Multiple Discrete-continuous Extreme Value Research Articles

Estimating Stockout Costs and Optimal Stockout Rates: A Case on the Management of Ugly Produce Inventory

Efficiently managing inventories requires an accurate estimation of stockout costs. This estimation is complicated by challenges in determining how to compensate consumers monetarily to ensure they will maintain the same level of utility they would have obtained had stockouts not occurred. This paper presents an analysis of these compensation costs as applied to the design of optimal stockout rates by an online retailer marketing to consumers aesthetically substandard fruits and vegetables rejected by mainstream grocery chains. Because growers face high uncertainty in their harvesting conditions and in the aesthetic quality of their crops and there are little data on hand to predict the value consumers attach to the availability of subpar produce, it is difficult to optimally match the supply of these products with consumers’ demand. Our analysis draws from a multiple discrete-continuous extreme value (MDCEV) choice model to calculate consumer compensations that the retailer can use to estimate the opportunity costs of stockouts to manage its inventory. We show that not taking into account these compensation costs could unduly inflate the optimal stockout rates for these products. Armed with these compensation cost estimates, we show how these costs can serve as incentives for retailers to source greater inventory amounts of imperfect produce from growers and how this will ultimately translate into less waste in the supply chain. This paper was accepted by Charles Corbett, operations management. Funding: Funding from Agriculture and Food Research Initiative (National Institute for Food and Agriculture, USDA) [Grant 2016-09900] is gratefully acknowledged. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2021.03174 .

Estimating Stockout Costs and Optimal Stockout Rates: A Case on the Management of Ugly Produce Inventory

Efficiently managing inventories requires an accurate estimation of stockout costs. This estimation is complicated by challenges in determining how to compensate consumers monetarily to ensure they will maintain the same level of utility they would have obtained had stockouts not occurred. This paper presents an analysis of these compensation costs as applied to the design of optimal stockout rates by an online retailer marketing to consumers aesthetically substandard fruits and vegetables rejected by mainstream grocery chains. Because growers face high uncertainty in their harvesting conditions and in the aesthetic quality of their crops and there are little data on hand to predict the value consumers attach to the availability of subpar produce, it is difficult to optimally match the supply of these products with consumers’ demand. Our analysis draws from a multiple discrete-continuous extreme value (MDCEV) choice model to calculate consumer compensations that the retailer can use to estimate the opportunity costs of stockouts to manage its inventory. We show that not taking into account these compensation costs could unduly inflate the optimal stockout rates for these products. Armed with these compensation cost estimates, we show how these costs can serve as incentives for retailers to source greater inventory amounts of imperfect produce from growers and how this will ultimately translate into less waste in the supply chain. This paper was accepted by Charles Corbett, operations management. Funding: Funding from Agriculture and Food Research Initiative (National Institute for Food and Agriculture, USDA) [Grant 2016-09900] is gratefully acknowledged. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2021.03174 .

A step in time: A sequence analysis and choice modelling approach to examine time allocation in individual activities and the role of neighbourhood crime

The Space-Time Budget (STB) method is used to collect spatial and temporal features of an individual’s activities and is an important technique to explore relationships between the environment and crime. This spatial and temporal approach to the study of everyday activity spaces reveals much about victimisation experiences, the relationship between place, time, and perceptions of safety, and where and when offending may occur. Few studies, however, consider the relationship between living in a criminogenic place (neighbourhood crime) and people’s daily activity patterns. Drawing on disaggregate app-based data for 50 participants tracked over a 7-day period, we use sequence analysis to first delineate time allocation to each activity on a minute-by-minute basis. Next, using result from the sequence analysis we introduce the multiple discrete-continuous extreme value (MDCEV) model to understand how neighbourhood crime and socio-demographic characteristics influence individuals’ time allocation to discrete daily activities. Results reveal that neighbourhood drug and violent incidents exert restrictions on an individual’s propensity to spend time outside the home. Females and older people appear more likely to be constrained by the presence of neighbourhood crime (in particular drug and property incidents) as they allocate less time to outdoor activities. The principal utility of the current study is its methodological advancement and the practical insights for urban planning regarding the design of crime prevention strategies to increase guardianship in public places.

