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Repair and maintenance services are among the most lucrative aspects of the entire automobile business chain. However, in the context of fierce competition, customer churns have led to the bankruptcy of several 4S (sales, spare parts, services, and surveys) shops. In this regard, a six-year dataset is utilized to study customer behaviors to aid managers identify and retain valuable but potential customer churn through a customized retention solution. First, we define the absence and presence behaviors of customers and thereafter generate absence data according to customer habits; this makes it possible to treat the customer absence prediction problem as a classification problem. Second, the repeated absence and presence behaviors of customers are considered as a whole from a lifecycle perspective. A modified recurrent neural network (RNN-2L) is proposed; it is more efficient and reasonable in structure compared with traditional RNN. The time-invariant customer features and the sequential lifecycle features are handled separately; this provides a more sensible specification of the RNN structure from a behavioral interpretation perspective. Third, a customized retention solution is proposed. By comparing the proposed model with those that are conventional, it is found that the former outperforms the latter in terms of area under the curve (AUC), confusion matrix, and amount of time consumed. The proposed customized retention solution can achieve significant profit increase. This paper not only elucidates the customer relationship management in the automobile aftermarket (where the absence and presence behaviors are infrequently considered), but also presents an efficient solution to increase the predictive power of conventional machine learning models. The latter is achieved by considering behavioral and business perspectives.
Jiawen Wang; Xinjun Lai; Sheng Zhang; W.M. Wang; Jianghang Chen. Predicting customer absence for automobile 4S shops: A lifecycle perspective. Engineering Applications of Artificial Intelligence 2019, 89, 103405 .
AMA StyleJiawen Wang, Xinjun Lai, Sheng Zhang, W.M. Wang, Jianghang Chen. Predicting customer absence for automobile 4S shops: A lifecycle perspective. Engineering Applications of Artificial Intelligence. 2019; 89 ():103405.
Chicago/Turabian StyleJiawen Wang; Xinjun Lai; Sheng Zhang; W.M. Wang; Jianghang Chen. 2019. "Predicting customer absence for automobile 4S shops: A lifecycle perspective." Engineering Applications of Artificial Intelligence 89, no. : 103405.
The anchor-based nested logit model is suitable to describe route choice behaviors since its abstract framework is consistent with style of travelers processing road network information. But in practice, the traditional definition of anchors is largely related to the properties of road network elements and too many anchors defined greatly increase computational burden. In this study, a data-driven anchor point generation method by community detection was proposed to address these issues. Travel communities are detected considering travel relationship topology by the massive individual trip data; and the frequently used bridges, expressways, and arterial roads in one community are identified as an anchor point which is in accordance with the mental representation of travelers’ route choice. The anchor points are employed to construct the nests in the route choice model to capture the choice correlation of travelers who pass through the same anchor points; and the small number of travel communities means the nests can be significantly reduced in number comparing with the traditional anchor-based models so that the computing burden is much less, while the ability to capture the correlation of routes is still remained. A case study is carried out for Guangzhou City, and the results suggest that the proposed anchor point based model obtains satisfying results in goodness-of-fit and forecasting; in addition, the computation time counts about only one-tenth that of the traditional anchor-based model, making it suitable for route choice analysis in the large road networks. Moreover, some practical implications are drawn for traffic management from the empirical study.
Jun Li; Licheng Wan; Xinjun Lai. Optimizing generation of anchor points for route choice modeling by community detection. Travel Behaviour and Society 2019, 18, 1 -14.
AMA StyleJun Li, Licheng Wan, Xinjun Lai. Optimizing generation of anchor points for route choice modeling by community detection. Travel Behaviour and Society. 2019; 18 ():1-14.
Chicago/Turabian StyleJun Li; Licheng Wan; Xinjun Lai. 2019. "Optimizing generation of anchor points for route choice modeling by community detection." Travel Behaviour and Society 18, no. : 1-14.
The ageing population has become a global problem in which enhanced understanding on their activity-travel patterns is needed. In this paper, an analysis of retired and dual-earner couples is conducted to investigate how retirement would change their activity time use and patterns. In particular, intra-household interactions are considered, to explore the interdependencies among household members’ choices, social-demographics and travel behaviours. Household survey data from Hong Kong are employed. Results show that retirement would substantially increase joint participations and durations in various out-of-home activities. In addition, the importance of walkability is emphasised for retired couples in a mixed-land-use and transit-dependent city, and a potential social exclusion issue is identified for the low-income retired population. Scenarios analyses including changes of built environment and lifestyles (e.g., telecommuting, online shopping and food delivery) are conducted, to investigate how couples would reallocate the saved travel time. In summary, this paper highlights the importance of considering the group decision mechanism in a household for activity generation and travel demand forecasting. It sheds light on policies to improve quality-of-life for couples before and after the retirement.
