Random Utility Maximization Model Research Articles

A logistics provider’s profit maximization facility location problem with random utility maximizing followers

We introduce a strategic decision-making problem faced by logistics providers (LPs) seeking facility location decisions that lead to profitable operations. The profitability depends on the revenue generated through agreements with shippers, and the costs arising when satisfying these agreements. The latter depends, in turn, on the service levels and characteristics of the shippers’ customers. However, at a strategic level, the LP has imperfect information thereof.We propose a stochastic bilevel formulation where a given LP (leader) anticipates the decisions of shippers (followers) arising from a random utility maximization model. Using a sample average approximation and properties of the associated optimal solutions, we propose a heuristic that can compute high-quality solutions. It is based on a reduced single-level mixed integer linear programming formulation that can be solved by a general-purpose solver after a preprocessing phase. We can quickly identify situations that lead to zero expected profit for the LP. Experimental results show that expected profit highly depends on shippers’ price sensitivities. Underestimating price sensitivities can lead to an overestimation of the expected profit.

Comparative Analysis of Discrete Choice Approaches for Modeling Destination Choices of Urban Home-Based Trips to Work

Discrete choice models based on the Random Utility Maximization (RUM) approach are alternatives to traditional aggregated trip distribution models. However, the Random Regret Minimization (RRM) approach has emerged as an alternative to RUM for analyzing behavioral phenomena. This study compares the RUM and RRM approaches to model the destination choice of urban home-based trips to work, with a case study in the city of São Paulo, Brazil. The attributes of distance between traffic analysis zones (TAZs), total number of jobs, and number of jobs per type (industry and services) were considered, and the attributes referring to TAZs in commercial areas were tested in different models. We combined a method to estimate the optimal choice set size and a stratified sampling method to choose alternatives from available choices for a destination-choice problem with many alternatives. The RUM and RRM models produced similar results with respect to the final log-likelihood, [Formula: see text], Akaike information criterion, and Bayesian information criterion for the studied case. However, the RRM models required 52 min to be estimated on average, whereas estimation of the RUM models took only 31 s on average. Models derived from the RUM approach including the total number of jobs and distance produced higher accuracy, requiring less computational time to estimate the parameters.

Driven by utility or regret? Investigating the influence of decision-rule heterogeneity on public preferences for desertification control policies

In the matter of investigating public preferences and stated value for desertification control policies, the choice experiment (CE) could provide valuable insights. However, traditional CE studies modeled the data based on the random utility maximization (RUM) framework, which ignores the significant impact of decision rules on individual choice behavior, such as the random regret minimization (RRM). To examine the influence of decision-rule heterogeneity on public preferences for desertification control scenarios, this study introduced a generalized random regret minimization (G-RRM) model to analyze public choices and developed a hybrid latent class model incorporating the RUM, RRM, and G-RRM choice paradigms to clarify the formation mechanism of decision-rule heterogeneity. The findings indicate that all RRM models demonstrate a better fit with the data than the RUM model, and 68.77% of respondents express significant preference for the RRM choice paradigm. Regret can serve as an important driving factor in public choices for desertification control policies. The hybrid latent class model containing the G-RRM class with different attribute-specific values achieves the best fit, revealing that decision-rule heterogeneity significantly influences individuals' choice behavior, and such heterogeneity is not only among different respondents, but also in their trade-offs across various attributes. The results also reveal the relationship between respondents’ heterogeneous preferences for choice paradigms and their personality traits. Specifically, respondents with less education, residence years, and perceived usefulness of desertification control tend to prefer the RUM choice paradigm; female and respondents with more income, attention, and perceived usefulness of desertification control tend to prefer the RRM choice paradigm; as well as respondents with higher satisfaction to the current desertification situation show a greater decision-rule heterogeneity across different attributes. These results may provide interesting policy consequences, as they offer a precise comprehension of public choices for desertification control policies, through a combination of diverse decision rules.

