Applied Spatial Analysis and Policy

, Volume 11, Issue 4, pp 669–691 | Cite as

Freight Flow Modeling in the United States

  • Frank SouthworthEmail author


This paper overviews the different approaches being used by regional planning agencies to estimate the spatial patterns of freight flows within the United States. The narrative moves from a discussion of current modeling practice to consider how on-going research efforts are moving this practice towards new, improved and increasingly involved modeling frameworks. The discussion emphasizes how data limitations have impacted past and current modeling, and how new data sources can help future efforts. Recent advances in both top-down econometric modeling and bottom-up behavioral modeling are described, both capable of contributing to increasingly complex modeling frameworks in support of broad regional and high volume freight corridor applications. How effective future modeling practice will become will depend on its ability to respond to three areas of concern: the need for improved data quality and access; an improved behavioral understanding of freight agents’ transportation choices; and changes in the nature of freight handling technologies and services as well as in the physical nature of the freight itself.


Freight planning models Freight data needs United states 

Introduction and Motivation

Once considered a neglected stepchild of urban and regional planning models in the United States (US), the past three decades have seen a steady increase in the attention given to estimating and forecasting freight movements, both within and between metropolitan areas. A principal cause of such interest has been the continued growth in the volume of freight being transported, leading agencies at all levels of government to worry about both the carrying capacity and the costs to maintain the nation’s multi-modal transportation networks. With recent federal legislation in the form of the 2012 MAP-21 and 2015 FAST Acts promoting an increasingly quantifiable, performance-based planning and measurement paradigm, freight modeling is seeing more attention than ever before (FHWA 2017a), recognizing that empirically derived statistics alone cannot answer some important questions about how much, where, and when to invest in network capacity expansions or new rule-making initiatives.

Freight flows are spatial movements of goods between shipment origins and destinations, and flow models estimate origin-to-destination (O-D) flow matrices between dozens, sometimes hundreds of traffic analysis zones (TAZs). Depending on the spatial context, such zones may be as small as census blocks or as large as individual counties, metropolitan areas, or even entire states. Flows are usually expressed in terms of tons shipped, dollar values of goods traded, or in the number and class of vehicles or vessels used to transport them; on an annual, seasonal, daily or hourly basis, depending on the specific planning application. To date the major challenge faced by modeling practice (and also theory) has been limited data, which boils down to issues of sample size and coverage in public sector data sources, while competitive concerns over information sharing have resulted in limited access to private sector datasets. The following quote sums up the current situation: “Currently, public sector freight decision-making is largely reliant on datasets that are incomplete, outdated, insufficient, too highly aggregated to permit localized analyses, or simply unavailable” (FHWA Freight Operations Research & Development (R&D) Plan Webinar, July 30, 2015).

Freight planning requires estimates and forecasts of travel activity ‘in the aggregate’; that is, at a level of spatial resolution that allows roadway investment and other decisions to be made on the basis of daily and seasonal traffic volumes. In the US, this means using a mix of federal, state and local government supported data, sometimes supplemented by data from private sector sources. This in turn results in a data fusion exercise that proves difficult to validate on purely statistical grounds, a task hindered by inconsistent data element definitions (across modes of transport as well as across classes of commodities) and, for the purposes of forecasting, by limited access to information on potentially important causal variables. See, for example, the discussions in Transportation Research Board (TRB 2003), Hancock (2006) and Chase et al. (2013). As a result, it can be argued that to date as much modeling effort has been devoted to data gap filling as it has to explaining and projecting future freight flow patterns per se. Where large amounts of public funds may be invested, based (at least in part) on such modeling results, this situation warrants further attention by planners and policy makers, as well as by freight modelers.

To this end, this paper discusses the recent and expected near-term evolution of public agency-developed freight flow models within the US and how new methods and data sources might improve both model relevance and accuracy. It is argued that success will require parallel developments in the use of data modeling techniques that fuse ‘top-down’ methods that apply spatial disaggregation techniques to government funded datasets, with behaviorally and logistically motivated ‘bottom-up’ approaches that rely on the collection and subsequent aggregation of individual survey responses and individually tracked vehicles/cargos in order to meet planning level data needs. Linking these two approaches are concurrent developments in network-based and broadly logistical delivery cost modeling.

The paper is organized as follows. The next section reviews some recent improvements and adaptations to the top-down ‘four-step’ modeling framework currently used by most state and metropolitan planning agencies in the US. This is followed with a section that looks at some recent advances in bottom-up, behaviorally promising freight modeling approaches. As food for further thought, the fourth section completes the review by briefly listing some new freight handling technologies and delivery service options that are likely to offer a significant challenge to future freight forecasting models.

Top-Down Modeling Practice

Four-Step Planning Models

Most US modeling of freight movements has taken place within either a single urbanized area, or within a broader, statewide context. The former, intra-urban modeling has seen its major advances within large, including multi-county, metropolitan areas that fall under the planning umbrella provided by Metropolitan Planning Organizations (MPOs), while the most common applications of broader regional models are overseen by state Departments of Transportation (DOTs). Additionally, there has been a growing interest in modeling freight flows within both multi-state, nationally important freight corridors (FHWA 2017b) as well as multi-metro area linked ‘megaregions’ (Donnelly and Moeckel 2017; Livshits et al. 2017).

To date this modeling has relied heavily on modifications to the traditional ‘four step’ sequential and iterative freight generation (and attraction) – O-D distribution – mode choice-traffic route assignment framework developed in the 1950s to simulate urban, principally passenger traffic flows, notably during commuter-heavy peak traffic periods. Figure 1 shows this framework. The dashed arrow indicates the feedback loop between distribution, mode and route choice used to achieve a balance between flows and costs over these three steps. Metropolitan area freight modeling has used this framework to focus on the simulation of truck movements, with limited attention given to the other modes of transport; while statewide modeling has begun to pay attention to the potential for shifts between different long-haul modes: mainly between truck, rail and water options, with air freight and pipeline products usually treated separately.
Fig. 1

‘Four-step’ transportation planning model framework

A growing variety of additions and modifications to this process are now in use. Descriptions of a number of recent efforts, in both metropolitan area and statewide contexts can be found on the Federal Highway Administration’s TMIP-FMIP website (FHWA 2017d) where links to the most commonly used freight data sources can be found along with a bibliography containing over 800 pre-2014 freight modeling references (both US and non-US). Information on some recent MPO and state DOT efforts to test innovative freight data and modeling options can also be found at the Strategic Highway Research Program’s (SHRP2) Freight Demand Modeling and Data Improvement (C20) website: an activity supported by a partnership between the FHWA, the American Association of State Highway and Transportation Officials (AASHTO) and the Transportation Research Board (TRB) (see Mysore 2015; FHWA 2017d, e).