Xinjun Lai; William H.K. Lam; Junbiao Su; Hui Fu. Modelling intra-household interactions in time-use and activity patterns of retired and dual-earner couples. Transportation Research Part A: Policy and Practice 2019, 126, 172 -194.
AMA StyleXinjun Lai, William H.K. Lam, Junbiao Su, Hui Fu. Modelling intra-household interactions in time-use and activity patterns of retired and dual-earner couples. Transportation Research Part A: Policy and Practice. 2019; 126 ():172-194.
Chicago/Turabian StyleXinjun Lai; William H.K. Lam; Junbiao Su; Hui Fu. 2019. "Modelling intra-household interactions in time-use and activity patterns of retired and dual-earner couples." Transportation Research Part A: Policy and Practice 126, no. : 172-194.
The application of travel demand models to transportation planning has triggered great interests in issues that potentially improve the accuracy of model forecasts. These forecasts, however, are subject to various sources of input and model uncertainties. Focusing on travel choice behavior, this paper draws attention to the use of an ensemble-based model for addressing these uncertainties. A random multinomial logit (RMNL) model is developed by assembling a collection of multinomial logit (MNL) models. The bootstrapping procedure and the random feature selection are employed to capture the uncertainties in the model. A case study of investigating travel mode choice behaviors that illustrates situations necessitating the RMNL model is presented. Results suggest that the uncertainty related to predictions is reduced and the prediction accuracy is much improved. The RMNL model is computationally efficient and provides useful interpretations by estimating variable significance. Also, the RMNL model is able to deal with high-dimensional data.
Long Cheng; Xinjun Lai; Xuewu Chen; Shuo Yang; Jonas De Vos; Frank Witlox. Applying an ensemble-based model to travel choice behavior in travel demand forecasting under uncertainties. Transportation Letters 2019, 12, 375 -385.
AMA StyleLong Cheng, Xinjun Lai, Xuewu Chen, Shuo Yang, Jonas De Vos, Frank Witlox. Applying an ensemble-based model to travel choice behavior in travel demand forecasting under uncertainties. Transportation Letters. 2019; 12 (6):375-385.
Chicago/Turabian StyleLong Cheng; Xinjun Lai; Xuewu Chen; Shuo Yang; Jonas De Vos; Frank Witlox. 2019. "Applying an ensemble-based model to travel choice behavior in travel demand forecasting under uncertainties." Transportation Letters 12, no. 6: 375-385.
Drivers' route choice model is essential in transportation software such as navigation, fleet management, and simulation, where the random utility models (RUM) have dominated for years. The authors investigate here whether machine learning (ML) models could be applied into this field, and whether these approaches outperform the traditional models in goodness-of-fit and prediction. The application framework and data structure are proposed, where the challenging problems lie in: (i) to pool data from multiple origin–destination pairs; and (ii) to interpret results for behaviour analysis. All RUM and ML models are applied in a real network. Results suggest that the random forest, one of the ML models, has satisfying performances with acceptable computation time, making it suitable for large network and real-time analysis. This study shows that the ML models can be adopted for behaviour analysis, such as to prioritise the importance of variables, compute the elasticity, and forecast for scenarios. Future directions on combining the RUM and ML models are discussed.
Xinjun Lai; Hui Fu; Jun Li; Zhiren Sha. Understanding drivers' route choice behaviours in the urban network with machine learning models. IET Intelligent Transport Systems 2018, 13, 427 -434.
AMA StyleXinjun Lai, Hui Fu, Jun Li, Zhiren Sha. Understanding drivers' route choice behaviours in the urban network with machine learning models. IET Intelligent Transport Systems. 2018; 13 (3):427-434.
Chicago/Turabian StyleXinjun Lai; Hui Fu; Jun Li; Zhiren Sha. 2018. "Understanding drivers' route choice behaviours in the urban network with machine learning models." IET Intelligent Transport Systems 13, no. 3: 427-434.