Joint location and cost planning in maximum capture facility location under random utilities

We study a joint facility location and cost planning problem in a competitive market under random utility maximization (RUM) models. The objective is to locate new facilities and make decisions on the costs (or budgets) to spend on the new facilities, aiming to maximize an expected captured customer demand, assuming that customers choose a facility among all available facilities according to a RUM model. We examine two RUM frameworks in the discrete choice literature, namely, the additive and multiplicative RUM. While the former has been widely used in facility location problems, we are the first to explore the latter in the context. We numerically show that the two RUM frameworks can well approximate each other in the context of the cost optimization problem. In addition, we show that, under the additive RUM framework, the resultant cost optimization problem becomes highly non-convex and may have several local optima. In contrast, the use of the multiplicative RUM brings several advantages to the competitive facility location problem. For instance, the cost optimization problem under the multiplicative RUM can be solved efficiently by a general convex optimization solver, or can be reformulated as a conic quadratic program and handled by a conic solver available in some off-the-shelf solvers such as CPLEX or GUROBI. Furthermore, we consider a joint location and cost optimization problem under the multiplicative RUM and propose three approaches to solve the problem, namely, an equivalent conic reformulation, a multi-cut outer-approximation algorithm, and a local search heuristic. We provide numerical experiments based on synthetic instances of various sizes to evaluate the performances of the proposed algorithms in solving the cost optimization and the joint location and cost optimization problems.

Robust maximum capture facility location under random utility maximization models

We study a robust version of the maximum capture facility location problem in a competitive market, assuming that each customer chooses among all available facilities according to a random utility maximization (RUM) model. We employ the generalized extreme value (GEV) family of models and assume that the parameters of the RUM model are not given exactly but lie in convex uncertainty sets. The problem is to locate new facilities to maximize the worst-case captured user demand. We show that, interestingly, our robust model preserves the monotonicity and submodularity from its deterministic counterpart, implying that a simple greedy heuristic can guarantee a (1−1/e) approximation solution. We further show the concavity of the objective function under the classical multinomial logit (MNL) model, suggesting that an outer-approximation algorithm can be used to solve the robust model under MNL to optimality. We conduct experiments comparing our robust method to other deterministic and sampling approaches, using instances from different discrete choice models. Our results clearly demonstrate the advantages of our robust model in protecting the decision-maker from worst-case scenarios.

Multiple discrete choice and quantity with order statistic marginal utilities

This paper presents a random utility maximization model for individuals selecting discrete quantities from a set of n alternatives. Multiple alternatives with positive quantities may be selected. Diminishing marginal utility to quantity of each alternative is modeled via order statistics of independent Gumbel random variables. The model is parsimonious and tractable, admitting closed-form expressions for choice probabilities. As such, the model is amenable to maximum likelihood estimation of structural parameters from observed choices.Probability functions recover binary logit probabilities under binary choice and a maximum quantity of one unit, and probability is monotonic in the quantity of each alternative. The monotonic property likely restricts the application of the model to a narrow range of settings. The property is a manifestation of a recursive relationship among Gumbel order statistic probabilities. This relationship and related properties may lead to new models for capturing important complexities in a tractable manner.

Can healthcare choice be predicted using stated preference data? The role of model complexity in a discrete choice experiment about colorectal cancer screening