Development of Multiple Discrete-Continuous Extreme Value Model with Non-Monotonic Utilities: Formulation and Application to Outdoor Non-Mandatory Time-Use Decisions

This paper further explores multiple discrete-continuous extreme value (MDCEV) models. MDCEV models are widely used for time-use analysis because they can accommodate the diminishing marginal utility with respect to time consumption and benefit from simple closed-form likelihood expressions for estimation, while considering the overall constraints of time resource. However, all of the existing models adopt a monotonically increasing form of utility function, which does not accommodate possible non-monotonic utilities with respect to time-use. This paper further develops the MDCEV model by firstly introducing utility functions with a form of parabola to capture non-monotonic preferences in time allocation behaviors. A corresponding simple and computationally efficient forecasting algorithm to predict the time-use of individuals is also developed. The proposed MDCEV model with parabolic utilities is applied to analyze time-use decisions among a variety of outdoor non-mandatory activities on weekends using data from the 2019 American Time Use Survey. The proposed model is compared with traditional MDCEV models to show its ability to describe non-monotonic preferences in time-use in association with various explanatory variables. This paper makes an initial attempt to specify non-monotonic utilities for time-use analysis, but further studies are required to develop more sophisticated non-monotonic utility formulation to improve the goodness-of-fit of the model.

A framework for transportation and land use integration as a parallel constrained multiple discrete-continuous extreme value (PC-MDCEV) home production model

We propose a microeconomic foundation for transportation and land use choice model integration based on the theory of home production. A utility function is developed that considers both household monetary expenditure and individual time use. We introduce a parallel constrained multiple discrete-continuous extreme value (MDCEV) structure that allows for the inclusion of multi-person households in the model. An empirical application is provided for the Greater Toronto Area using a validated synthetic dataset. Empirical results demonstrate an economy of scale in time devoted to home production, analogous to scaling exhibit in market production. It was found that the mix of dwelling types (detached, apartment, etc.) has a significant influence on both time use and consumption. Finally, we provide several directions for future research to advance the practice of urban modelling and better capture the complex dynamics of household decision-making.

The influence of working from home and underlying attitudes on the number of commuting and non-commuting trips by workers during 2020 and 2021 pre- and post-lockdown in Australia

Since the start of 2020, we have seen major changes in the way communities operate. Mobility behaviour has been drastically impacted by work from home (WFH) and by lockdowns and restrictions in different jurisdictions. This study investigates the influence of WFH and different lockdown patterns on commuting and non-commuting trips in Australia by workers between early 2020 and late 2021. The data includes three waves of data collection to represent different lockdown periods. A multiple discrete–continuous extreme value (MDCEV) model is estimated to represent the number of one-way trips undertaken weekly with different purposes (commuting, work-related, education, shopping, personal business/social recreation), and by different modes (car, public transport, active modes). Explanatory variables include socioeconomic characteristics, location, the time period during the pandemic (i.e., waves). In addition, latent variables were included representing underlying attitudes such as satisfaction towards life or concern about the use of public transport – which might certainly play an important role in understanding individual weekly travel behaviour decisions. The model structure has the advantage that it estimates commuting and non-commuting activity together, allowing for a substitution effect between them. The results suggest that across all waves and jurisdictions, respondents who WFH more are more likely to have a higher number of shopping trips and personal business/social recreation trips, perhaps substituting these trips in replacement of their lesser commuting trips. Interestingly, all other influences held constant, individuals who are more concerned about the use of public transport are more likely to undertake commuting trips by all modes, more likely to do shopping trips, and less likely to undertake personal business/social recreation trips – suggesting they are prioritising essential trips rather than social/personal trips and perceive the risk of COVID-19 to be higher due to this travel.

