation policy analysis with a geographic information system: The virtual network of freight transportation in Europe

This paper presents a multi-modal freight transportation model based on a digitized geographic network. A systematic analysis and decomposition of all the transport operations i.e. moving, loading and unloading, transshipping and transiting, leads to the development of a virtual network where each virtual link corresponds to a specific operation, and all transportation modes and means are inter-linked. Software, called NODUS, automatically generates the virtual network so that the model can be conveniently applied to large networks. The analytical structure of the links notation makes it easy to attach specific cost functions to each virtual link. The model is applied to the trans-European freight network of roads, railways and inland waterways for the transportation of wood. Cost functions are built up for each operation by each mode/means combination. A detailed point-to-point origin-destination matrix, calibrated on Eurostat statistics, is generated by a Monte-Carlo technique. Then, the total transportation cost is minimized with respect to the choices of routes, modes and means. This provides estimations of transportation services demands as well as modal splits, to the extent that the two hypotheses of demand based on generalized cost minimization and market contestability are accepted. A sensitivity analysis on the relative road cost is made, which provides measures of arc-elasticities.