Demand Estimation Problem Research Articles

A novel approach for demand estimation under a flexible mixed logit model

This study explores customer heterogeneity and proposes a flexible mixed logit (FML) model without prior knowledge. We investigate a demand estimation problem under the FML model to estimate the choice probabilities of customers and identify the best-fitting mixing distribution for these probabilities. To address this problem, we introduce the loss-likelihood estimation (LLE) method to convert the estimation problem into a constrained convex problem and then design the Frank-Wolfe based (FWB) algorithm to solve the constrained convex problem and prevent model misspecification. This two-stage approach is referred to as the LLE-FWB approach. To validate this approach, we conduct a convergence analysis to calculate its convergence rate and perform numerical experiments to examine its effectiveness and robustness. The theoretical results show that the convergence rate of the LLE-FWB approach is O(1/k), and the simulation results show that this approach performs better, particularly for large data volumes and assortment sizes. Besides, we apply this approach to real-world data to support the implementation of personalized marketing strategies. The results show that the average expected revenue obtained in real-world instances is 17.42 % higher than the actual revenue.

Archimedes optimization algorithm based approaches for solving energy demand estimation problem: a case study of Turkey

Archimedes optimization algorithm based approaches for solving energy demand estimation problem: a case study of Turkey

Estimating Large-Scale Tree Logit Models

In “Estimating Large-Scale Tree Logit Models,” S. Jagabathula, P. Rusmevichientong, A. Venkataraman, and X. Zhao tackle the demand estimation problem under the tree logit model, also known as the nested logit or d-level nested logit model. The model is ideal for scenarios in which products can be grouped naturally based on their attributes into a hierarchy or taxonomy, such as flight itineraries grouped by departure time (morning or evening) and number of stops (nonstop or one stop). The current estimation methods are not practical for real-world applications that can involve hundreds or even thousands of products. The authors develop a fast, iterative method that computes a sequence of parameter estimates using simple closed-form updates by exploiting the structure of the negative log-likelihood objective. Numerical results on both synthetic and real data show that their proposed algorithm outperforms state-of-the-art optimization methods, especially for large-scale tree logit models with thousands of products.

Simulation-based dynamic origin–destination matrix estimation on freeways: A Bayesian optimization approach

This study focuses on dynamic origin–destination demand estimation problem on freeway networks. Existing studies on this problem rely on high-coverage of traffic measurements and assumptions on travel times, exhibiting limitations in real-world applications. We formulate the problem as a bi-level programming model, where micro-simulations are incorporated to precisely model traffic flows/travel times on freeways. The bi-level programming model cannot provide explicit closed-form expressions for the objective function and its derivatives, and also intrinsically high-dimensional. Thus, it is highly challenging to find efficient solution algorithms. In this regard, a problem-specific and computationally efficient Bayesian optimization approach is designed. Herein, a novel surrogate model is proposed by embedding a physical surrogate model (it characterizes underlying physical mechanisms and provides global yet less precise approximations) into a functional surrogate model (it provides precise local approximations). The embedding provides problem-specific knowledge for the surrogate model. More importantly, it also restricts the feasible region, enabling the surrogate model to efficiently deal with high-dimensional problems. Gaussian process can be served as the functional surrogate model. Two linear physical surrogate models are proposed to capture interactions between travel demand and traffic measurements. To deal with constraints in the surrogate model, a projection-distance based acquisition function is designed. In searching for new points, the proposed acquisition function is capable of assigning unique weight of exploration to each feasible solution. The proposed approach is validated based on a freeway corridor example, which indicates its outperformance over existing dynamic origin–destination estimation methods in terms of computational efficiency and solution accuracy.