The analysis of travel mode choice is important in transportation planning and policy-making in order to understand and forecast travel demands. Research in the field of machine learning has been exploring the use of random forest as a framework within which many traffic and transport problems can be investigated. The random forest (RF) is a powerful method for constructing an ensemble of random decision trees. It de-correlates the decision trees in the ensemble via randomization that leads to an improvement of forecasting and reduces the variance when averaged over the trees. However, the usefulness of RF for travel mode choice behavior remains largely unexplored. This paper proposes a robust random forest method to analyze travel mode choices for examining the prediction capability and model interpretability. Using the travel diary data from Nanjing, China in 2013, enriched with variables on the built environment, the effects of different model parameters on the prediction performance are investigated. The comparison results show that the random forest method performs significantly better in travel mode choice prediction for higher accuracy and less computation cost. In addition, the proposed method estimates the relative importance of explanatory variables and how they relate to mode choices. This is fundamental for a better understanding and effective modeling of people’s travel behavior.
Long Cheng; Xuewu Chen; Jonas De Vos; Xinjun Lai; Frank Witlox. Applying a random forest method approach to model travel mode choice behavior. Travel Behaviour and Society 2018, 14, 1 -10.
AMA StyleLong Cheng, Xuewu Chen, Jonas De Vos, Xinjun Lai, Frank Witlox. Applying a random forest method approach to model travel mode choice behavior. Travel Behaviour and Society. 2018; 14 ():1-10.
Chicago/Turabian StyleLong Cheng; Xuewu Chen; Jonas De Vos; Xinjun Lai; Frank Witlox. 2018. "Applying a random forest method approach to model travel mode choice behavior." Travel Behaviour and Society 14, no. : 1-10.
The selection of fresh product suppliers is a multi-criteria decision making (MCDM) problem with great significant and application value. This requires trade-offs between multiple criteria to prove its ambiguity and uncertainty. Therefore, a novel two-stage fuzzy integrated MCDM method to select suitable suppliers is employed. In the first stage, two collective relationship matrixes are constructed by quality function development (QFD), and relationships among customer requirements (CRs), company strategies (CSs) as well as selection criteria are considered separately in the two matrixes. Subjective criteria weights are obtained by fuzzy best-worst method (BWM) appropriately. In the second stage, the objective criteria weights are obtained using Shannon’s entropy method, and the fuzzy multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA) is applied to rank suppliers. Finally, an application case is applied to prove the feasibility of the proposed method. These conclusions can help companies improve their CSs and increase their market competitiveness.
Aijun Liu; Yaxuan Xiao; Xiaohui Ji; Kai Wang; Sang-Bing Tsai; Hui Lu; Jinshi Cheng; Xinjun Lai; Jiangtao Wang. A Novel Two-Stage Integrated Model for Supplier Selection of Green Fresh Product. Sustainability 2018, 10, 2371 .
AMA StyleAijun Liu, Yaxuan Xiao, Xiaohui Ji, Kai Wang, Sang-Bing Tsai, Hui Lu, Jinshi Cheng, Xinjun Lai, Jiangtao Wang. A Novel Two-Stage Integrated Model for Supplier Selection of Green Fresh Product. Sustainability. 2018; 10 (7):2371.
Chicago/Turabian StyleAijun Liu; Yaxuan Xiao; Xiaohui Ji; Kai Wang; Sang-Bing Tsai; Hui Lu; Jinshi Cheng; Xinjun Lai; Jiangtao Wang. 2018. "A Novel Two-Stage Integrated Model for Supplier Selection of Green Fresh Product." Sustainability 10, no. 7: 2371.
Xinjun Lai; Zhi Li; Jun Li. Modeling risks and uncertainties in residents’ license choice behaviors under a vehicle restriction policy. Transportation Planning and Technology 2018, 41, 497 -518.
AMA StyleXinjun Lai, Zhi Li, Jun Li. Modeling risks and uncertainties in residents’ license choice behaviors under a vehicle restriction policy. Transportation Planning and Technology. 2018; 41 (5):497-518.
Chicago/Turabian StyleXinjun Lai; Zhi Li; Jun Li. 2018. "Modeling risks and uncertainties in residents’ license choice behaviors under a vehicle restriction policy." Transportation Planning and Technology 41, no. 5: 497-518.