IntroductionThe validity of discrete choice experiments (DCEs) is crucial to its usage in healthcare decision-making, but there is only a limited number of health contexts in which external validity is demonstrated. This study aims to assess the internal and external validity of the DCE in the context of colorectal cancer (CRC) screening, and gather insights into the discrepancy between stated and revealed preferences. MethodsStated and revealed preferences were elicited on an individual level from Dutch residents eligible for CRC screening in a DCE and a field experiment, respectively (N = 568). To identify the determinants of CRC screening participation and their relative importance, five random utility maximisation models that varied in complexity were used. We assessed the accuracy with which the models based on stated preferences predict individual-level screening choice in a holdout task (internal validity) and in the actual screening choice (external validity). Insights into the discrepancy between stated and revealed preferences were gathered by comparing groups of respondents. ResultsOur findings show high internal and external validity. Choices could be accurately predicted for 95% of the respondents in the holdout task, and 90% in the actual screening choice. When scale and preference heterogeneity were taken into account model fit improved; individual-level prediction accuracy slightly increased for the holdout task but not for the actual screening choice. Respondents for whom stated preferences matched revealed preferences were generally in better health and found the GP's support for their screening decision more important. DiscussionEvidence was found that revealed preferences can be predicted accurately on an individual level. Incorporating heterogeneity improved internal validity but not external validity. Differences between stated and revealed preferences can be attributed to respondents’ health and the support of their GP. We suggest researchers to continue investigating the internal and external validity of discrete choice experiments, and the role of model complexity.

Community priorities for obesity prevention among low-income adults in Kuala Lumpur: a discrete choice experiment.

Non-communicable diseases and associated risk factors, such as obesity, are prevalent and increasing in Malaysia. To address this burden and the heightened vulnerability of low-income communities to these risk factors, the Better Health Programme Malaysia conducted a partial-profile discrete choice experiment (DCE) to inform the design of a community-based obesity-prevention programme. The DCE survey was conducted with community members (n = 1453) from three publicly supported low-cost, high-rise flat complexes in urban Kuala Lumpur. In the survey, community members were asked to choose between different sets of potential evidence-based interventions for obesity prevention. Their responses to these choice tasks were analysed to quantify preferences for these different health interventions using a random utility maximization model. Based on these results, we determined participants' relative prioritization of the different options. The most preferred interventions were those that reduced the price of fruit and vegetables; altered cooking practices at restaurants and food vendors to reduce salt, sugar and oil; and offered reward incentives for completing online educational activities. Community members did not prioritize several evidence-based interventions, including changes to product placement or product labelling, suggesting that these effective approaches may be less familiar or simply not preferred by respondents. The DCE enabled the clear articulation of these community priorities for evidence-based interventions that focus on the supply and promotion of affordable healthy foods within the local food environment, as well as community demand for healthier food options.

Random regret minimization for analyzing driver actions, accounting for preference heterogeneity

Increasingly more studies have implemented random regret minimization (RRM) as an alternative to random utility maximization (RUM) for modeling travelers’ choice-making behaviors. While for RUM, the focus is on utility maximization, for RRM the emphasis is on the regret of not selecting the best alternative. This study presented RRM and RUM for modeling actions made by drivers that resulted in crashes. The RRM method was considered in this study as the actions made before crashes might be the resultants of avoidance of regrets across the alternatives rather than the maximization of the utility related to the considered attributes. In addition, we extended the considered models to account for the unobserved heterogeneity in the datasets. Finally, we gave more flexibility to our model by changing the means of random parameters based on some observed attributes. This is one of the earliest studies, which considered the technique in the context of traffic safety for modeling drivers’ action while accounting for heterogeneity in the dataset by means of the random parameter. In addition, we considered the impact of inclusion of various predictors in the model fit of RRM and RUM. The results showed that while the standard RUM model outperforms the RRM model, the standard mixed models and the mixed models accounting for observed heterogeneity outperform the other techniques. As expected from the methodological structure of RRM, we found that the RRM performance is very sensitive to the included attributes. For instance, we found that by excluding the attributes of drivers’ condition and drivers under influence (DUI), the RRM model significantly outperforms the RUM model. The impact might be linked to the fact that when drivers are under abnormal conditions or influenced by drugs or alcohol, based on the sum of pairwise regret comparison, the inclusion of those attributes deteriorates the goodness-of-fit of the RRM model. It is possible that those parameters do not make a difference on regret pairwise comparison related to alternatives. The discussions at the end of this article examined possible reasons behind this performance.

