This section provides the summary of literature on freight mode choice. The publications on freight mode choice are divided into: econometric modeling and supply chain modeling. Of these two approaches, econometric modeling is widely used, and also recommended for analyzing freight mode choice policies. Econometric modeling was also recommended by various publications. For example, these two approaches were compared by Gray (1982), which recommends the econometric approach because of the physical restrictions and obligations from the optimization techniques, and the importance of loyalty between the shipper/carrier and receiver on mode choice that could be captured by the econometric models. Winston (1983) compared the model significance produced by econometric methods (aggregate, and disaggregate) and optimization models. He concluded that the disaggregate data would produce a better model as it could capture the finite-level details affecting the modal choice. The sections below provide a brief review of the relevant literature.

**Econometric Modeling**

McGinnis et al. (1981) analyzed freight mode choice using a one-way analysis of variance (ANOVA) and MNL on a group of shippers. The authors found that the shippers that use for-hire truckload shippers do not transport high-value products, but assign a big importance to special services (diversion, stop-off privileges, and processing en route), and damage of goods. Shippers using Less than a Truckload (LTL) tend to ship smaller quantities and give more importance to speed and reliability, and are also concerned with loss and damage of goods. Rail-dominant users attach a big importance to freight rates and availability of special services; the products they ship are usually not fragile and are shipped in larger quantities. Parcel shippers tend to utilize small package services with high product values, so they give lower importance to freight rates and to loss and damage than do users of other modes. Finally, in the case of private carriage shippers, who tend to have fragile products that are difficult to handle, and a high proportion of intra-company shipments, these types of shippers place a great deal of importance on speed and reliability. Winston (1981) used a binary probit model to study mode choice and elasticities, and concluded that shippers of perishable goods and their supporting goods, such as packing materials and metals, give high priority to the quality of a mode’s services. As the travel time of the mode increases, the firm’s inventory cost also increases. The traffic is more elastic to price than service quality for goods with large transportation costs, whereas agricultural products and chemical petroleum products would display a huge modal change to rail with an increase in the quality of service.

Young et al. (1982) analyzed the predominant variables affecting mode choice using an Elimination-by-Aspects model for shippers including manufacturers, and non-manufacturers. For a typical shipper, the most significant attributes that influence a choice of rail are convenience, damage, reliability, capacity and freight rates. Young et al. (1982) concluded that reliability is most significant for manufacturers, whereas capacity and freight rate are the most significant factors for non-manufacturers. Winston (1983) provided a detailed review of freight mode choice modeling techniques, aggregate and disaggregate models. He concluded that the disaggregate models provide more accurate analysis, and an estimate of user satisfaction for a given mode, depending on the availability of data.

McFadden et al. (1986) was the first to analyze shipment size and mode choice simultaneously using a discrete-continuous model using produce transportation data. McFadden et al. (1986) found that shipment size is dependent on the attributes of the modes, such as freight rate, transit time, frequency and reliability. In policy-induced mode shifts, the total logistics pattern will be affected, so the shipment size will need to be adjusted to be compatible with the new mode. The authors conclude that in markets dominated by motor carriers, diversion to rail can be achieved by sizeable improvements in transit time, along with fixing the rates in response to market demand. Wilson et al. (1986) used linear logit models to examine the factors that influence the mode choice decisions for the alternatives of hired truck, private truck, and rail. Mode choice is affected by transit time, reliability in transit time, and length of hauls. Rail is more likely to be selected for long hauls and truck for short hauls; this is consistent with expected shipper behavior. As frequency increases, there is a move away from hired truck to private truck. The provision of pickup services and shipment-tracking promotes the use of rail. Intercept terms of private truck and rail had the highest explanatory power, implying that factors not considered in the model are influencing choices.