Purpose The purpose of this paper is to propose an effective and economical management platform to realize real-time tracking and tracing for prepackaged food supply chain based on Internet of Things (IoT) technologies, and finally ensure a benign and safe food consumption environment. Design/methodology/approach Following service-oriented architecture, a flexible layered architecture of tracking and tracing platform for prepackaged food is developed. Besides, to reduce the implementation cost while realizing fine-grained tracking and tracing, an integrated solution of using both the QR code and radio-frequency identification (RFID) tag is proposed. Furthermore, Extensible Markup Language (XML) is adopted to facilitate the information sharing among applications and stakeholders. Findings The validity of the platform has been evaluated through a case study. First, the proposed platform is proved highly effective on realizing prepackaged food tracking and tracing throughout its supply chain, and can benefit all the stakeholders involved. Second, the integration of the QR code and RFID technologies is proved to be economical and could well ensure the real-time data collection. Third, the XML-based method is efficient to realize information sharing during the whole process. Originality/value The contributions of this paper lie in three aspects. First, the technical architecture of IoT-based tracking and tracing platform is developed. It could realize fine-grained tracking and tracing and could be flexible to adapt in many other areas. Second, the solution of integrating the QR code and RFID technologies is proposed, which could greatly decrease the cost of adopting the platform. Third, this platform enables the information sharing among all the involved stakeholders, which will further facilitate their cooperation on guaranteeing the quality and safety of prepackaged food.
Zhi Li; Guo Liu; Layne Liu; Xinjun Lai; Gangyan Xu. IoT-based tracking and tracing platform for prepackaged food supply chain. Industrial Management & Data Systems 2017, 117, 1906 -1916.
AMA StyleZhi Li, Guo Liu, Layne Liu, Xinjun Lai, Gangyan Xu. IoT-based tracking and tracing platform for prepackaged food supply chain. Industrial Management & Data Systems. 2017; 117 (9):1906-1916.
Chicago/Turabian StyleZhi Li; Guo Liu; Layne Liu; Xinjun Lai; Gangyan Xu. 2017. "IoT-based tracking and tracing platform for prepackaged food supply chain." Industrial Management & Data Systems 117, no. 9: 1906-1916.
Nowadays, the society is paying more and more attention to the issues that plague the environment. There is a growing need for enterprises to design and manufacture environmentally friendly products, in order to take up the responsibility of sustainable development of the society. The entire product life cycle consists of design, manufacturing, usage and recycling phases. These phases involve various economic and environmental factors that affect the recyclability of products. Previous researchers mainly focused on the single phase of the product’s life cycle. Moreover, they did not take into account the dynamic change of the recyclable material’s cost. In this paper, a time-series forecasting methodology is proposed to evaluate the product’s recyclability at the product design phase. It considers various economic and environmental factors of different stages of the product’s life cycle. In addition, a time-series forecasting method is utilised for predicting the cost of the recycled material at the product’s end-of-life. To demonstrate the effectiveness of this methodology, a case study of a cylinder engine design was presented. The results showed that the proposed methodology was fully capable of providing decision support to the designers by accessing the recyclability of the product at the design phase.
Zhi Li; Jiadong He; Xinjun Lai; Yunbao Huang; Tao Zhou; Ali Vatankhah Barenji; W.M. Wang. Evaluation of product recyclability at the product design phase: a time-series forecasting methodology. International Journal of Computer Integrated Manufacturing 2017, 31, 457 -468.
AMA StyleZhi Li, Jiadong He, Xinjun Lai, Yunbao Huang, Tao Zhou, Ali Vatankhah Barenji, W.M. Wang. Evaluation of product recyclability at the product design phase: a time-series forecasting methodology. International Journal of Computer Integrated Manufacturing. 2017; 31 (4-5):457-468.
Chicago/Turabian StyleZhi Li; Jiadong He; Xinjun Lai; Yunbao Huang; Tao Zhou; Ali Vatankhah Barenji; W.M. Wang. 2017. "Evaluation of product recyclability at the product design phase: a time-series forecasting methodology." International Journal of Computer Integrated Manufacturing 31, no. 4-5: 457-468.
A novel concept is presented to capture route choice behaviours and to account for the correlation of routes in the logit model. The issue that route choice models are easily affected when irrelevant alternatives are included in the choice set is tackled. The concept of equivalent impedance is presented to simplify and aggregate a set of links based on the idea that people tend to remember and process road network information at an abstract level. Then, the equivalent impedance is utilized to derive a correction term for the utility of a multinomial logit model in which the advantages of a closed-form structure and easy computation remain unchanged. The results from the numerical examples suggest that the proposed model obtains reasonable results and provides more stable predictions than comparable models when the composition of the choice set changes. An application in a real urban network with GPS data is presented, and estimation results suggest that the new model is practical due to its robustness.
Jun Li; Xinjun Lai. Modelling travellers’ route choice behaviours with the concept of equivalent impedance. Transportation 2017, 46, 233 -262.