A recent scan of statewide freight models by Donnelly and Moeckel (2017) found that of the 26 states indicating they model long distance freight flows (out of 47 states responding), 20 made use of some form of commodity flow model. That is, O-D flows are estimated in terms of tons or dollar valued trades rather than vehicle (truck, railcar and barge) trips per se. However, only half of these states reported modeling mode choice, the rest focusing on truck transportation. And of these 13 states, six used simple rule-based applications (e.g. short-distance trips are by truck, long-distance, high value-to-weight freight goes by air) and the rest used logit-based, principally modal ‘diversion’ models that estimate how much (or typically how little) currently reported freight volumes are likely to shift from one mode to another; with two States using a combination of rule-based and logit-based models.

In a more research focused mode of enquiry, different takes on recent US/North American practice over the past decade can also be found in the reports and papers by Pendyala et al. (2000), Southworth (2003), Hancock (2006), Cambridge Systematics Inc (2007), Cambridge Systematics Inc (2008), Cambridge Systematics Inc et al. (2008), Kuzmyak (2008), Chow et al. (2010), Southworth (2011), Zhou and Dai (2012), and Doustmohammadi et al. (2016). The following paragraphs overview some US adaptations to each of the four modeling steps shown in Fig. 1. For comparison, similar modeling issues and approaches to those discussed below, notably where intra-urban goods movements are concerned, are also reported in recent reviews of European modeling (for example, Comi et al. 2012; Gonzalez-Feliu and Routhier 2012; Ben-Akiva et al. 2013; Tavasszy and De Jong 2014).

Freight Generation/Attraction Modeling

Trip Based and Commodity Based Models

Past freight generation (i.e. production) and attraction (i.e. consumption) modeling has progressed along two different lines: direct estimation of the number of vehicles or vessels leaving or entering a facility or analysis zone, versus estimation of the volume of cargo (in tons, dollars, bushels, etc.) originated or received, with subsequent use of cargo-to-vehicle or vessel conversion factors derived from data or from load-factor modeling. Where urban freight modeling is concerned the emphasis has been on truck trip models. Collecting establishment level data for these models is costly and response rates are typically low. Data for heavily used ‘special generators’ such as seaports and inland transshipment centers also requires a different treatment, with time-series data on the other modes (rail, water, air) that receive or deliver cargo proving useful for estimating, for example, the number of truck containers entering or leaving an inter-modal facility (for examples see Fischer and Han 2001, and Southworth 2011).

In contrast, statewide and broader regional, as well as nationwide modeling in the US has begun to favor commodity tonnage or dollar value-based models, with subsequent conversion to vehicle trips at the mode or route choice stage. Following similar developments in Europe, some US States have looked to input-output (I-O) modeling to derive the mix and total dollar-value of commodities produced and consumed within specific counties or TAZs. Given a set of Leontief inter-industry multipliers, amn, the demand for a particular industry m’s output is estimated as:
$$ {\mathrm{X}}_{\mathrm{m}}=\sum \mathrm{n}=1,\mathrm{N}\left({{\mathrm{a}}_{\mathrm{m}\mathrm{n}}}^{\ast }\ {\mathrm{X}}_{\mathrm{n}}\right)+{\mathrm{Y}}_{\mathrm{m}} $$

That is, as the sum of the demands for industry m’s products by all other industries n = 1, 2,…N, plus ‘final demand’, given here as Ym and usually represented as a combination of household and government consumption plus exports. Hence, for forecasting purposes, an increase (decrease) in the final demand for industry m’s products initiates an increase (decrease) in production of the goods and services of its supplying industries, which in turn sets off a chain reaction that results in additional (or fewer) goods and services being required by these supplying industries. The beauty of this approach lies in its ability to account for transactions between all industrial sectors in a national or regional economy. To obtain the volumes of a specific commodity produced or consumed in a region, however, requires a translation from an industry-based to a commodity-based set of inputs and outputs, reflected in what are termed ‘make’ and ‘use’ tables. Sources include a set of national I-O tables provided by the Bureau of Economic Analysis (BEA), as well as tables produced by a number of private vendors.

However, while offering a direct link between economic activity and freight production /consumption, a weakness of this I-O approach is again the spatially aggregate (as well as static) nature of the I-O tables used to generate the coefficients used in Eq. (1). In reality, a good deal of variation in multipliers exists both within some industrial sectors and across different regions.

An alternative approach to estimating freight ‘trip ends’ (i.e. Os and Ds) has been to fit regression models at the level of some rather broad geographic analysis regions. The most common explanatory variables used in these highly data aggregated regressions are resident population and industry-specific employment and earnings or payrolls, with some studies using the Bureau of Economic Analysis inter-industry make and use tables to identify which industries’ employment and earnings estimates to include in their regression equations: especially when trying to associate the often numerous commodities destined for manufacturing industries. The dependent variable is shipper sample-based annual tons or dollars going out of each state or each US Commodity Flow Survey (CFS) analysis zone (of which there are only 132 such zones in the latest, 2012 CFS: see below). See, for example, Parsons Brinckerhoff (2009), Ruan and Lin (2010), Chapter 5 in Cambridge Systematics Inc. et al. (2013), and Oliviera-Neto et al. (2012). Model fits have varied a good deal by commodity class, requiring a mix of methods and data sources to obtain the total dollar value of goods shipped into and out of specific TAZs. Adding further uncertainty to the resulting estimates, subsequent flow distribution modeling needs these regression-model totals to be spatially disaggregated, usually to the county level for statewide modeling. This raises concerns over using results from one level of spatial analysis at a more disaggregate level. In practice, this usually means having to re-adjust the resulting, regression model based county trip end estimates to be compatible with the original, CFS reported regional activity totals. Validating the accuracy of these disaggregated flow totals is then more than a little problematic.