A Novel Framework for Road Side Unit Location Optimization for Origin-Destination Demand Estimation

This study deals with the problem of road side unit (RSU) location optimization for origin-destination (OD) demand estimation. With the point-to-point measurement provided by RSUs in connected vehicle environment, the errors of OD demand estimation come from two sources: 1) the lack of enough path flow information; and 2) the vehicle-to-RSU (V2R) communication delay. However, increasing the amount of path flow information collected by RSUs results in the increase of V2R communication delay encountered by each collected data packet. Moreover, it is difficult to find a global optimal solution by formulating the problem as a single objective program. To address the investigated problem, this study proposes a novel framework consisting of solving a bi-objective RSU location optimization problem and an OD demand estimation problem. This RSU location optimization problem is formulated as a bi-objective nonlinear binary integer program to balance the maximization of the amount of path flow information and the minimization of V2R communication delay. The OD demand estimation problem is formulated as a least square estimator to identify the RSU location scheme with the smallest OD demand estimation error, among the Pareto optimal solutions to the bi-objective program. An efficient <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula> -constraint method is developed to generate the Pareto optimal solutions. The numerical example demonstrates that the proposed framework achieves 6.95 lower root-mean-square error of OD demand estimation, compared with the baseline framework.

Estimating Personalized Demand with Unobserved No-Purchases Using a Mixture Model: An Application in the Hotel Industry

Problem definition: Estimating customer demand for revenue management solutions faces two main hurdles: unobservable no-purchases and nonhomogenous customer populations with varying preferences. We propose a novel and practical estimation and segmentation methodology that overcomes both challenges simultaneously. Academic/practical relevance: We combine the estimation of discrete choice modeling under unobservable no-purchases with a data-driven identification of customer segments. In collaboration with our industry partner, Oracle Hospitality Global Business Unit, we demonstrate our methodology in the hotel industry setting where increased competition has driven hoteliers to look for more innovative revenue management practices, such as personalized offers for their guests. Methodology: Our methodology predicts demand for multiple types of hotel rooms based on guest characteristics, travel attributes, and room features. Our framework combines clustering techniques with choice modeling to develop a mixture of multinomial logit discrete choice models and uses Bayesian inference to estimate model parameters. In addition to predicting the probability of an individual guest’s room type choice, our model delivers additional insights on segmentation with its capability to classify each guest into segments (or a mixture of segments) based on their characteristics. Results: We first show using Monte Carlo simulations that our method outperforms several benchmark methods in prediction accuracy, with nearly unbiased estimates of the choice model parameters and the size of the no-purchase incidents. We then demonstrate our method on a real hotel data set and illustrate how the model results can be used to drive insights for personalized offers and pricing. Managerial implications: Our proposed framework provides a practical approach for a complicated demand estimation problem and can help hoteliers segment their guests based on their preferences, which can serve as a valuable input for personalized offer selection and pricing decisions. History: This paper has been accepted as part of the 2021 Manufacturing &amp; Service Operations Management Practice-Based Research Competition. Funding: This work was supported by Oracle Labs, part of Oracle America, Inc. [Gift 2380]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.1094 .

Analytical and simulation-based estimation of public transport demand

We consider the problem of public transport demand estimation. For the practical use of many models of transit assignment in any planning study, the knowledge of the transport demand systematized as an origin-destination matrix is required. Generally, this matrix is very expensive and difficult to obtain. In Bhouri et al. (2021) we proposed to estimate the OD-matrix through the numerical solution of a bilevel optimization problem. One disadvantage of this formulation is the difficulty of obtaining descent directions; therefore, we proposed a derivative-free method for the resolution of the optimization problem. Our goal in this work is to extend the study to larger networks, combining analytical modeling and simulation-optimization methodology. We use both approaches to perform the demand estimation over a section of a real network, and compare the obtained results for different scenarios and parameters.

Travel Demand Estimation in Urban Road Networks as Inverse Traffic Assignment Problem

Abstract Nowadays, traffic engineers employ a variety of intelligent tools for decision support in the field of transportation planning and management. However, not a one available tool is useful without precise travel demand information which is actually the key input data in simulation models used for traffic prediction in urban road areas. Thus, it is no wonder that the problem of estimation of travel demand values between intersections in a road network is a challenge of high urgency. The present paper is devoted to this urgent problem and investigates its properties from computational and mathematical perspectives. We rigorously define the travel demand estimation problem as directly inverse to traffic assignment in a form of a bi-level optimization program avoiding usage of any pre-given (a priori) information on trips. The computational study of the obtained optimization program demonstrates that generally it has no clear descent direction, while the mathematical study advances our understanding on rigor existence and uniqueness conditions of its solution. We prove that once a traffic engineer recognizes the travel demand locations, then their values in the road network can be found uniquely. On the contrary, we discover a non-continuous dependence between the travel demand locations and absolute difference of observed and modeled traffic values. Therefore, the results of the present paper reveal that the actual problem to be solved when dealing with travel demand estimation is the problem of recognition of travel demand locations. The obtained findings contribute in the theory of travel demand estimation and give fresh managerial insights for traffic engineers.