AMA StyleJun Li, Xinjun Lai. Modelling travellers’ route choice behaviours with the concept of equivalent impedance. Transportation. 2017; 46 (1):233-262.
Chicago/Turabian StyleJun Li; Xinjun Lai. 2017. "Modelling travellers’ route choice behaviours with the concept of equivalent impedance." Transportation 46, no. 1: 233-262.
A subpath-based methodology is proposed to capture the travellers’ route choice behaviours and their perceptual correlation of routes, because the original link-based style may not be suitable in application: (1) travellers do not process road network information and construct the chosen route by a link-by-link style; (2) observations from questionnaires and GPS data, however, are not always link-specific. Subpaths are defined as important portions of the route, such as major roads and landmarks. The cross-nested Logit (CNL) structure is used for its tractable closed-form and its capability to explicitly capture the routes correlation. Nests represent subpaths other than links so that the number of nests is significantly reduced. Moreover, the proposed method simplifies the original link-based CNL model; therefore, it alleviates the estimation and computation difficulties. The estimation and forecast validation with real data are presented, and the results suggest that the new method is practical.
Xinjun Lai; Jun Li; Zhi Li. A Subpath-based Logit Model to Capture the Correlation of Routes. Promet - Traffic&Transportation 2016, 28, 225 -234.
AMA StyleXinjun Lai, Jun Li, Zhi Li. A Subpath-based Logit Model to Capture the Correlation of Routes. Promet - Traffic&Transportation. 2016; 28 (3):225-234.
Chicago/Turabian StyleXinjun Lai; Jun Li; Zhi Li. 2016. "A Subpath-based Logit Model to Capture the Correlation of Routes." Promet - Traffic&Transportation 28, no. 3: 225-234.
Xinjun Lai; Michel Bierlaire. Specification of the cross-nested logit model with sampling of alternatives for route choice models. Transportation Research Part B: Methodological 2015, 80, 220 -234.
AMA StyleXinjun Lai, Michel Bierlaire. Specification of the cross-nested logit model with sampling of alternatives for route choice models. Transportation Research Part B: Methodological. 2015; 80 ():220-234.
Chicago/Turabian StyleXinjun Lai; Michel Bierlaire. 2015. "Specification of the cross-nested logit model with sampling of alternatives for route choice models." Transportation Research Part B: Methodological 80, no. : 220-234.
A Logit-based route choice model is proposed to address the overlapping and scaling problems in the traditional multinomial Logit model. The nonoverlapping links are defined as a subnetwork, and its equivalent impedance is explicitly calculated in order to simply network analyzing. The overlapping links are repeatedly merged into subnetworks with Logit-based equivalent travel costs. The choice set at each intersection comprises only the virtual equivalent route without overlapping. In order to capture heterogeneity in perception errors of different sizes of networks, different scale parameters are assigned to subnetworks and they are linked to the topological relationships to avoid estimation burden. The proposed model provides an alternative method to model the stochastic route choice behaviors without the overlapping and scaling problems, and it still maintains the simple and closed-form expression from the MNL model. A link-based loading algorithm based on Dial’s algorithm is proposed to obviate route enumeration and it is suitable to be applied on large-scale networks. Finally a comparison between the proposed model and other route choice models is given by numerical examples.
Jun Li; Yulin Huang; Xinjun Lai. Modeling Stochastic Route Choice Behaviors with Equivalent Impedance. Mathematical Problems in Engineering 2015, 2015, 1 -10.
AMA StyleJun Li, Yulin Huang, Xinjun Lai. Modeling Stochastic Route Choice Behaviors with Equivalent Impedance. Mathematical Problems in Engineering. 2015; 2015 ():1-10.
Chicago/Turabian StyleJun Li; Yulin Huang; Xinjun Lai. 2015. "Modeling Stochastic Route Choice Behaviors with Equivalent Impedance." Mathematical Problems in Engineering 2015, no. : 1-10.