New Microdata Based Models

While none of the above approaches is entirely satisfactory, a recent data-driven development appears to promise improved model accuracy. Pointing out that the number of vehicles or vessels used to move a given amount of cargo is the result of logistical decisions concerning shipment size, frequency of deliveries, and the vehicle/mode used, Holguín-Veras et al. (2017) have recently produced a guidebook containing hundreds of commodity class specific, linear and non-linear regressions in the form of both freight cargo volume and freight trip-based generation and attraction models, also including a set of (largely overlooked to date) service trip regression models: each calibrated using disaggregate, establishment level data, including for the first time, the microdata samples specifically made available for the purpose from the 2007 CFS. That is, models that are validated against a large and diverse establishment-level dataset.

Accounting for Empty Trips

A further data collection or sub-modeling task associated with truck trip generation /attraction models is the estimation of empty vehicle trips. For a mode such as rail, where significant economies of scale are offered by multi-car ‘unit trains’ carrying bulk commodities such as coal and grain, long-distance empty return runs are common, and this is a major cost issue to consider when it comes to mode selection. Similarly, most truck traffic includes empty backhaul and repositioning legs. Data sources for trucking are again the most problematic, especially for urban areas, with the US Census Bureau’s Vehicle Inventory and Use Survey last performed in 2002, requiring States (such as California) to conduct their own survey or search for other sources. Modeling options vary from the use of simple average load factors to more involved estimation procedures including the derivation of multi-stop truck loading factors. See for example Holguín-Veras et al. (2010a) and also Maks Inc. (2016) for the approach used by the FAF4 nationwide highway (truck) network assignment model.

Freight Distribution (O-D) Modeling

Use of Nationwide Freight Flow Datasets

Estimating O-D freight flow volumes remains the most challenging of the four modeling steps shown in Fig. 1. All efforts to date suffer from the ability to collect sufficient spatial detail on the flows at reasonable cost, making it difficult to both calibrate and validate an O-D based demand model’s findings. This data gap is most notable where truck movements are concerned. However, capturing true origin and destination locations for many rail and inland waterway movements is also hindered by a lack of ‘first mile-last mile’ details, many of which involve quite long trucking legs: while railcar waybill data can pose additional problems when interlining between two railroads takes place (cf. Fig. 3). The main source of data on inter-regional freight activity for all modes takes the form of commodity flows. These data are obtained from the shipper establishments sampled by the US Commodity Flow Surveys (CFS) and their subsequent incorporation, along with numerous other carrier and industry-supplied, mode and commodity specific data sources, within the US Department of Transportation’s Freight Analysis Framework (FAF) dataset (BTS 2017a, b). Collected and processed by the US Census Bureau on a 5 year cycle, an often cited limitation of the CFS/FAF, even for statewide flow modeling, is its coarse level of spatial resolution, a limitation of sample size. The latest, Version 4 of the FAF, based on 2012 data, provides a broadly aggregated 132 origin (O) × 132 destination (D) × 43 commodity (C) × 7 primary mode (M) domestic flows matrix, plus flows between these metro area and rest of state TAZs and 8 broadly defined foreign regions (Fig. 2).
Fig. 2

FAF versions 3 and 4 domestic freight analysis regions (see Hwang et al. 2016)

The principal use of FAF by state DOTs and some of the larger MPOs is as a source of external and through-freight flow estimates, as well as a set of trip end control totals on movements between counties both within and across state borders. To date there have been four FAF datasets, the latest representing 2012 flows, so that (despite some changes in TAZs and other definitions), it is beginning to provide a useful time-series of nationwide freight activity. It is important to note, however, that this FAF dataset is itself the solution to a complex fusion of numerous data sources, a combination of shipper establishment and carrier data sampling plus a good deal of modeling to estimate most likely values for many otherwise missing data cells. At the heart of this data fusion exercise is an original to FAF approach that links the results of a log-linear model with an iterative proportional fitting (IPF) procedure that uses information supplied by the model’s maximum likelihood parameters to fill in missing data cells. The flow model is a multiplicative one, converted for computational purposes into a “saturated” log-linear model of the form:
$$ {\displaystyle \begin{array}{c}\mathrm{Ln}\ \left({\mathrm{F}}^{\mathrm{O}\mathrm{D}\mathrm{C}\mathrm{M}}\ \right)={\uplambda}_0+{\uplambda}^{\mathrm{O}}+{\uplambda}^{\mathrm{D}}+{\uplambda}^{\mathrm{C}}+{\uplambda}^{\mathrm{M}}+{\uplambda}^{\mathrm{O}\mathrm{D}}+{\uplambda}^{\mathrm{O}\mathrm{C}}+{\uplambda}^{\mathrm{O}\mathrm{M}}+{\uplambda}^{\mathrm{D}\mathrm{C}}+{\uplambda}^{\mathrm{D}\mathrm{M}}+{\uplambda}^{\mathrm{C}\mathrm{M}}\\ {}+{\uplambda}^{\mathrm{O}\mathrm{D}\mathrm{C}}+{\uplambda}^{\mathrm{O}\mathrm{D}\mathrm{M}}+{\uplambda}^{\mathrm{O}\mathrm{C}\mathrm{M}}+{\uplambda}^{\mathrm{D}\mathrm{C}\mathrm{M}}+{\uplambda}^{\mathrm{O}\mathrm{D}\mathrm{C}\mathrm{M}}\end{array}} $$
where Ln(F ODCM) = the natural log of the annual flow of commodity class C, by mode M, from origin O to destination D, λO = origin O effect; λD = destination D effect; λC = commodity class C effect; λM = mode M effect; and λOD, λODC and λODCM = an origin-destination effect, an origin-destination-commodity effect, and an origin-destination-commodity-mode effect, etc., and λ0 = a “grand mean” scaling parameter.

