Constrained nested logit model: formulation and estimation

Abstract

A model of traveller behaviour should recognise the exogenous and endogenous factors that limit the choice set of users. These factors impose constraints on the decision maker, which constraints may be considered implicitly, as soft constraints imposing thresholds on the perception of changes in attribute values, or explicitly as hard constraints. The purpose of this paper is twofold: (1) To present a constrained nested logit-type choice model to cope with hard constraints. This model is derived from the entropymaximizing framework. (2) To describe a general framework to deal with (dynamic) nonlinear utilities. This approach is based on Reproducing Kernel Hilbert Spaces. The resulting model allows the dynamic aspect and the constraints on the choice process to be represented simultaneously. A novel estimation procedure is introduced in which the utilities are viewed as the parameters of the proposed model instead of attribute weights as in the classical linear models. A discussion on over-specification of the proposed model is presented. This model is applied to a synthetic test problem and to a railway service choice problem in which users choose a service depending on the timetable, ticket price, travel time and seat availability (which imposes capacity constraints). Results show (1) the relevance of incorporating constraints into the choice models, (2) that the constrained models appear to be a better fit than the counterpart unconstrained choice models; and (3) the viability of the approach, in a real case study of railway services on the Madrid-Seville corridor (Spain).

Railway Timetabling With Integrated Passenger Distribution

“…For estimating passenger distributions in public transport applications the logit model is most commonly applied. To adjust to certain requirements, the logit model is constantly developed further, for example Espinosa-Aranda et al (2018) propose a constrained nested logit model to model passenger distributions on routes in public transport. Since recently, choice models in general and the logit model in specific are applied in optimization approaches for public transport applications.…”

High-speed railway scheduling based on user preferences

“…The utilities for the passengers are calculated following the approach proposed in Espinosa-Aranda et al (2014). In this subsection we describe this approach and give an illustrative example.…”

“…In this computational experiment we have considered the utility functions based on Gaussian kernels estimated in Espinosa-Aranda et al (2014). The Table 9 Potential total trips ( g w ) Fig.…”

“…In the HSR-TTP model, the proposed demand model allows us to establish implicitly a relation between the attributes of the timetable and travel behaviour and mode choice. The complete definition and the process by which it was calibrated is described inEspinosa-Aranda et al (2014).This model supposes there are various types of users defined by different reasons for travelling, economic and social characteristics and origin-destination. Hierarchical multinomial logit demand for railway service choice…”

Pricing optimization and competition under the linear nested stochastic choice model

“…Designed to relax the independence among all alternatives, the nested logit (NL) model proposed by McFadden (1978) identifies different substitution patterns and classifies similar products into the same nest. The studies of the NL model and its variants can be found in a lot of literature, such as transportation (Espinosa‐Aranda et al, 2018; Lu et al, 2017), facility location (Ramaul & Ramaul, 2018) and retailing (Chen & Jiang, 2020). Nevertheless, an inherent characteristic, an exponential preference function in terms of price, composes a strict constraint on the applicability of this model.…”