A closed-form mixed Logit approach is proposed to model the stochastic route choice behaviours. It combines both the advantages of Probit and Logit to provide a flexible form in alternatives correlation and a tractable form in expression; besides, the heterogeneity in alternative variance can also be addressed. Paths are compared by pairs where the superiority of the binary Probit can be fully used. The Probit-based aggregation is also used for a nested Logit structure. Case studies on both numerical and empirical examples demonstrate that the new method is valid and practical. This paper thus provides an operational solution to incorporate the normal distribution in route choice with an analytical expression.1. IntroductionRoute choice is one of the crucial issues in transportation analysis because it models the travelling behaviours so as to provide predictions for the future demand. Drivers always try to maximize their travelling welfare when choosing a path from a given origin-destination (OD) pair. However not all of them choose the best alternative because of the imperfect knowledge of network. To model this perception error and the stochastic route choice behaviour, Probit and Logit models are two of the most wildly used methods. The utility of each alternative is decomposed into a deterministic and a random portion. Assume that there are paths between an OD pair and the route choice set is ; the utility (welfare) of an alternative path can be represented aswhere is the utility of path , is the deterministic part which is composed by attributes such as length and cost that can be explicitly captured, and is the random term that captures the perception error. A rational traveller would select a path with the maximum utility among the alternatives in .Probit assumes that the random portion is normally distributed; besides, it provides a highly flexible structure for correlation. However, it is limited due to the computation burden. It does not have a closed-form formula when there are more than two alternatives. Generally, the computation of multinomial Probit requires either Clark’s approximation [1, 2], Monte Carlo simulation [3], or numerical integration [4]. Yai et al. [5] used the multinomial Probit model in the context of route choice in the Tokyo rail network, but the maximum number of alternatives is limited to four. On the other hand, Logit is more popular for its analytical tractability. Logit assumes that the error term is type I extreme value (EV) distributed. Moreover, it assumes each of the error terms is independently identically distributed (IID), which leads to a closed-form mathematical structure to simplify the computation in estimation and prediction. As a consequence, Logit has two main disadvantages because of the IID assumption: (1) it cannot represent the path correlation which leads to enlarged probabilities of the overlapped paths, namely, the overlapping problem and (2) it cannot represent the heterogeneity in perception errors which would produce unreasonable results, namely, the scaling problem.There are several modified methods to address the two drawbacks of Logit in the context of route choice. Regarding the first disadvantage, the overlapping problem, the improved models are classified into two types.(i)Modifications of multinomial Logit (MNL), such as path size Logit (PSL) [6–9], C-Logit [10], and implicit availability/perception (IAP) model [11]: in these models, an additional term is introduced in the utility function to capture the correlations of paths, so as to decrease the attraction of the overlapped path. This method maintains the simple form of MNL. Besides, the log-likelihood function of this method is globally concave, so it guarantees a global optimum for parameters estimations. However, the additional terms are convenient approximations. Previous researches show that they might be too sensitive to the composition of the choice set [9, 12].(ii)Generalized extreme value (GEV) proposed by McFadden [13]: the most widely used methods of this type in route choice are the link-based crossed nested Logit (CNL) [14, 15] and the paired combinatorial Logit (PCL) [16–19] model. These two models all have a tree structure to represent the link-path relation, where alternatives with shared attributes are classified into the same nest so the correlation can be explicitly captured. The link-based CNL model treats each link as a nest, and each path uses several links which are classified into the corresponding nests. The PCL model compares paths by paired combinations, and each path pair is a nest. The CNL model has a large set of parameters that need to be estimated, so some researches provide approximated formulas [14, 20]. Besides, some researchers suggest that the parameters can be achieved by solving a system of equations of the correlation and constraints [21, 22]. Likewise, the PCL model also requires a parameter to represent the correlation, and the specifications are provided by Gliebe [23] and Prashker and Bekhor [24].As for the second drawback of Logit, the scaling problem, Pravinvongvuth and Chen [18] propose origin-destination specific scaling factor to represent the different scale of diverse networks. Chen et al. [25] examine the scaling effect when applying route choice model in stochastic equilibrium models. Miwa et al. [26] examine how to set the scale parameter (dispersion parameter) and apply a multiclass stochastic user equilibrium (SUE) assignment model to consider differences in drivers’ perception errors.Some researches combine both advantages of Probit and Logit, and the most representative model is the mixed Logit [27], also named as Logit kernel, error component, or hybrid Logit. It incorporates other distributions other than type I EV to provide a flexible and tractable form to represent the correlation across alternatives, the alternative specific variances, and also taste heterogeneity. Frejinger and Bierlaire [8] use the error component to model