Flow units are modeled in annual tons shipped, and also in annual dollar value of trades, with post analysis to ensure reasonable dollar/ton commodity flow valuations. The result is a database of over 10.4 million data cells. An iterative proportional fitting (IPF) routine subsequently modifies these results to ensure compliance with all survey reported flow totals, at all levels of empirically reported flow aggregation. Given the limited sample size of the CFS upon which this model is based, a method was devised to identify cells that are most likely to contain missing flow data. In the latest versions of the FAF (i.e. FAF3 and FAF4) additional datasets were brought into this modeling process, notably railcar waybill and waterborne commerce data, to help seed the model with more informed O-D-C-M effects. Complicating the process further, some commodities not covered by the above CFS-based modeling have their flows estimated using conventional spatial interaction models, with their Os and Ds estimated using input-output make and use tables (cf. section above). And the O-D details of both exports, and in particular import shipments also require spatial interaction modeling to link the appropriate seaports to domestic-foreign O-D flows. This somewhat complex data processing program, including procedures to recognize the difference between missing cell values and structurally sensible zero flow cells, is described in Southworth et al. (2011) for FAF3 and Hwang et al. (2016) for FAF4. See also Fullenbaum and Grillo (2016) on FAF forecasting using these flow estimates.

In terms of this present review, the key point is that even this broadly aggregated O-D-C-M flow data is itself the result of extensive ‘data modeling’. While the FAF program arguably provides a more comprehensive perspective on shipper-based, industry and commodity specific freight activity than is found in perhaps any other developed country, and while carrier surveyed rail and waterborne commerce shipments are more easily associated with major rail lines and inland waterways, obtaining and verifying O-D specific data on the nation’s truck movements (representing roughly 63% of the nation’s freight tonnage, and 69% if its dollar value in 2012) continues to present a major challenge, both within and between urban centers (see TRB 2003, and the symposium papers in Hancock 2006 for a good cross-section of still current data gaps).

Spatial Disaggregation Methods

Given FAF-supplied inter-regional flow control totals, the next step for State DOTs and large MPOs is to disaggregate these flows spatially. A common spatial unit for such disaggregations is the county level, with further spatial breakdowns sometime modeled within metro areas or to capture known, heavily trafficked freight producing or receiving sites. A number of approaches to disaggregation have been used, from simple apportioning of freight activity on the basis of industry-cum-commodity defined employment, annual payroll, and resident population, to the use of the above described regression or I-O modeling of trip ends to capture the volume of goods shipped from, say, industry m in origin county i to industry n in destination county j. Here, not only the FAF produced Os and Ds but also FAF O-D flows can be used as control totals on this spatial interaction. For example, for a FAF TAZ with three counties found to supply a given commodity to a FAF TAZ with four counties, we have a 3 × 4 matrix of inter-county flows that can apportioned on the basis of the selected surrogate economic activity variable(s). The resulting allocation is then adjusted to fit the FAF O-D flow total. For large TAZs, distance-impacted transportation costs may be introduced into this process, for example using the doubly constrained form after Wilson (1967):
$$ {\mathrm{T}}_{\mathrm{ijm}}={{\mathrm{A}}_{\mathrm{im}}}^{\ast }\ {{\mathrm{B}}_{\mathrm{jm}}}^{\ast }\ {{\mathrm{O}}_{\mathrm{im}}}^{\ast }\ {{\mathrm{D}}_{\mathrm{jm}}}^{\ast }\ \mathrm{F}\left({\mathrm{c}}_{\mathrm{ijm}}\right) $$

where Tijm = volume of commodity m shipped from i to j, where i and j are two traffic zones in the set of 1,2,,,i,…j,…Z such zones; Oim = volume of commodity m shipped from location (traffic zone; Djm = volume of m received at location j; cijm = the cost of shipping a unit of m from i to j, and F(cijm) = a distance-dependent (e.g. power or negative exponential) function of transportation costs; and the Aim and Bjm terms represent the model’s well known trip end “balancing factors”. The result of combining input-output modeling of trip end Os and Ds with such interaction models results in a series of commodity specific (and commodity separable) inter-regional input-output models, as demonstrated in the often cited textbook by Wilson (1970). US applications of an I-O based approach to inter-regional flow modeling include Kim et al. (2002),  the random-utility-based multiregional input-output (RUBMZIO) model of production, trade, and travel using Texas data described by Zhao and Kockelman (2004) and Kockelman et al. (2005), and Giuliano et al.’s (2007) modeling of Los Angeles highway flows.

Freight Cost Modeling

The cijm cost terms in (3) usually take the form of some linear additive combination of time-plus-distance and load impacted monetary (e.g. fuel + labor + insurance + operation and maintenance) costs, and represent an important modeling task in and of themselves (see, for example, Holguin-Veras 2013). O-D cost data usually comes in one of three forms: from statistical sampling and subsequent averaging of reported trip costs or carrier offered rates, from the development of econometric costing models from this reported data, or, where insufficient sample data exists (as is often the case) from engineering cost models that build up expected transport costs from data on labor, fuel, operation and maintenance, depreciated capital (e.g. vehicle purchase), tolls and tariffs, profit margins, and other commodity class and situation specific movement expenses.

A number of mode specific costing models are publicly available in the US. These include the Surface Transportation Board’s rail rate data supported Uniform Railroad Costing System (URCS) software (STB 2017). The user is responsible for determining the rail line, rail car size and number, commodity type and mileage (origin-to-destination), among other parameters. The model then generates costs based on tonnage shipped. Terminal costs, terminal switching costs, and intermodal costs are also calculated by the program, while ‘special service costs’ are also considered for certain shipping scenarios, including the shipment of automobiles. The US DOT’s ITIC-ST (Intermodal Transportation and Inventory Costing Model State Tool) is also publicly available. It can be used to examine truck and rail shipment details between specific origins and destinations, also considering intermodal transfers between truck and rail (FHWA 2017c). Detailed, average cost item specific per mile trucking cost estimates, principally based on reporting by a large sample of long-haul trucks, are also made available annually by the American Transportation Research Institute (Hooper and Murray 2017). Statistical as well as engineering element based inland barge costing models are produced by the US Army Corps of Engineers (USACE), although generally not so readily available (but see, for example, ORNL 2001).

Some States have also developed freight costing models, usually oriented towards their specific commodities and transportation corridors. Seedah et al. (2014), for example, recently developed a truck-rail intermodal modeling toolkit for the Texas DOT “to help planners equally compare truck and rail freight movements for specific corridors”. With potential for mode shifts in mind, they provide a spreadsheet based toolkit and user manual for computing detailed, component based costs associated with each mode.