Modal Splits Before, During, and After the Pandemic in Switzerland

The MOBIS-Covid data provides a unique opportunity to put mobility adjustments observed during the crisis in perspective. A large panel has been tracked from before the crisis up until the end of 2022. Starting with 1370 participants and observing a gradual drop-off, around 250 kept tracking throughout the whole study period of over 2 years. Switzerland lifted its measures counteracting the virus spread in mid-February 2022, reaching a potential new equilibrium in the months after. Descriptive indicators have been constructed for Switzerland in order to disentangle the narrative of the crisis from the perspective of transport demand. The descriptive findings are supplemented by a mixed multiple discrete-continuous extreme value model (MMDCEV). We find a shift in modal splits away from car and train, where in particular bus could expand its mode share. While the cycling and walking booms were temporary, the bicycle still shows slightly higher mode distance shares. There are observable differences between the working arrangements (home office, mixture and in-office), however, we do not find evidence that preferences differ substantially. This suggests that the working arrangement segments the population along socioeconomic dimensions with different mobility behaviors and mode preferences. Modes are more satiated in the post-pandemic world, hinting that people use fewer modes in their weekly modal mix but use them more intensely. However, the model suggests that the pandemic should not be read as a structural break in mode preferences. We will therefore likely see further convergence to the pre-pandemic equilibrium.

다중 이산 연속선택모형을 이용한 원산지 및 용도별 쇠고기 수요 분석

There has been a steady increase in the consumption of Korean beef in recent years, with the per capita consumption of beef reaching a record high in 2022. The domestic beef market provides consumers with more choices, so traditional methods of demand analysis that rely on whole beef products are likely to become less useful. Employing the multiple discrete-continuous extreme value model (MDCEV), we analyze scanner data on consumer panels over a long period. Our findings indicate Hanwoo beef demand is less price sensitive than other beef types. Furthermore, Hanwoo beef has a relatively larger cross-price elasticity than other alternatives. Consumers' income, age, and household size also significantly affect the interrelationship between demand and supply.
 Higher-income consumers are more likely to choose Hanwoo beef and less likely to choose imported beef. Larger families are more likely to select beef for grilling rather than cooking. These results explain current beef expenditure patterns and help understand how consumers make decisions.

Are Telecommuters’ and Non-Telecommuters’ Daily Time-Use Behaviors Different? An Episode-Level Model for Non-Mandatory Activities

Telecommuters (individuals working from home), and non-telecommuters (individuals working at the workplace) might have significantly different daily time-use patterns. For example, telecommuters might be able to engage in more episodes of non-mandatory activities such as recreation and pick-up/drop-off of children, as many telecommuters have a relatively flexible work arrangement in relation to their work location and schedule. This study aims to explore the non-mandatory activity engagement and duration decisions of these two worker profiles at a disaggregated-episode level. To do so, a multiple discrete continuous extreme value with ordered preferences (MDCEV-OP) model is adopted, using the 2018 travel survey data from the Central Okanagan region of British Columbia, Canada. This model accounts for multiple occurrences of each activity type (i.e., episodes) along with their corresponding durations. In doing so, the model adopts a logical ordering ensuring that the jth episode is not predicted without the occurrence of the ( j–1)th episode of an activity type. The model results reveal that telecommuters are more likely to engage in higher episodes of non-mandatory activities, compared with non-telecommuters. For instance, female teleworkers are found to be more likely to participate in higher episodes of activities associated with household-related responsibilities such as shopping. In contrast, female non-telecommuters are associated with participating in more episodes of personal business-related activities. The findings of this study provide important behavioral insights into the activity-time-use patterns of telecommuters and non-telecommuters, which can be utilized to develop more effective and equitable travel demand management plans, policies, and models.

Modelling activity patterns of wild animals - An application of the multiple discrete-continuous extreme value (MDCEV) model

Advanced econometric models used in the field of transport or marketing are becoming increasingly sophisticated and able to capture complex decision making and outcomes. In this paper, we apply state-of-the-art discrete-continuous choice models to the field of Ecology, in particular to model activity engagement of the population of Swedish Brown bears. Using data from GPS collars that track wild animals over time, we estimate a Multiple Discrete-Continuous Extreme Value (MDCEV) model to understand activity engagement and duration as a function of both bear characteristics and other external factors. We show that the methodology is not only suitable to address this aim, but also allows us to produce insights into the connection between the animal's age and gender and activity engagement as well as the links with climate variables (temperature and precipitation) and human activity (hunting).