the subnetwork so as to represent the path overlap in an network. Bekhor et al. [28] estimate an error component model based on the Boston route choice data. However, the mixed Logit does not have a closed-form expression; consequently the estimation and prediction all require the simulation-based method. Researches [20, 29] show that the simulation-based method requires a large number of draws to achieve stable predictions. Besides, currently there is no efficient path-based SUE traffic assignment for solving the route choice model with the mixed Logit model [18].To fully use the advantages of Probit and Logit, this paper proposes a mixed Logit method with a closed-form to model the stochastic route choice behaviours. With a closed-form expression, the computation burden in estimation and prediction would be relieved. Moreover, the closed-form formula alleviates the difficulties in the path-based SUE assignment with a mixed Logit model. The paper is organized as follows. Section 2 describes the methodology, including the nested model structure and the Probit-based aggregation. The validation from a numerical example is presented in Section 3. The new method is applied to real data in Section 4. Finally conclusions and discussions for future study are given in Section 5.2. Methodology2.1. Model StructureThe proposed model has a similar structure as the PCL model. Paths are compared by paired combination. Consider alternatives in the choice set between an OD pair; by paired combination there are totally paths pairs. The new model has a two-level nest structure. Each path pair is a nest; within the nest there is actually a binary choice case. The expected maximum utility [7] of each path pair is used as the utility of the nest. In the upper level, it is a multinomial choice model with nests. Consider a three-alternative case, as shown in Figure 1, paths , , and , and the path pairs are , , and . The probability that path is chosen among three paths is a combination of the marginal probability of the nest and the conditional probability within the nest, which isFigure 1: Model structure of a three-alternative case.In order to relax constraints of the Logit model, the error part in (1) is decomposed into two parts, and . The first error , which is IID EV distributed, captures the differences of nests; the second error , which obeys normal distribution, captures the differences within the nest. For the first nest that includes paths and , their utilities arewhere and , and are attributes of paths and ; is a vector of parameters that to be estimated. and are nest specific, and they capture the unobserved attributes shared by alternatives in the same nest, so consequently they are the same, which is . The variance of nest is , where is the scale parameter. and are alternative-specific, and they capture the unobserved attributes specific to alternatives and . and are assumed to be normally distributed with the expectation of zero and the variances and , respectively. Sheffi [30] argues that the variance can be assumed to be proportional to the deterministic utility of paths, so as to link the perception error to the paths attributes. Hence the variance-covariance matrix of paths , iswhere is the correlated utility of paths and , such as the overlapped links; is the scale parameter of the lower-level and it is to be estimated.The probability that traveller chooses path given the nest is chosen asBecause and are both normally distributed with zero means, is also normally distributed with expectation zero but with variance , where is the correlation. We havewhere is the standard cumulative normal distribution function. Since the Probit model is only used in a binary choice case with a closed-form expression, the advantages of Probit, such as flexible form of correlation and alternative-specific variance, could be fully exploited in our model.The expected maximum utility of each nest is the aggregation of the paths
Xinjun Lai; Jun Li. Modelling Stochastic Route Choice Behaviours with a Closed-Form Mixed Logit Model. Mathematical Problems in Engineering 2015, 2015, 1 -9.
AMA StyleXinjun Lai, Jun Li. Modelling Stochastic Route Choice Behaviours with a Closed-Form Mixed Logit Model. Mathematical Problems in Engineering. 2015; 2015 ():1-9.
Chicago/Turabian StyleXinjun Lai; Jun Li. 2015. "Modelling Stochastic Route Choice Behaviours with a Closed-Form Mixed Logit Model." Mathematical Problems in Engineering 2015, no. : 1-9.
An improved paired combinatorial Logit route choice model with Probit-based equivalent route impedance is proposed to simplify the calculation and resolve the homoscedasticity problem of the Logit model. The model comprises a two-level structure: the lower level employs a binary Probit choice model to address the problem of route overlapping. Clark's approximation for normal distribution is employed to compute the equivalent impendence for each route pair in the upper level. The homoscedasticity problem is resolved through the introduction of the normal distribution. The upper level is a classical multinomial Logit model with relative impedance that reduces the defect of variance-homogeneity in the upper level. The probability of route selection is determined by marginal and conditional probabilities. The proposed model combines the advantages of both Probit and Logit models with close-form formulations, which can be easily calculated. Two numerical tests, which were performed on the well-known examples, indicate that the proposed model produces more reasonable and stable results.
Jun Li; Xinjun Lai; Zhi Yu. A Paired Combinatorial Logit Route Choice Model with Probit-Based Equivalent Impedance. Journal of Transportation Systems Engineering and Information Technology 2013, 13, 100 -104.
AMA StyleJun Li, Xinjun Lai, Zhi Yu. A Paired Combinatorial Logit Route Choice Model with Probit-Based Equivalent Impedance. Journal of Transportation Systems Engineering and Information Technology. 2013; 13 (4):100-104.