Travel demand models are most useful from a policy perspective (and hopefully more accurate also) when using travel cost functions that reflect freight agent (carrier, shipper, customer) values. Here disaggregate, survey response-based bottom-up, utility maximizing models have played an important role, with many past applications building on McFadden’s (1973) multinomial logit formulation. In recent years, this has led to the inclusion of freight on-time service reliability within more traditional freight generalized trip time and monetary operating cost formulas. A number of different ways to measure service (un)reliability have been modeled, and a wide range of delay-based costs obtained, differentiated on the basis of commodity type, distance travelled, and mode used. For example, the generalized cost (GC) of a specific O-D flow might be represented by:
$$ \mathrm{GC}=\upalpha {1}^{\ast }\ \mathrm{Money}\ \mathrm{cost}+\upalpha {2}^{\ast}\mathrm{Travel}\ \mathrm{time}+\upalpha {3}^{\ast }\ \mathrm{Travel}\ \mathrm{time}\ \mathrm{reliability} $$

where α2/α1 represents the monetary value of extra trip time, α3/α1 produces a time reliability-based travel cost, and dividing α3 by α2 produces a “reliability ratio”, which is taken to represent the relative importance of on-time arrival reliability versus expected in-transit shipment time. These models yield a wide range of values of time, with delivery delays costing anywhere from a few dollars to hundreds of dollars per hour (Cambridge Systematics Inc 2008; Cambridge Systematics Inc et al. 2008; Mei and Horowitz 2011; Southworth 2016). Factors affecting such time-costs include the sensitivity of the freight agents involved to a late vehicle arrival time (for pickups as well as deliveries), the nature of the commodity shipped, shipment distance and trip duration, the type of vehicle used, the type of contractual arrangements involved, and the nature and extent to which traffic-related delays are present.

Over the past decade of good deal of research has looked into ways to best measure reliability, including statistical range methods, buffer time methods, probabilistic and tardy trip measures: this last including such measures as the ‘misery index’, which compares the average travel time over all reported trips with the average of the worst 20% of trip times (see, for other examples, Lomax et al. 2003; TTI/CSI 2006; Southworth and Gillett 2011). However, as this literature demonstrates, inconsistency can exist between these different measures when applied to the same dataset. This is problematic, as on-time service reliability can play an important role in the choice of both freight carriers and suppliers, and in some instances in the choice of mode as well as route taken. Compounding the problem, different data collection methods may produce different results. An increasingly attractive approach from which to infer the variability in trip times, on both a cost-savings and non-intrusion basis, is to use GPS tracking of individual vehicle trips based on weeks or months of reporting across major corridors or planning regions (see Short 2014 and FHWA 2017a for GPS data used in trucking). However, the importance of such delays to the agents involved is less easily determined.

To date no standard method for measuring the monetary impacts of travel service unreliability on mode choice has been adopted, either in the US or elsewhere. Indeed carrier, shipper and customer perceptions about various logistics-impacting cost changes can be expected to differ, each driven by their own business-sensitive profit motives. Interviews with freight agents testify to the often considerable importance of service reliability in making mode selections (FHWA 2010; Kittelson and Associates Inc. 2014). In particular, any unexpected or un-planned-for cost changes may affect different agents in different ways. A number of studies have used stated preference sampling of shipper or carrier responses to ask questions about possible hypothetical shipment alternatives (e.g. a faster trip versus a less expensive one) with the design of such surveys itself something of a challenge (see, for example, Gong et al. 2012). This leads into a topic of growing interest: the effects on product supply chains and their influence on both short and longer term freight flow patterns due to significant freight network disruptions (GTRI et al 2012). The observable effects of such disruptions to service are often the most accessible way to gauge freight system sensitivity to changing business conditions, albeit under more extreme than usual circumstances.

‘Link-OD’ Models

Efforts to improve the accuracy of aggregate O-D flow models include modifying the interaction matrices from distribution models to better align with the only wide area truck movement data available to most State DOTs and MPO: traffic counts. While model formulations are very much application specific, most of these ‘link-OD models’ can be expressed as special cases of the following general optimization model (Southworth 2011):
$$ \operatorname{Minimize}\ \mathrm{F}\left({\underline {\mathrm{T},\mathrm{T}}}^{'}\right)+\mathrm{F}\left({\underline {\mathrm{V},\mathrm{V}}}^{'}\right) $$
subject to:
$$ \mathrm{V}=\mathrm{M}\left(\mathrm{T}\right) $$

a vector of observed O-D freight flows (converted from commodity dollars or tons to equivalent truck trips);


an observed set of network link or terminal specific freight traffic volume or throughput measures;

T’, V

the model estimated versions of T and V;


a ‘mapping’ between V and T; and

F(T,T’) and F(V,V

refer to measures of the differences in the values of the observed versus model estimated O-D flows and site specific traffic volume counts, respectively.

In practice the amount of importance placed on both truck counts and O-D flow estimates can be adjusted to reflect the level of confidence in either type of input: noting that count data is itself subject to hour-to-hour and day-to-day variability, and sometimes also measurement errors. Recent U.S. applications to truck O-D matrix estimation include the work of Horowitz (2010) and Jansuwan et al. (2016).

Direct Demand and Structural Equation Modeling (SEMs)

Recent promise has also been achieved at the level of top-down, notably statewide O-D flow estimation via the use of ‘direct demand models’. Applications in the US include its use by Vaddepalli et al. (2004) to simultaneously model O-D flow volumes and their associated modal splits within the state of Florida, and more recently by Ritchie et al. (2013) and Ranaiefar et al. (2013, 2014) to model trip generation, attraction, and O-D flow volumes for the California DOT. These latter authors have built the SEMCOD model, a multi-commodity direct demand model with a structural equation modeling (SEM) framework that allows endogenous variables to serve as causal variables for other endogenous variables. Of particular interest is the ability of models such as SEMCOD to simultaneously calibrate the impacts of cost or other market changes on both the trip generation (how much to ship) and distribution (where and how far to ship): something that proves to be a weakness in four step models which traditionally have not linked transportation cost impacts back to the trip generation step (either because there was no strong, direct linkage exhibited by the passenger flow models for which the framework was principally designed, or because of data limitations, or both). In its translog (second order log) form, a SEM also supports readily interpretable demand elasticities, allowing, for example, the activity in one industrial or commodity-driven sector to influence another, either directly and indirectly, in effect inferring the unobserved supply chain relationships between one sector and another at an aggregate level, and offering in some cases improved fits to freight generation models applied to aggregate data sources (see Ranaiefar et al. 2013).