Hybrid random utility-random regret model in the presence of preference heterogeneity, modeling drivers’ actions

Despite the importance of drivers’ actions and behaviors, the underlying factors to those actions have not received adequate attention. Understanding the factors contributing to various drivers’ actions before crashes could help policy makers to take appropriate actions to tackle those behaviors before crashes occur. One of the first steps could be to identify contributing factors to drivers’ actions by using a reliable statistical technique. It is reasonable to assume that drivers vary in their decision-making processes. Thus, in this study, in addition to the random utility maximization (RUM), the random regret minimization (RRM), as a psychological representation of the choice-making process, was considered. While most of the past studies, in the context of traffic safety, focused on either the RRM or RUM, both models’ frameworks as hybrid models might be needed to account for the heterogeneity of drivers’ decision-making behaviors. In addition, we accounted for the additional dimensions of preference heterogeneity in the latent class (LC) that the model might not capture. The results showed a significant improvement in the model fit of the mixed hybrid LC model compared with the standard hybrid and simple mixed RRM and RUM models. The emotional conditions of drivers, distraction, environmental conditions, and gender are some of the factors found to impact drivers’ choices. The results suggest that while the majority of attributes are processed according to the RUM, a significant portion of attributes are processed by the RRM. The hybrid model provides a richer understanding regarding factors to drivers’ actions before crashes based on different paradigms.

On the Estimation of Discrete Choice Models to Capture Irrational Customer Behaviors

The random utility maximization model is by far the most adopted framework to estimate consumer choice behavior. However, behavioral economics has provided strong empirical evidence of irrational choice behaviors, such as halo effects, that are incompatible with this framework. Models belonging to the random utility maximization family may therefore not accurately capture such irrational behavior. Hence, more general choice models, overcoming such limitations, have been proposed. However, the flexibility of such models comes at the price of increased risk of overfitting. As such, estimating such models remains a challenge. In this work, we propose an estimation method for the recently proposed generalized stochastic preference choice model, which subsumes the family of random utility maximization models and is capable of capturing halo effects. In particular, we propose a column-generation method to gradually refine the discrete choice model based on partially ranked preference sequences. Extensive computational experiments indicate that our model, explicitly accounting for irrational preferences, can significantly boost the predictive accuracy on both synthetic and real-world data instances. Summary of Contribution: In this work, we propose an estimation method for the recently proposed generalized stochastic preference choice model, which subsumes the family of random utility maximization models and is capable of capturing halo effects. Specifically, we show how to use partially ranked preferences to efficiently model rational and irrational customer types from transaction data. Our estimation procedure is based on column generation, where relevant customer types are efficiently extracted by expanding a treelike data structure containing the customer behaviors. Furthermore, we propose a new dominance rule among customer types whose effect is to prioritize low orders of interactions among products. An extensive set of experiments assesses the predictive accuracy of the proposed approach by comparing it against rank-based methods with only rational preferences and with more general benchmarks from the literature. Our results show that accounting for irrational preferences can boost predictive accuracy by 12.5% on average when tested on a real-world data set from a large chain of grocery and drug stores.

Structural behavioral models for rights-based fisheries

Rights-based management is prevalent in many fisheries, yet conventional spatiotemporal models of fishing behavior do not reflect such institutional settings. We adapt random utility maximization (RUM) models of spatiotemporal fishing behavior to capture the general equilibrium dynamics of catch-share fisheries by incorporating endogenously determined equilibrium quota prices. We demonstrate how a structural estimation strategy is capable of recovering policy-invariant behavioral parameters and predicting out-of-sample counterfactual policies. We illustrate the utility of our structural modeling approach by evaluating the efficacy of “ecosystem-based” policies, such as spatial closures, in a catch-share-managed fishery. Simulation results reveal that such policies have the potential to distort price signals in the quota market and prevent quota prices from coordinating fishing behavior in an efficient manner. Ecosystem-based policies may thus fall short of their intended objectives when introduced into rights-based managed fisheries. Importantly, we demonstrate that such conclusions cannot easily be drawn from behavioral models that omit or approximate the general equilibrium dynamics of rights-based fisheries.