A bilevel model for public transport demand estimation

For the case of public transport, we consider the problem of demand estimation. Given an origin-destination matrix representing the public transport demand, the distribution of flow among different lines can be obtained assuming that it corresponds to a certain equilibrium characterized by an optimization problem. In particular we will focus on the assignment model proposed by Cepeda et al. (2006). However the knowledge of origin-destination matrix is expensive and sometimes unaffordable in practice. Traditionally, it is estimated using statistical or econometrical considerations. In this work, we explore the estimation through the numerical solution of a bilevel optimization problem. One disadvantage of this formulation is the difficulty of obtaining descent directions, hence, for the resolution of the optimization problem we use a derivative-free method. This method was applied for small networks getting good results.

An inverse bilevel equilibrium problem for public transport demand estimation

We consider the problem of demand estimation for public transport networks. Given an origin-destination matrix representing the public transport demand, the distribution of flow among different lines can be obtained assuming that it corresponds to a certain equilibrium characterized by an optimization problem. The knowledge of the origin-destination matrix is expensive and sometimes unaffordable in practice. Traditionally, it is estimated using statistical or econometrical considerations. In this work, we explore the estimation through the numerical solution of a bilevel optimization problem. One disadvantage of this formulation is the difficulty of obtaining descent directions, therefore we proposed a derivative-free method for the resolution of the optimization problem. The method is firstly tested on small networks using a derivative-free optimization method and then, using an approach based on simulation. This simulation-optimization methodology showed as good results as analytical modeling, opening the door to handle bigger networks where analytical computation is hard to accomplish.

Boundaries of Differentiated Product Markets and Retailer Pricing

This paper studies the effects of misspecified boundaries of competition on optimal retail pricing using store-level supermarket scanner data. We focus on two types of misspecification: (i) misspecification of the demand estimation problem, which can arise from either defining the product market to be too narrow or specifying an overly restrictive model of demand; (ii) misspecification of the retailer's decision problem, which can arise from the retailer separately optimizing prices in each category but failing to account for, and thus internalize, cross-category effects. Both sources of misspecification are relevant in differentiated product markets where goods are broadly related but in ways that may not be immediately a priori. Quantifying the costs associated with either form of misspecification is challenging because it requires a flexible yet valid demand system. To this end, we take a nonparametric approach to estimating a multi-category demand system that imposes minimal restrictions on the sign/magnitude of cross-price effects and also satisfies key properties required by economic theory. Our first set of empirical results is descriptive. We use data across nine diverse product groups to show that cross-category effects exists and are often nuanced in their sign and magnitude. That is, many categories are neither obvious substitutes' nor obvious We then zoom in on refrigerated juices and estimate demand nonparametrically across five juice categories where we find empirical support for a flexible model that can accommodate both substitutes and complements. We solve for optimal prices under both sources of misspecification and estimate profit losses to be in the 5-15% range.

Non-linear optimization for continuous travel demand estimation

Models and methods of traffic distribution are being developed by researchers all over the world. The development of this scientific field contributes to both theory and practice. In this article, the non-linear optimization of traffic flow re-assignment is examined in order to solve continuously the travel demand estimation problem. An approach has been developed in the form of computational methodology to cope with the network optimization problem. A uniqueness theorem is proved for a certain type of road network. Explicit relations between travel demand and traffic flow are obtained for a single-commodity network of non-intersecting routes with special polynomial travel time functions. The obtained findings contribute to the theory and provide a fresh perspective on the problem for transportation engineers.