On modeling future workplace location decisions: An analysis of Texas employees

In this paper, we examine work place location (WPL) preferences of workers in an unpredictable and evolving future by investigating how workers would prefer to allocate their monthly working days among the three WPL alternatives of working from home, from the work office, and from a variable third WPL. In contrast to earlier studies that typically focus on telework as a binary of whether an individual is a teleworker or not, we focus our attention on workers’ preferences for specific combinations of all three WPLs over a period of a month (including, but not limited to, only selecting one WPL for all days of the month). In our analysis, we employ the multiple discrete–continuous extreme value (MDCEV) model, using a 2022 stated preference survey of future work preferences of employees residing in the state of Texas. The results indicate that single young women with very young children, those with long commutes and “intolerable” traffic congestion to the work office, individuals with a private study in their homes, self-employed workers, and those in non-essential service occupations have the highest preference for working from home. On the other hand, older men, individuals from low income households, those residing in rural areas, and workers in essential service occupations have the highest preference for the work office. And, for the third WPL, young non-single women with very young children, individuals from low income households, part-time employees, and those in professional, managerial or finance occupations have the highest predisposition. These results should provide valuable insights to urban planners, homebuilders, employers, travel demand modelers, and a whole host of other businesses to achieve specific desired end states. From a data collection standpoint, our study underscores the need to collect detailed information about work patterns in future activity-travel surveys.

Exploring joint activity-tour participation, time allocation, and mode choice decisions

ABSTRACT This paper presents the findings of an activity-based tour-level model that jointly investigates individuals’ decisions of activity-tour participation, time allocation, and mode choice. A multiple discrete continuous extreme value (MDCEV) model is developed that explores the participation and time allocation decisions for mandatory, maintenance, and discretionary activity-tour types. Mixed logit (MXL) models are developed to evaluate the mode choice decisions of individuals for different activity-based tours. Logsum values, which represent the modal accessibility, are introduced within the MDCEV modeling framework as feedback mechanisms from mixed logit models that exclusively examine the influence of individuals’ mode choice on their activity-tour engagement decisions as well as ensure the integrity of the decision modeling system. Findings of this study would assist the policymakers to develop effective strategies for better transportation investment decisions.

A multiple discrete-continuous extreme value model with ordered preferences (MDCEV-OP): Modelling framework for episode-level activity participation and time-use analysis

This paper formulates a novel, multiple discrete-continuous extreme value model with ordered preferences (MDCEV-OP) to analyze multiple discrete-continuous (MDC) choices at a disaggregate level, including the number of instances different alternatives are chosen and the amount of consumption at each instance of choice. In doing so, the proposed model ensures a logically consistent prediction of multiple choice instances of an alternative. Specifically, the model prevents the prediction of positive allocation to the jth instance (i.e., a frequency of j episodes) of a good while predicting zero allocation to the (j-1)th or lower-numbered instances of that alternative. This is achieved by imposing a non-increasing order on the baseline-preference parameters of different choice instances of an alternative. The model results in a conditional likelihood function, where the likelihood arising from the optimality conditions of the utility maximization problem is conditioned on the ordering of baseline marginal utilities. Combining this strategy with independent and identically distributed (IID) Gumbel stochastic terms in the utility functions results in a closed-form likelihood expression that is not much more difficult than that of the MDCEV model. The proposed framework is applied for an empirical analysis of disaggregate, episode-level activity participation and time allocation behavior of non-working adults in Los Angeles, California. The empirical MDCEV-OP model provided better fit and predictive accuracy (in both estimation and validation datasets) for analyzing episode-level activity participation than a disaggregate MDCEV model that does not recognize the logical ordering of episodes. At the same time, the activity-level predictions aggregated from the episode-level predictions of the MDCEV-OP model do not deviate significantly from the predictions of an aggregate MDCEV model. These results highlight the efficacy of the proposed model for analyzing episode-level activity generation and time allocation.