A comparative study of machine learning, deep neural networks and random utility maximization models for travel mode choice modelling

Traditionally, Random Utility Maximization (RUM) models have been widely applied to travel mode choice modelling. Currently, Machine Learning (ML) models are being applied as an alternative to RUM models, since they provide better results in terms of prediction capability and they can manage large volumes of data. In this paper, a comprehensive comparison between classic RUM models and ML models, including single and ensemble classifiers as well as Deep Neural Networks (DNNs), is provided in order to assess systematically the performance of different models over two different datasets which have different sizes and nature of data. Numerical experiments show Random Forest (RF) is the best classifier in terms of accuracy index and the computational cost to train the model.

Submodularity and local search approaches for maximum capture problems under generalized extreme value models

We study the maximum capture problem in facility location under random utility models, i.e., the problem of seeking to locate new facilities in a competitive market such that the captured user demand is maximized, assuming that each customer chooses among all available facilities according to a random utility maximization model. We employ the generalized extreme value (GEV) family of discrete choice models and show that the objective function in this context is monotonic and submodular. This finding implies that a simple greedy heuristic can always guarantee a (1−1/e) approximation solution. We further develop a new algorithm combining a greedy heuristic, a gradient-based local search, and an exchanging procedure to efficiently solve the problem. We conduct experiments using instances of different sizes and under different discrete choice models, and we show that our approach significantly outperforms prior approaches in terms of both returned objective value and CPU time. Our algorithm and theoretical findings can be applied to the maximum capture problems under various random utility models in the literature, including the popular multinomial logit, nested logit, cross nested logit, and mixed logit models.

Dynamic Process Models for the Evaluation of the Compliance Level Evolution: Evidence from Italy

Decision support systems are used in different contexts, including tax policies. In these pages a theoretical analysis is proposed, based on random utility maximization and dynamic process models, to forecast the evolution of the taxable income produced by the application of a rewarding-based compliance methodology recently introduced in Italy. We will briefly describe the econometric characteristics of the new fiscal methodology (SIR); then, we will focus on the theoretical aspects concerning the evolution of the taxable income, in case of both a stochastic and a deterministic process, the latter commonly used to estimate a limit condition of the process (usually a worst-case scenario). The results here obtained can be extended to different kind of tax compliance models and are supposed to be as a basic step to implement an effective IT decision support model. The theoretical connection between SIR and sector studies, the previous compliance methodology, will be discussed. Finally, a numerical example of a deterministic process model based on synthetic data will be provided.

Effect of decision rules in choice experiments on hunting and bushmeat trade.

Providing insight on decisions to hunt and trade bushmeat can facilitate improved management interventions that typically include enforcement, alternative employment, and donation of livestock. Conservation interventions to regulate bushmeat hunting and trade have hitherto been based on assumptions of utility- (i.e., personal benefits) maximizing behavior, which influences the types of incentives designed. However, if individuals instead strive to minimize regret, interventions may be misguided. We tested support for 3 hypotheses regarding decision rules through a choice experiment in Tanzania. We estimated models based on the assumptions of random utility maximization (RUM) and pure random regret maximization (P-RRM) and combinations thereof. One of these models had an attribute-specific decision rule and another had a class-specific decision rule. The RUM model outperformed the P-RRM model, but the attribute-specific model performed better. Allowing respondents with different decision rules and preference heterogeneity within each decision rule in a class-specific model performed best, revealing that 55% of the sample used a P-RRM decision rule. Individuals using a P-RRM decision rule responded less to enforcement, salary, and livestock donation than did individuals using the RUM decision rule. Hence, 3 common strategies, enforcement, alternative income-generating activities, and providing livestock as a substitute protein, are likely less effective in changing the behavior of more than half of respondents. Only salary elicited a large (i.e. elastic) response, and only for one RUM class. Policies to regulate the bushmeat trade based solely on the assumption of individuals maximizing utility, may fail for a significant proportion of the sample. Despite the superior performance of models that allow both RUM and P-RRM decision rules there are drawbacks that must be considered before use in the Global South, where very little is known about the social-psychology of decision making.

