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Solving Multi-objective Transportation Problem under Cost Reliability Using Utility Function
Published in Mangey Ram, Mathematics in Engineering Sciences, 2019
Gurupada Maity, Dharmadas Mardanya, Sankar Kumar Roy
The advantages using LLUF and RLUF in the decision-making problems are as follows: DM can easily formulate the MOTP by taking into account their preference mappings with utility functions in real-life situation andThe two linear utility models represented as linear form can be easily solved using software.
Cordon toll pricing in a multi-modal linear monocentric city with stochastic auto travel time
Published in Transportmetrica A: Transport Science, 2018
Ya-Juan Chen, Zhi-Chun Li, William H. K. Lam
A2: Three types of stakeholders are concerned in the urban system: households, property developer and the authority. All households are supposed to be homogenous in terms of their income level and utility function. Each household has a quasi-linear utility function and aims to maximize its own utility by determining the residential location, size of housing space and amount of non-housing goods within the budget constraint (e.g. Song and Zenou 2006; Kono et al. 2012). The property developer is assumed to maximize its net profit by determining its capital investment intensity. The authority seeks for the cordon toll pricing scheme in terms of toll level and location that maximizes the social welfare of the urban system.
Understanding risky choice behaviour with travel time variability: a review of recent empirical contributions of alternative behavioural theories
Published in Transportation Letters, 2020
The power utility specification has been commonly used to account for nonlinearity in parameters. Some reviewed studies (e.g. Razo and Gao 2013; Wen, Wu, and Fu 2017) used the simple form (i.e. , where α is the risk attitude parameter indicating the attitude toward risk) and others (e.g. Li and Hensher 2011; Balbontin, Hensher, and Collins 2017) used the general form (i.e. , where (1- α) is the corresponding risk attitude parameter. Both forms are behaviorally plausible for explaining risk attitudes; however, the general form is superior from a statistical perspective. Suppose that the nonlinear model with a general form provides a parameter estimate for α which is not statistically significant at the 95 percent confidence interval. Given that all statistical software packages directly present the results based on the t-test against zero, this suggests the risk attitude parameter (1-α) is statistically indifferent from one, implying risk neutrality. If the parameter estimate of α is not statistically significant under the simple power utility specification, that is, the risk attitude parameter is indifferent from zero, the value of is one and therefore the EUT, RDUT or CPT component in the total utility function would be a constant. For example, within a CPT framework with a simple power specification, Wen, Wu, and Fu (2017) estimated the risk attitude parameters which are not statistically significantly different from zero (with the best t-value being 1.37). Thus, the CPT component in their utility function actually reduced to a constant (, where is the length of a shorter delay and is its probability of occurrence; is the length of a long delay), suggesting that the choice behavior was only explained by the deterministic attributes (e.g. compensation and seat arrangement). Statistically speaking, their CPT model is indifferent to a linear-additive utility functional form under random utility maximization. Therefore, their ‘risk-seeking’ conclusion is not supported by the modeling results with insignificant risk attitude parameters (, for any value of x). Therefore, the general power specification () is preferred, in which indicates risk neutrality (i.e. a linear utility model); if, the risk attitude parameter () indicates a decreasing marginal disutility in the context of travel time variability (source of disutility with negative preference parameter estimates), that is, a risk-seeking attitude; and if the risk attitude parameter () indicates an increasing marginal disutility, that is, risk aversion.