A Big Data Demand Estimation Model for Urban Congested Networks

Abstract The origin-destination (OD) demand estimation problem is a classical problem in transport planning and management. Traditionally, this problem has been solved using traffic counts, speeds or travel times extracted from location-based sensor data. With the advent of new sensing technologies located on vehicles (GPS) and nomadic devices (mobile and smartphones), new opportunities have emerged to improve the estimation accuracy and reliability, and more importantly to better capture the dynamics of the daily mobility patterns. In this paper we frame this new data in a comprehensive framework which estimates origin-destination flows in two steps: the first step estimates the total generated demand for each traffic zone, while the second step adjusts the spatial and temporal distribution on the different OD pairs. We show how mobile data can be used to obtain OD matrices that reflect the aggregated movements of individuals in complex and large-scale instances, while speed information from floating car data can be used in the second step. We showcase the added value of big data on a realistic network comprising Luxembourg’s capital city and its surrounding. We simulate traffic by means of a commercial simulation software, PTV-Visum, and leverage real mobile phone data from the largest telco operator in the country and real speed data from a floating car data service provider. Results show how OD estimation improves both in solution reliability and in convergence speed.

Integration of Departure Time Choice Modeling and Dynamic Origin–Destination Demand Estimation in a Large-Scale Network

Time-dependent origin–destination (OD) demand estimation using link traffic data in a large-scale network is a highly underdetermined problem. As a result, providing an accurate initial solution is crucial for obtaining a more reliable estimated demand. In this paper, we discuss the necessity of having a comprehensive demand profiling model that considers the spatial differences of OD pairs and we demonstrate its application in the calibration of large-scale traffic assignment models. First, we apply a departure choice model that adds a time dimension to the OD demand flows concerning their spatial differences. The time-profiled demand is then fed into the time-dependent OD demand estimation problem for further adjustment. Results show that in addition to reducing the error between simulation outputs and the observed link counts, the estimated demand profile more accurately reflects the spatial correlation of the OD pairs in the large-scale network being studied. Results provide practical insights into deployment and calibration of simulation-based dynamic traffic assignment models.

Estimating Personalized Demand with Unobserved No-purchases using a Mixture Model: An Application in the Hotel Industry

Estimating customer demand for revenue management solutions faces two main hurdles: unobservable no-purchases and non-homogenous customer populations with varying preferences. We propose a novel and practical estimation and segmentation methodology that overcomes both challenges simultaneously. We combine the estimation of discrete choice modeling under unobservable no-purchases with a data-driven identification of customer segments. In collaboration with our industry partner, Oracle Hospitality Global Business Unit, we demonstrate our methodology in the hotel industry setting, where increased competition has driven hoteliers to look for more innovative revenue management practices such as personalized offers for their guests. Our methodology predicts demand for multiple types of hotel rooms based on guest characteristics, travel attributes, and room features. Our framework combines clustering techniques with choice modeling to develop a mixture of multinomial logit discrete choice models and uses Bayesian inference to estimate model parameters. In addition to predicting the probability of an individual guest's room type choice, our model delivers additional insights on segmentation with its capability to classify each guest into segments (or a mixture of segments) based on their characteristics. We first show using Monte-Carlo simulations that our method outperforms several benchmark methods in prediction accuracy, with nearly unbiased estimates of the choice model parameters and the size of the no-purchase incidents. We then demonstrate our method on a real hotel dataset and illustrate how the model results can be used to drive insights for personalized offers and pricing. Our proposed framework provides a practical approach for a complicated demand estimation problem, and can help hoteliers segment their guests based on their preferences, which can serve as a valuable input for personalized offer selection and pricing decisions.

Incorporating trip chaining within online demand estimation

Time-dependent Origin–Destination (OD) demand flows are fundamental inputs for Dynamic Traffic Assignment (DTA) systems and real-time traffic management. This work introduces a novel state-space framework to estimate these demand flows in an online context. Specifically, we propose to explicitly include trip-chaining behavior within the state-space formulation, which is solved using the well-established Kalman Filtering technique. While existing works already consider structural information and recursive behavior within the online demand estimation problem, this information has been always considered at the OD level. In this study, we introduce this structural information by explicitly representing trip-chaining within the estimation framework. The advantage is twofold. First, all trips belonging to the same tour can be jointly calibrated. Second, given the estimation during a certain time interval, a prediction of the structural deviation over the whole day can be obtained without the need to run additional simulations. The effectiveness of the proposed methodology is demonstrated first on a toy network and then on a large real-world network. Results show that the model improves the prediction performance with respect to a conventional Kalman Filtering approach. We also show that, on the basis of the estimation of the morning commute, the model can be used to predict the evening commute without need of running additional simulations.