Developed around Citilabs’ Cube software, this direct demand approach has become a component of the recently developed California Statewide Freight Forecasting Model (CSFFM) (Ritchie et al. 2013) which contains a number of novel advances in both model formulations and data sources. The modeling framework is composed of a top down FAF-disaggregated and commodity-based freight generation and distribution direct demand/SEM Module, a Mode Split Module composed of separate domestic, import and export, O-D and commodity class specific aggregate logit share equations, a Transshipment Module for truck-rail and truck-air intermodal O-Ds, a Seasonality and Payload Factor Module, an inventory theory based microsimulation to break down the model’s aggregate annual commodity flows into annual and daily firm-to-firm truck flows; a Network Module that carries out highway multi-vehicle class and rail all-or-nothing route assignments, the former making use of ATRI supplied GPS truck data; and a Model Validation Module that makes use of different national and regional sources of data on location-specific truck counts, truck weigh-in-motion, vehicle classification and payload data, sample GPS truck routings, and railcar waybill data (Ritchie et al. 2013).

Freight Modal Choice Modeling

Logits and Other Discrete Choice Models

Modal choice, or mode split, modeling also continues to present a challenge, facing difficulties due to well-known modal agency ‘data silos’ that rely on different commodity class definitions. Assigning consistently derived total logistics based operating costs to modal options, especially to inter-modal options, presents a further challenge. Binary logits and probits, multinomial, nested and mixed logit and also tobit models have all been tried, making use of either aggregate share based data sources, including FAF data applied to long haul mode choice, or using individual survey respondents’ data to calibrate the relationship between mode selection and variously quantified delivery times and costs. Example aggregate modal share models include the truck-rail versus truck-waterway logit regressions reported by Southworth et al. (2007) for wheat shipments through the Pacific Northwest, the binary logit and linear regression models applied to cereal grain shipment choices between truck and rail by Shen and Wang (2012), the commodity specific logit regressions of freight moving into, out of and through the state of Maryland by Mishra et al. (2013) and by Wang et al. (2013), and the above referenced California model (Ritchie et al. 2013). Examples of disaggregate mode choice models include the studies by Train and Wilson (2006) and Samimi et al. (2011, 2014). Survey instruments dedicated to specific commodities and regions offer the best datasets to date. For example, Train and Wilson use a combination of stated and revealed preference data from a dedicated shipper survey to calibrate a multinomial logit model of rail, river barge, truck-rail and truck-barge shipments paralleling the Columbia River, with freight rates, transit times and service reliability all showing up as significant modal choice factors: and with reliability measured as the percentage of times shippers perceived their shipments to arrive on time at final destination.

Efforts to expand survey instruments to other freight agents or broader geographic areas have run into low response rates. Samimi et al. (2011) obtained establishment and shipment details from a sample of 316 shippers, receivers and third party logistics (3PL) brokers to calibrate binary logit and probit models of truck versus rail choice, with shipment weight and value as well as mode-specific haulage times and monetary costs all found to influence mode selection. However, their on-line survey obtained only a 7% response rate, showing how difficult it is to obtain such information, and how important the FAF and other federally supported datasets are to current freight modeling exercises. As with trucking, Global Positioning System (GPS) tracking data as well as cellular communications, active radio frequency identification (RFID) devices and bar code readers all offer promising data sources from which to capture daily vehicle routings as well as stop activity durations and in transit travel speeds across all modes and broader geographies, although these sources of information have seen limited application within operational freight planning models to date.

Joint Mode and Shipment Size Modeling

In conjunction with the growing attention given to freight logistics costs and how they vary by vehicle or vessel configurations, mode selection is increasingly linked to within-mode shipment size issues. For example Pourabdollahi et al. (2013) used data collected from a nationwide establishment survey (yielding 1003 responses) to apply an Archimedean copula function to link these two interdependent choices. And recently Stinson et al. (2017) applied 2012 CFS microdata (cf. earlier section) for the Phoenix and Tucson, Arizona mega-region within a logit model in which shipment size options are nested within the choice of each primary mode (i.e. of truck, rail and parcel/air).

Freight Traffic Assignment (Route Choice) Modeling

Assigning mode specific traffic volumes to routes across a region’s highway /railway/ waterway networks first of all requires that O-D commodity flows be converted into the numbers of mode-specific vehicles (trucks, railcars, barges, …) needed to transport them. For the purposes of model validation, this routing step can draw on network link specific truck size class counts, as well as commodity and vehicle/vessel class counts for rail (STB) and inland waterways (US Army Corps of Engineers). These are the same counts discussed above under Link-OD modeling. However, while useful for helping to both adjust and validate the results of traffic routing models, a challenge for freight planning, notably forecasting, is to match these network assigned ‘link counts’ to the specific O-D flows that produce them. A number of off-the-shelf stochastic, equilibrium, multi-vehicle class, static and dynamic assignment models now exist for doing this, each capable of reflecting the impacts of traffic congestion on route choices and journey times. These include the often used TransCAD (Caliper Corporation 2018), Cube (Citilabs 2018) and also EMME (INRO 2018) software programs. The present author used Caliper Corporation’s origin constrained multi-class equilibrium assignment model and its GIS-supported select link analysis tool to identify the connection between a network link’s assigned traffic and the likely set of O-D specific truck flows that are routed over it (Southworth and Smith 2016).