Abdelwahab and Sargious (1990) explained the use of instrumental variable approaches to the discrete-continuous choice model for the choices of mode and shipment size, while Abdelwahab and Sargious (1991) provided two alternative estimation methods that can be modeled with data similar to that of a conventional mode choice model. The two alternative estimation methods are: simultaneous equation model, which uses two equations to predict shipment size by each mode and a third equation to predict the choice of mode; and two-stage least squares (TSLS) estimation, which uses maximum likelihood probit to estimate the mode choice and ordinary least squares (OLS) to estimate shipment size. Similarly, Abdelwahab and Sargious (1992) provided the three-equation model i.e., two equations from TSLS for shipment size in trucks and rail, and one equation from a binary probit model to identify the mode by which the shipment was transported. The results of cross-elasticities indicated the existence of some degree of competition between the two modes, which seemed to intensify as the direct elasticities of demand for either mode increases. Nam (1997) found that the disaggregate models by commodity type produce better estimates for freight mode choice. Jiang et al. (1999) used a nested logit model to analyze the mode choice, and found that with an increase in transportation distance and shipment frequency, the probability of choosing rail and combined modes increases, and an increase in the shipment size leads to an increase in the probability of choosing rail.

Holguín-Veras (2002) used a discrete continuous model with shipment size as the continuous variable, distance as the instrument, an MNL model for the choice of vehicle (truck type), and calculated elasticities calculated using both MNL and Heteroscedastic Extreme Value (HEV) methods (Bhat 1995). The results suggest that carriers chose pick-ups or trucks more often than semi-trailers. Any change in the cost or shipment size in trucks affects the market share of other modes negatively. Imposing permissible axle load limits causes more congestion due to the increased number of pick-ups. This paper emphasizes the limitations of commodity-based models, as they do not account for empty trips, which comprise 15-40% of total trips (Holguín-Veras 1984). Kim (2002) used inherent random heterogeneity logit models to assess the effect of cost, arrival time, and reliability on selecting the preferred mode among ferry, new ferry, shuttle and through rail. Norojono and Young (2003) analyzed the hierarchical preference data using a nested logit (NL) model and heteroscedastic extreme value (HEV) model to analyze the final results. The authors found that users give more emphasis to delivery time and safety (quality). Time of departure and distance to rail terminal are not significant. Rail mode is more elastic to cost and time, which may explain the greater decrease in rail mode compared to trucks.

Train and Wilson (2006) improved the existing aggregate models used by Army Corps of Engineers (ACE) to estimate shippers’ choice between rail and barge, by replacing them with disaggregate MNL models that include spatial effects. The authors found that rate, transit times and reliability have statistically significant effects on choices, and a number of unobserved characteristics have important effects. Shippers located close to the river are more likely to use the river as opposed to rail, and as the distance from the river increases, shippers switch to rail. Arunotayanun and Polak (2007) used a mixed multinomial logit model to analyze the data for random taste heterogeneity and panel effects, for three modes: small truck, large truck and rail. Results indicated that electronic commodities are not sensitive to either cost or time; leather commodities are not sensitive to cost, and only moderately sensitive to time. Departure time is a significant attribute for electronics, whereas train formation is significant in the case of food. Food and electronic commodities are sensitive to frequency of service in terms of small trucks, and textiles are sensitive to frequency of service in terms of rail. The authors revealed the existence of significant amounts of taste heterogeneity amongst shippers in relation to service attributes, quality and flexibility. Patterson et al. (2007) analyzed freight mode choice accounting for random effect using mixed logit model, and found that increases in cost, damage risk and security risk decrease the probability that a carrier is chosen, while an increase in on-time reliability increases that probability. The authors concluded that shippers are very mistrustful of using rail to move their consignments, so increasing rail market share may be tremendously challenging.

Cavalcante and Roorda (2010) used a discrete-continuous model with shipment size as the continuous variable, and vehicle-type as the discrete variable. The results indicated that small vehicles are more likely to be chosen for higher value, time sensitive shipments, and services (as opposed to goods shipments), as well as for larger vehicles for long distance shipments. De Jong (2009) concluded that discrete-continuous is the preferred model, and that discrete-discrete model might be preferable when there is no data available, and the model that assumes independence of mode and shipment is not preferred. Samimi et al. (2011) examined the competition between truck and rail for a given commodity movement, using binary choice (probit and logit) models. Rail is preferred for longer distances and large shipments. Rail is found to be more sensitive to cost, whereas truck shippers are found to be sensitive to shipping time. The shippers, who chose truck two years ago, are less likely to choose rail over truck and the coclusion is drawn that the modal decisions with respect to fuel cost are inelastic. Pourabdollahi et al. (2013) used MNL-MNL copula expression to derive the probabilities of choosing a mode and shipment size. The results indicate that shipping cost is the most significant variable. Lloret-Batlle and Combes (2013) showed that the Box-Cox transformation to density times the air distance, which covers an extremely large range of values, improved the likelihood function substantially. Abate and de Jong (2014) investigated the allocation of different truck sizes, and the factors affecting the allocation. A discrete choice continuous model with shipment size as the continuous variable is used using Multinomial Logit (MNL) model. The choice of vehicle includes the five truck types of increasing capacities. As an extension to Holguín-Veras (2002), this paper introduces a cross-alternative correlation parameter assuming normally distributed disturbances, to overcome the IIA assumption in MNL. The results were verified by a nested logit with rigid trucks grouped in one nest. The probability of choosing heavy vehicles decreases with an increase in the fixed costs or vehicle age, and will increase with an increase in the distance or fleet. Whether the carrier is an owner or hired is also significant in vehicle choice, as hired vehicles can aggregate the demand.