Spatial and Temporal Analyses for Estimation of Origin-Destination Demands by Time of Day Over Year

This paper proposes a two-stage model for the estimation of origin-destination (OD) demands by the time of day over the year with the use of offline traffic data from the real-time travel information system. In the first stage, a travel time recursive function is proposed to use the offline travel speed data for the investigation of the spatial and temporal relationships between time-dependent OD demands and traffic counts. As such, it is not required to carry out the time-consuming dynamic traffic assignment (DTA) process which is frequently used in the conventional time-dependent OD estimation models. Using the results in the first stage together with the available traffic count data, a least-squares method is adopted to formulate the time-dependent OD demand estimation problem as a quadratic programming model in the second stage. A solution algorithm is adapted for solving the proposed model. Then, the proposed method is easy for implementation in practice. Particularly, when the traffic accident occurs in the network, the estimated time-dependent OD demands can be helpful for understanding the complex travel behavior (e.g., departure time choice) under uncertainty condition. The numerical examples are presented to illustrate the applications of the proposed model.

A Flexible Demand Model for Complements Using Household Production Theory

We utilize household production theory to address the problem of micro-level demand estimation across complementary goods. According to this theory, consumers buy inputs and combine them to produce final goods from which they derive utility. We use this idea to build a structural model of demand for complements that can be estimated on purchase data in the presence of corner solutions and indivisible packages. We find that, even when reusing the same functional form as some previous models of demand for substitutes, our model can accommodate very different patterns of consumer preferences over complements and lead to a flexible demand system from perfect complementarity to no complementarity. We estimate the model on purchase data from a panel of consumers and show how it can be used to increase the profitability of couponing strategies by taking into account the spillover effect of coupons on demand for complementary categories. We also show how our model can be used by manufacturers to make decisions regarding the size of packages by taking into account cross-category consumption.

Improving the measurement of the Korean emergency medical System's spatial accessibility

Measuring spatial accessibility for healthcare service is an important prerequisite for public health policy decision. While existing literature offers spatial accessibility measures, applying those measures to healthcare services reveals some weaknesses for improvement. In this study, we propose an improved accessibility measure. The proposed measure is based on the floating catchment area method but improved in some aspects. We use two distance decay functions to distinguish their respective effects in measuring accessibility. A local distance decay function, expressed as a logistic cumulative density function, accounts for region-specific patient visit patterns. A global distance decay function, also defined as a logistic density function, incorporates patients’ inherent resistance to travel in the measure. To address the problem of potential demand estimation, which distorts the resulting accessibility values, we introduce effective potential demand which is defined as the ratio of potential demand to total nearby capacity by care providers as an adjustment factor. To examine the effectiveness, we apply the measure to identify the medically underserved areas in Korea for emergency medical services. Compared with the existing floating catchment area measure, the proposed measure provides more proper spatial accessibility information.

Estimating multi-year [formula omitted] origin-destination demand using high-granular multi-source traffic data

Dynamic origin-destination (OD) demand is central to transportation system modeling and analysis. The dynamic OD demand estimation problem (DODE) has been studied for decades, most of which solve the DODE problem on a typical day or several typical hours. There is a lack of methods that estimate high-resolution dynamic OD demand for a sequence of many consecutive days over several years (referred to as 24/7 OD in this research). Having multi-year 24/7 OD demand would allow a better understanding of characteristics of dynamic OD demands and their evolution/trends over the past few years, a critical input for modeling transportation system evolution and reliability. This paper presents a data-driven framework that estimates day-to-day dynamic OD using high-granular traffic counts and speed data collected over many years. The proposed framework statistically clusters daily traffic data into typical traffic patterns using t-Distributed Stochastic Neighbor Embedding (t-SNE) and k-means methods. A GPU-based stochastic projected gradient descent method is proposed to efficiently solve the multi-year 24/7 DODE problem. It is demonstrated that the new method efficiently estimates the 5-min dynamic OD demand for every single day from 2014 to 2016 on I-5 and SR-99 in the Sacramento region. The resultant multi-year 24/7 dynamic OD demand reveals the daily, weekly, monthly, seasonal and yearly change in travel demand in a region, implying intriguing demand characteristics over the years.