Socio-demographics, neighborhood characteristics, time use, and leisure-time physical activity engagement patterns over the life course

Physical inactivity remains a major public health challenge today. Understanding the determinants of changes in habitual leisure-time physical activity patterns by type across the life course is important for developing targeted interventions. This study presents a multiple discrete-continuous extreme value model to examine the determinants of habitual participation in and time allocation to multiple leisure-time physical activities over the life course. A comprehensive set of socio-demographics, life transitions, neighborhood characteristics, and time-related factors are considered as determinants of each activity type, including sports, recreational walking, cycling, outdoor playing, and dog walking. Results estimated on retrospective survey data collected in the Netherlands show significant differences in the determinants of the different types of leisure-time physical activity. Social-demographic factors have a strong influence on sports participation, followed by recreational walking, cycling, outdoor playing, and then dog walking. Life transitions have different effects. A change in marital status appears to be the most important life event for sports participation while changing jobs is the most important event for the other two activities. Neighborhood characteristics primarily affect participation in recreational walking, cycling, outdoor playing, and dog walking. As for time-related factors, they mainly impact sports engagement. The findings of this study could help develop effective interventions to promote leisure-time physical activity participation during life transitions and encourage healthy living.

An Episode-Level Joint Model for Activity Engagement, Duration, and Destination Location Choice Decisions

ABSTRACT This paper presents an episode-level activity generation and destination choice model. The model accommodates the occurrence of multiple episodes of an activity and captures interdependencies among travel choice dimensions that vary at the episode-level such as occurrence, duration, and destinations of episodes. A multiple discrete-continuous extreme value model with ordered preferences (MDCEV-OP) is adopted. This ordered preference extension of the modified MDCEV model imposes a restriction that the higher-numbered episodes do not occur without the occurrence of lower-numbered episodes. Further, destination accessibility from the destination choice utility is derived using a multinomial logit (MNL) model, which provides feedback to the MDCEV-OP through a logsum component. The findings of this study demonstrate the benefits of modeling activity engagement, duration, and destination at the granular level of episodes, including offering an enhanced behavioral realism of the model and the potential to improve forecasting accuracy and insights of activity-based models.

Exploring elderly people's daily time-use patterns in the living environment of Beijing, China

To develop an age-friendly society, it is a basic task to deeply understand what and how factors would affect elderly people's daily multiple-activity time-use patterns. In the literature, the impacts of built environments as the physical aspects of living environments have been widely studied. However, the impacts of social environments as the social aspects of living environments on multiple activity participation and duration constrained by time budgets have not been found. To fill this gap, this paper makes efforts to propose various social environmental indicators and incorporate them into a multiple discrete-continuous extreme value (MDCEV) model to test the significance of each variable and to explore the impacts of living environments on elderly people's daily multiple-activity time-use behaviours. In addition to socio-economic compositions, the social environmental indicators are extended to social ties of people, living pressure, social resources distribution, social safety and policy. Then a joint elasticity analysis for multiple activity participation and duration with constraints is proposed for deriving policy and practice implications. The specifications and joint elasticity analysis in Beijing of China which is a representative city affected by Confucian culture and faced with aging problem in Eastern and South-eastern Asia help find out significant factors and their impacts on elderly people's multiple-activity time-use patterns. Policy and practice implications are suggested to improve elderly people's out-of-home activity participation and duration so that an age-friendly society is expected.

Matching reality: A basket and expenditure based choice experiment with sensory preferences

This article introduces a basket and expenditure based choice experiment design to elicit consumer preferences for multiple products. This design is utilized to imitate a more realistic shopping scenario for consumers when choosing among many different products simultaneously. This approach allows participants to choose both multiple items, in this case vegetables, and related quantities/expenditures to place in a basket of goods. We provide an application of the experimental design to a vegetable choice experiment. This is done in conjunction with a sensory experiment to provide a contextual component to the experiment and econometric model. This type of experiment lends itself to the use of the Multiple Discrete-Continuous Extreme Value (MDCEV) class of models. More specifically, we use the extended version of the MDCEV model proposed by Palma and Hess (2020) that relaxes the need for a budget while also accounting for substitution and complementarity among products. We find that the proposed design and class of econometric methods present a flexible way to analyze consumer choice when the desire is to elicit preferences for a basket of goods rather than simple discrete alternatives or attributes.