**Supply Chain Modeling**

In addition to ITIC model, there are a number of publications that use supply chain or inventory theory methods. For example, Baumol and Vinoud (1970) combined standard inventory theory with the abstract mode technique to estimate freight demand for various modes. The method used by Baumol and Vinoud (1970) estimated the change in mode, quantity, frequency for respective change in the relevant attributes such as shipping time or shipping cost by minimizing the total logistics costs. The logistic cost function minimized constitutes total direct shipping cost, in-transit carrying cost, ordering cost and recipient’s inventory carrying cost; which is derived to obtain the optimal frequency of reordering. Samuelson (1977) modeled freight tariffs to yield a better understanding of rate structure, and explained mode choice using mileage, shipment size, weight, density and value of the commodity, special handling requirements, and geographic region. The significant variables are mileage, weight and value of the commodity in terms of rail carload models. Railroads favor value of service pricing, emphasizing value of the commodity in rate determination, while trucks favor cost of service pricing, emphasizing density of the commodity in rate determination. Cunningham (1982) provided a theoretical model for supply chain method and concluded that the model choice is a function of costs incurred by the competing modes of carriage, the shipper’s predispositions toward the various competing modes and carriers, and the total transportation and non-transportation cost to the shipper.

Hall (1985) explained the interdependence of shipment size and mode choice by analyzing three transport alternatives: truckload (TL) contract carriers (focused on large shipments), less-than-truckload (LT) carriers and United Parcel Service (UPS) (for small shipments). Furthermore, Hall included capacity constraints of the various modes to the model that minimizes the sum of transportation and inventory cost to estimate the optimal shipment size. Tyworth (1992) integrated the inventory elements such as ordering replenishments and holding (cycle, safety, and in-transit) stock, with transportation components such as freight rate, speed and the consistency of delivery to define each mode or carrier, in order to obtain optimal costs. Casavant et al. (1993) used least cost spatial equilibrium model using the linear programming that minimizes the total cost comprised of assembly cost, elevation cost, shipment and handling cost, subject to several constraints such as production, elevator, and storage capacities. Leachman et al. (2005) evaluated the economic viability of the additional port user fees and the potential of using the revenue from the fee to improve the infrastructure, using a supply chain model that minimizes the total logistic costs of the importers using the port. Two scenarios were considered: As–Is (without improvements in shipment lead times) and Congestion Relief (including the impact of major improvements in lead time distributions). An aggregate demand curve of port demand versus fee value was constructed, whose slope is the elasticity of imports with respect to user fees. Leachman et al. (2005) included in the model different strategies for the importation process, varying from direct shipping to consolidation-deconsolidation practices for import cargo at San Pedro Bay (SPB) ports.

Blauwens et al. (2006) used inventory-theoretic framework to estimate implications from different mode shift policies that aim to decrease congestion. Results indicate that an increase in the transportation cost of road by 20% will increase the rail mode share from 16 to 27%. Leachman (2008) developed an supply chain model and used it to determine the most cost-effective way for each importer to transport from Asia to the Regional Distribution Centers (RDCs) in USA. Leachman (2008) considered alternative ways to reach the RDCs including direct shipping, exclusive shipment for single commodity, or consolidation-deconsolidation of various goods. Brogan et al. (2013) used the supply chain methods to analyze the possibility of shifting from less fuel efficient modes to more fuel efficient and greener options with hypothetical changes in policies.