Quantum probability: A new method for modelling travel behaviour

There has been an increasing effort to improve the behavioural realism of mathematical models of choice, resulting in efforts to move away from random utility maximisation (RUM) models. Some new insights have been generated with, for example, models based on random regret minimisation (RRM, μ-RRM). Notwithstanding work using for example Decision Field Theory (DFT), many of the alternatives to RUM tested on real-world data have however only looked at only modest departures from RUM, and differences in results have consequently been small. In the present study, we address this research gap again by investigating the applicability of models based on quantum theory. These models, which are substantially different from the state-of-the-art choice modelling techniques, emphasise the importance of contextual effects, state dependence, interferences and the impact of choice or question order. As a result, quantum probability models have had some success in better explaining several phenomena in cognitive psychology. In this paper, we consider how best to operationalise quantum probability into a choice model. Additionally, we test the quantum model frameworks on a best/worst route choice dataset and demonstrate that they find useful transformations to capture differences between the attributes important in a most favoured alternative compared to that of the least favoured alternative. Similar transformations can also be used to efficiently capture contextual effects in a dataset where the order of the attributes and alternatives are manipulated. Overall, it appears that models incorporating quantum concepts hold significant promise in improving the state-of-the-art travel choice modelling paradigm through their adaptability and efficient modelling of contextual changes.

Modeling preference heterogeneity in recreation random utility models when relevant information about users is limited

We suggest a novel approach to analyze revealed preference heterogeneity in recreation random utility maximization models when information about users is limited to their place of residence. We assume that recreationists living in the same place act as a “cohort” and that their preferences are hence homogeneous. We adopt a location-specific distribution criterion. We empirically test the suitability of this spatial approach by comparing its econometric performance and welfare estimates with that of the standard individual framework. We use data on hunting in Sicily to empirically test the cohort approach. Results from individual-specific and location-specific mixed logit models suggest that econometric performance improves when modeling heterogeneity with a location-specific conditional distribution. Further, marginal willingness-to-pay mean values and distributions for site characteristics differ significantly.

A multicut outer-approximation approach for competitive facility location under random utilities

This work concerns the maximum capture facility location problem with random utilities, i.e., the problem of seeking to locate new facilities in a competitive market such that the captured demand of users is maximized, assuming that each individual chooses among all available facilities according to a random utility maximization model. The main challenge lies in the nonlinearity of the objective function. Motivated by the convexity and separable structure of such an objective function, we propose an enhanced implementation of the outer approximation scheme. Our algorithm works in a cutting plane fashion and allows to separate the objective function into a number of sub-functions and create linear cuts for each sub-function at each outer-approximation iteration. We compare our approach with the state-of-the-art method and, for the first time in an extensive way, with other existing nonlinear solvers using three data sets from recent literature. Our experiments show the robustness of our approach, especially on large instances, in terms of both computing time and number instances solved to optimality.

Choice modelling in social networks using stochastic actor-oriented models

Combining choice modelling with social network analysis, we show how the stochastic actor-oriented model for the co-evolution of networks and behavior (SAOM) can be used as a powerful statistical framework to empirically analyze network-related choices. We discuss the underlying assumptions of SAOMs and show that they can be interpreted to represent a random utility maximization model (RUM). Network-related choices pertain both to decisions to engage in (or disengage from) specific social relationships and decisions to adapt behavior to that of social contacts. We demonstrate the usefulness of SAOM for the choice modelling community. We further illustrate how SAOM can be used to study network-related choices by providing an exemplary empirical analysis.