Investigation of Shifts in Time Use Behavior during the COVID-19 Pandemic: A Mixed Multiple Discrete-Continuous Extreme Value Approach with Panel GPS Data

Typical patterns of time use and travel behavior have been transformed by the COVID-19 pandemic. The drastic change has been documented in several studies to date, especially in the realm of transport, which have asked respondents about how their behavior has changed compared with their prepandemic routines. This work complements those efforts, offering a valuable evaluation of the decision-making process behind choosing which activities to engage in and for how long. A mixed multiple discrete-continuous extreme value (MMDCEV) model was applied to panel GPS data collected between September 2019 and October 2020. The estimation results uncovered how different demographic and mobility tool ownership characteristics affected the choice of activities and their duration. Additional interaction effects of different time periods exogenously introduced into the model allowed for the assessment of the differential effects of these components. Our findings revealed that the choice to participate in out-of-home activities strongly differed with respect to prepandemic conditions. Not only were individuals choosing to spend more time at home during the pandemic, but when they did engage in out-of-home activities, it was also for a shorter duration. Notably, age, gender, education level, and income all affected the propensity to engage in out-of-home activities during the pandemic. These results and their implications for policy as we try to plan for the “new normal” daily life are discussed.

An analysis of the role of residential location on the relationships between time spent online and non-mandatory activity-travel time use over time

Although the associations between the use of information and communications technologies (ICT) and individuals' daily travel and activity patterns have been extensively investigated for several decades, few studies have examined the amount of time spent using ICT, its implications on activity-travel behavior, and how such ICT-travel relationships may vary over time and according to residential location. This study takes a quasi-longitudinal perspective to explore how the amount of time individuals spend on the Internet for personal or non-work purposes correlates to their activity-travel for non-mandatory maintenance and leisure purposes, as well as how such associations evolve over a decade. More importantly, it examines how the role of people's residential locations in determining the associations between time spent on the Internet and travel has changed over time. Our approach utilizes two datasets from two major cross-sectional surveys in Scotland: the 2005/06 Scottish Household Survey (SHS) and the 2015 Integrated Multimedia City Data (iMCD) Survey, which were similarly structured and developed. To accommodate the multiple discreteness characterizing activity-travel choice and duration, the multiple discrete-continuous extreme value (MDCEV) model was employed to capture the Internet–travel relationships for the full sample and the urban, town, and rural sub-samples in both 2005/06 and 2015. Our findings suggest that use of the Internet for personal purposes increasingly tends to discourage rather than facilitate physical activity and travel for non-mandatory purposes over time, especially for those who spend high levels of time on the Internet (over ten hours per week). However, such Internet–travel relationships are generally weaker among people living in remote areas than those living in urban areas. While the relationships regarding maintenance activity purposes are significant for almost all levels of Internet users among the urbanites in both years, they were not significantly found at all among rural residents in either 2005/06 or 2015.

Modeling Urban Mode Choice Behavior During the COVID-19 Pandemic in Switzerland Using Mixed Multiple Discrete-Continuous Extreme Value Models

This paper describes and models the behavioral response to the COVID-19 pandemic in Switzerland. The MOBIS-COVID GPS tracking dataset, which includes a pre-pandemic reference base, is used. Trip-level data are transformed in weekly distance proportions per mode per week, and the data are modeled using a mixed multiple discrete-continuous extreme value (MMDCEV) model. Four distinct segments are derived, from September 2019 until the end of 2020, and used to uncover natural and forced behavioral adaptations. The descriptive and model estimation results confirm the trends partly observed around the globe, that is, a large decrease in public transport usage, recovered car usage, and a cycling boom. Behavioral insights are further provided as well as policy recommendations.