Chicago/Turabian StyleJun Li; Xinjun Lai; Zhi Yu. 2013. "A Paired Combinatorial Logit Route Choice Model with Probit-Based Equivalent Impedance." Journal of Transportation Systems Engineering and Information Technology 13, no. 4: 100-104.
Jun Li; Liang-Hui Xie; Xin-Jun Lai. Route Reconstruction from Floating Car Data with Low Sampling Rate Based on Feature Matching. Research Journal of Applied Sciences, Engineering and Technology 2013, 6, 2153 -2158.
AMA StyleJun Li, Liang-Hui Xie, Xin-Jun Lai. Route Reconstruction from Floating Car Data with Low Sampling Rate Based on Feature Matching. Research Journal of Applied Sciences, Engineering and Technology. 2013; 6 (12):2153-2158.
Chicago/Turabian StyleJun Li; Liang-Hui Xie; Xin-Jun Lai. 2013. "Route Reconstruction from Floating Car Data with Low Sampling Rate Based on Feature Matching." Research Journal of Applied Sciences, Engineering and Technology 6, no. 12: 2153-2158.
Xinjun Lai; Zhi Yu; Jun Li. Derivation, Implementation and Examination of Logit Route Choice Model with Relative Impedance. Journal of Transportation Systems Engineering and Information Technology 2012, 12, 85 -90.
AMA StyleXinjun Lai, Zhi Yu, Jun Li. Derivation, Implementation and Examination of Logit Route Choice Model with Relative Impedance. Journal of Transportation Systems Engineering and Information Technology. 2012; 12 (2):85-90.
Chicago/Turabian StyleXinjun Lai; Zhi Yu; Jun Li. 2012. "Derivation, Implementation and Examination of Logit Route Choice Model with Relative Impedance." Journal of Transportation Systems Engineering and Information Technology 12, no. 2: 85-90.
This paper presents a modified paired combinatorial Logit route choice model that takes the advantages of both Probit and Logit models to produce more reasonable flow prediction with close-form probabilities that can be easily calculated. To better account for the observation error of the model, parameters are calculated basing that the variance of impendence is related to the measured travel time. The concept of stochastic equivalent impendence is proposed to calculate the utility of each route pair and Clark's approximation for normal distribution is used to compute the equivalent impendence. The proposed equivalence concept also eliminates the need of computing similarity index as shown in most modified Logit model. Two numerical tests on the well-known examples show that the proposed model is more close to Probit model than original PCL model with reasonable errors.
Jun Li; Xinjun Lai; Lianghui Xie. A Modified Paired Combinatorial Logit Route Choice Model with Probit-Based Equivalent Impedance. ICTE 2011 2011, 1 .
AMA StyleJun Li, Xinjun Lai, Lianghui Xie. A Modified Paired Combinatorial Logit Route Choice Model with Probit-Based Equivalent Impedance. ICTE 2011. 2011; ():1.
Chicago/Turabian StyleJun Li; Xinjun Lai; Lianghui Xie. 2011. "A Modified Paired Combinatorial Logit Route Choice Model with Probit-Based Equivalent Impedance." ICTE 2011 , no. : 1.
The high traffic volume in Chinese universities brings issues including accessibility and safety, which requires careful evaluation of campus-traffic with a quantitative and qualitative method. A multilevel index system based on attribute mathematical recognition is proposed. The upper-level includes five indexes, namely efficiency, accessibility, comfort, safety and traffic calming, which are further divided into the lower-level indexes. The indexes' weights are determined by variation coefficient method and the campus traffic level was identified by the confidence rules to avoid unreasonable estimation. A case study of Sun Yat-sen University East Campus is presented, whose travel environment was just passable in 2007 but greatly improved since 2009 after the road reconstruction and traffic regulations suggested by the authors. The evaluation accords with the opinion poll and the method is practical, rational and suitable for comparison.
Xinjun Lai; Jun Li; Zhi Yu. Evaluating University Campus Traffic by Attribute Mathematical Recognition. ICTIS 2011 2011, 1 .
AMA StyleXinjun Lai, Jun Li, Zhi Yu. Evaluating University Campus Traffic by Attribute Mathematical Recognition. ICTIS 2011. 2011; ():1.
Chicago/Turabian StyleXinjun Lai; Jun Li; Zhi Yu. 2011. "Evaluating University Campus Traffic by Attribute Mathematical Recognition." ICTIS 2011 , no. : 1.