Long-Haul Multi-Modal Freight Corridor Modeling

Where a limited number of non-highway routing options exist between a region’s major O-D pairs, an alternative approach for long haul freight modeling is to replace the sequential mode and route choice models with a joint mode-route selection model, a technique that may be useful when studying modal competition along specific long distance corridors. However estimated, obtaining additional information on stakeholder (shipper, carrier, final customer) preferences for alternative modes is needed, including insights into how such freight agents base their modal choices on past experience with, and perceived business benefits obtainable from, such modal shifts. While such information has been difficult to come by, one of the more important advances in recent years has been the added attention given to the full range of freight handling costs involved: including ‘first mile-last mile’ loading and unloading costs, cargo transfer costs incurred at truck freight distribution centers (DCs) and inter-modal transfers at truck-rail, truck-water, rail-water and truck-airport and terminals. This may include delays due to paperwork snafus or insufficient in place cargo handling assets such as docking spaces, containers, chassis, operating cranes or other essential freight handling equipment. A number of different multi-modal network formulations (i.e. network data models) offer complex multi-link representations of such cargo handling cost elements as part of the freight routing process. The most popular method is to assign different costs to both physical and notional network links, allowing simple summation over all within-route links to get O-to-D costs. In the US, at least one public domain and nationwide network database, produced originally for CFS shipment record routing and subsequent ton-mileage calculations by Oak Ridge National Laboratory, is available for this purpose (see Fig. 3, and Southworth and Peterson 2002).
Fig. 3

Example intermodal (truck-rail-truck) link-based network cost modeling

Bottom-Up Modeling: Agent-Based and Microsimulation-Based Supply Chains

While most of the above described model developments can be fit into extended versions of the traditional four step planning model framework shown in Fig. 1, a number of recent developments suggest that freight planning models will gradually move towards more complex, multi-step data collection-cum-analysis frameworks. The search for behavioral realism suggests that bottom-up, disaggregate modeling approaches are likely to play a large part in these new modeling frameworks. Three connected lines of model development that show considerable promise, especially when combined within a single planning model are micro-simulation of individual vehicle and vessel movements, agent-based activity decision modeling, and the placing of freight activity within product supply chain logic: with subsequent aggregation of model generated flows to levels of spatial resolution of interest to planners.

Agent-Based Modeling

Current freight flow forecasts suffer from a limited understanding of how the various freight agents’ motivations translate into freight activity outcomes: a condition that Donnelly et al. (2010, p. 26) associate with “the paucity of spatially indexed behavioral data”. This is a challenge compounded by the many different types of freight agent potentially involved in a shipment, i.e. carriers, shippers, brokers, warehousers, port and terminal operators, and customers, each with their own business goals and stakeholder interests, and each subject to government regulations as well as industry/commodity specific supply chain and associated logistical/delivery cost complexities (Fig. 4).
Fig. 4

Agents involved in freight supply chains

A promising approach here is agent-based modeling (ABM) (for a primer, see Zheng et al. 2013) which seeks to bring more behavioral realism into the estimation and forecasting process by incorporating the different objectives and value judgements displayed by these different classes of freight agents. A major research and development task involves finding a way to represent these agent-specific decision-making practices, using either rule-based profit maximizing, or some other decision making concepts. For example, what sort of information do shippers, carriers or receivers use to assess their business options, and under what circumstances do freight brokers enter and influence this goods movement process?

Given the complexity and variety of possible responses to such a question, summations over large numbers of micro-analytically simulated, agent-directed trip making activities offers one way to build up a set of planning level freight flows: guided by specific rule-based logic, with simulated actions based on either direct sampling from agent survey responses, or from the probabilities generated by survey respondent-based utility maximizing demand models that reflect the stated or perceived importance of time, cost, service reliability and any other factors found to influence freight flow decision-making. While most of the research papers on this topic to date come from Europe, some recent ABM efforts in the US also show promise. See, for example, Livshits et al.'s (2017) mega-region modeling of freight flows in  Arizona, and RSG et al.'s (2015) and Pourabdollahi et al.'s (2017) agent-based modeling for the Chicago region.  These studies tend to place ABM modeling of specific transport choices within broader, multi-step flow forecasting frameworks: either adding to or moving increasingly away from the traditional iterative four-step framework described in the previous section.

Capturing Supply Chain Effects

A second promising direction for freight models is their incorporation of supply chain logic within their estimation process. According to the Canadian Supply Chain Logistics Council ( a supply chain is “a system of organizations, people, activities, information, and resources involved in moving a product or service from supplier to customer”. When applied to freight transportation specifically Tatineni and Demetsky (2005) offer a useful scoping of the activities that need to be modeled, referring to supply chain management a set of functions “including demand forecasting, sourcing and procurement, coordinating the manufacturing activities and logistics management”, with this last defined as the process of managing the physical distribution of goods in a firm, and which in turn involves managing the inbound and outbound movements along with the firm’s inventory. Efforts to introduce such ideas into practice, making use of both micro-simulation and agent-based methods in the process, are now beginning to enter planning practice.

For example, RSG Inc. et al. (2015) describe how the Chicago Metropolitan Agency for Planning (CMAP) has invested in an agent-based supply chain model that synthesizes a database of individual firms within analysis zones across the entire US. In this model (see also Gliebe et al. 2013; Outwater et al. 2013), firms within the region attempt to fulfill their production needs by purchasing input commodities from other (US and foreign) firms that sell the commodity they need. For each commodity market an iterative ‘procurement market game’ is played in which a pool of buyers attempt to procure inputs from a pool of sellers. An agent-based simulation matches consumers and producers of commodities, accounting for tradeoffs in cost, supplier responsiveness, risk and other factors, such as past experience. As an input to the game is the results of a transport-logistics chain model that simulate the choice of distribution channel, shipment size (weight) and mode for each prospective buyer-supplier pair, thereby enabling the calculation of logistics costs and shipping times for those O-D flows. Four primary modes (road, rail, air, and water) are modeled, and four types of distribution channel are identified – direct, one, two and three stop types, where stop type is a warehouse, distribution center or consolidation center, with selection determined by firm size and industry type. After an acceptable solution to the buyer-seller matching game has been simulated and the freight converted into vehicle loads, these vehicles can then be assigned to their respective modal networks, which in the case of truck movements may involve micro-simulating a multi-stop tour containing two or more truck O-Ds. See also Nagurney et al. (2002) and Xu et al. (2003) for an ambitious (if as yet data restricted) approach to supply chain modeling at the enterprise level, linking transportation, informational and financial network aspects of supply chain devlopment. 

