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Predictive network models forecast freight movements in the freight transport system by representing the transportation network explicitly. The models capture decisions and interactions of key stakeholders involved in freight transportation such as producers, consumers, shippers, carriers and governments, using the three common modeling methodologies: freight network equilibrium models, spatial price equilibrium models, integrated network equilibrium models (Harker, 1985; Crainic, 2002; Valsaraj, 2008). In addition, Nash equilibrium models and compensation principle models are also used to formulate alternative stakeholder behavior and decision making process (Wang, 2001; Zhang, 2008).
These modeling techniques have been used extensively in the freight modeling literature. Harker (1985) provides a good summary of research in this field up to 1985. Most of the models reviewed in his paper focus on one or two stakeholder problems considering shippers or/and carriers in the intercity freight transport system (Fang & Peterson, 1980; Florian & Los, 1982; Harker, 1983; Friesz et al., 1983; Freisz et al., 1984; Pang, 1984; Harker et al., 1986a; Harker et al., 1986b; Harker et al., 1986c; Dafermos & Narguney, 1987; Harker, 1988; Guelat et al., 1990; Miller et al., 1991; Hurley & Petersen, 1994; Fernandez et al., 2003; Agrawal & Ziliaskopoulos, 2006; Cheng, 2006; Yang et al., 2007; Xu & Holguin-Veras, 2009). Xiao & Yang (2007) studied relationships among three stakeholder groups such as one shipper, and multiple carriers and infrastructure companies. The models frequently used freight network equilibrium (Harker, 1988; Guelat et al., 1990; Hurley & Petersen, 1994; Fernandez et al., 2003; Agrawal & Ziliaskopoulos, 2006; Cheng, 2006; Xiao & Yang, 2007), spatial price equilibrium (Fang & Peterson, 1980; Florian & Los, 1982; Friesz et al., 1983; Freisz et al., 1984; Pang, 1984; Dafermos & Narguney, 1987; Xu & Holguin-Veras, 2009) and integrated network equilibrium (Harker, 1983; Harker et al., 1986a; Harker et al., 1986b; Harker et al., 1986c) approaches. Some used Stackelberg game (Miller et al., 1991; Yang et al., 2007) to analyze the multiple and sequential behavior of stakeholders on networks.