In a similar vein, but using a different collection of methods, Livshits et al. (2017) describe a data-driven modeling system to micro-simulate commodity O-Ds to, from, and within the Phoenix and Tucson Megaregion in the southwestern U.S. See also Stinson et al. (2017) and Hong et al. (2017). First, firm based agents are synthesized by combining various location and industrial sector specific attributes from available aggregate data sources. Firms are then clustered and their suppliers selected. Creation of supplier-buyer pairs is based here on an agent-based computational economics approach, using a Roth and Peranson auctioning algorithm to allocate buyers to suppliers based on a set of buyer-supplier preference scores. Next, annual commodity flows for each supplier-buyer pair are chosen and broken into individual shipments for each supplier-buyer pair. Mode choice is then modeled for each shipment before assignment of vehicles to the transportation network. A disaggregate nested logit model is used to estimate mode choice and shipment size, and the choice of vehicle type and various (truck) tour options, including transload points are evaluated before generating individual shipments to be routed in a traffic assignment model. Truck, rail, air and parcel modes are included in the model.

Tour Based Truck Trip Models

Both of the above modeling frameworks incorporate the simulation of multiple pickup and drop urban truck tours. GPS tracking is becoming an increasingly important data source for such models, especially for tracking daily urban trucking activity. While bulk commodities such as those transported by dump trucks commonly involve direct trips to and from work sites, many types of freight are delivered via daily multi-stop pickup-and-drop circuits. This includes household-destined or office-serving activities, from overnight parcel deliveries to residential garbage removal. These daily truck delivery tours, or circuits, make significant contributions to urban vehicle miles of travel and so being able to reproduce them is important not just for estimating highway use, but also for estimating the average and marginal costs of such movements (see, for example, Figliozzi 2010). While the idea of using such tour data within logit demand models has been around for some time (see Southworth 1982), the availability of GPS data is starting to offer improved modeling options as an alternative or, preferably, a supplement to the more expensive truck driver or establishment based survey instruments.

While gaining sufficient data to directly aggregate to observed traffic volumes remains a future possibility for most cities, a good deal of information can already be obtained that is useful for simulating individual daily vehicle activity patterns based on statistics such as the number of stops and range of daily miles covered per vehicle, possibly broken down by vehicle or industry/commodity class. Holguín-Veras et al. (2010b) provided an early example of combining GPS positioning truck data with a survey instrument adapted to elicit the opinions of freight carriers (management and drivers) and receivers in New York. Other examples of tour based micro-simulation include: the establishment survey based modeling in Canada and the US by Hunt and colleagues, including Gliebe et al.’s (2007) study for the Ohio DOT’s statewide model; the Freight Activity Microsimulation Estimator (FAME) modeling framework developed by Samimi et al. (2010); Ruan et al.’s (2012) modeling of truck tours in Texas cities; Outwater et al.’s (2013) urban freight modeling work for Chicago, Illinois; and Lee and Ross’s (2016) use of GPS tracking of truck tours in Atlanta, Georgia and Birmingham, Alabama. In this last study, for example, multinomial logit models were used to first of all identify primary tour destinations, then select the number and location of each intermediate destination between a tour origin and this primary destination, using 8 weeks of GPS data from 5000 different trucks to generate data on tour start times, distances, durations, locations and numbers of stops per tour.

Modeling Future Freight Flows: Hopes and Concerns

As demonstrated by California’s Statewide Freight Forecasting Model, as well as the Chicago and Phoenix-Tucson MPO models, the traditional four-step transportation planning model is starting to be replaced by more elaborate multi-stage simulation models of both the top down and bottom up variety: with a mix of both approaches likely to become the future norm. The high, and no doubt much higher speed of future computing make microsimulation based models increasingly attractive. Future models should get a significant boost from a variety of automated identification technologies, including expanded utilization of GPS satellite and cellular tower based vehicle tracking, and the use of bar codes, magnetic strips, integrated circuit cards, optical laser discs, and RFID tags for marking or ‘tagging’ individual cargo items, equipment, pallets, or containers: across all of the primary freight modes. GPS data in particular offers a very promising data source for truck flow model validation purposes: and not only for showing truck routing choices and minute by minute link-specific travel speeds, but also for locating overnight truck positioning as an aid to truck trip generation modeling. To gain insights into how future freight activity patterns are likely to evolve, however, will also require in-depth information gathering via survey instruments and expert freight agent panels, encompassing stated as well as revealed freight service delivery preferences. Forecasting cannot rely on current activity measures alone.

Making forecasting more challenging, however, will be changes in the freight industry. While warranting a paper devoted entirely to these anticipated changes, a shortlist should include the impacts of at least three areas of concern: new freight handling technologies; new freight products; and new types of industry-supporting financial, informational and communication technologies and services. The use of fuel cell and electric powered trucks and bicycles for urban pickup and drop services, drones for rural deliveries, and the long haul economies offered by semi-autonomous and connected truck platoons, megaships, and possibly airships (balloons) are all possibilities. The expanded use of robotics and other advances in cargo lifting, transfer and storage at ports and intermodal terminals also appear likely to play a role in the not too distant future of freight transportation. And all of the above options are likely to be impacted by the evolution of energy storage technologies applied to the transportation sector. As a result O-D shipment costs are likely to change a good deal as some of these technologies gain significant market penetration, affecting mode choices as well as flow volumes.

The nature as well as value and volume of the freight itself is also likely to continue to change. New production methods such as additive manufacturing (or 3-D printing) suggest potential substitutions for different types of intermediate (between raw material and finished) products, with the potential to radically alter the transportation needs and plant location practices of some industrial sectors. New types of for-hire freight delivery service are also likely to emerge, in part to meet the demands for these new and more cost-effectively transportable products. One example is the use of grocery or small equipment delivery centers made up of firm or household rented delivery boxes, as an alternative to traditional store pickups and home or office deliveries. Internet scheduled, direct-from-distribution center deliveries are another trend worth tracking. Regulations permitting, future intra-urban mixed passenger and freight delivery services might also see a rise in popularity. Effective freight forecasting models would do well to consider the potential for, and impacts of, different market penetration levels associated with such technology-driven freight services, before they become part of the new freight normal.


Compliance with Ethical Standards

Conflict of Interest

The author declares that he has no conflict of interest.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.School of Civil and Environmental EngineeringGeorgia Institute of TechnologyAtlantaUSA

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