Convex Optimization for Bundle Size Pricing Problem

2021 ◽  
Author(s):  
Xiaobo Li ◽  
Hailong Sun ◽  
Chung Piaw Teo
Keyword(s):  
Convex Optimization ◽  
Order Statistics ◽  
Covariance Matrix ◽  
Discrete Choice ◽  
State Of The Art ◽  
Choice Model ◽  
Partial Sums ◽  
Second Moments ◽  
Size Number ◽  
Bundle Size

We study the bundle size pricing (BSP) problem in which a monopolist sells bundles of products to customers and the price of each bundle depends only on the size (number of items) of the bundle. Although this pricing mechanism is attractive in practice, finding optimal bundle prices is difficult because it involves characterizing distributions of the maximum partial sums of order statistics. In this paper, we propose to solve the BSP problem under a discrete choice model using only the first and second moments of customer valuations. Correlations between valuations of bundles are captured by the covariance matrix. We show that the BSP problem under this model is convex and can be efficiently solved using off-the-shelf solvers. Our approach is flexible in optimizing prices for any given bundle size. Numerical results show that it performs very well compared with state-of-the-art heuristics. This provides a unified and efficient approach to solve the BSP problem under various distributions and dimensions. This paper was accepted by David Simchi-Levi, revenue management and market analytics.

scholarly journals Comparing the State-of-the-Art Efficient Stated Choice Designs Based on Empirical Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Li Tang ◽  
Xia Luo ◽  
Yang Cheng ◽  
Fei Yang ◽  
Bin Ran
Keyword(s):  
Discrete Choice ◽  
State Of The Art ◽  
Choice Model ◽  
Orthogonal Design ◽  
Asymptotic Variance ◽  
Parameter Estimates ◽  
Efficient Design ◽  
Stated Choice ◽  
Reliable Parameter ◽  
Efficient Data

The stated choice (SC) experiment has been generally regarded as an effective method for behavior analysis. Among all the SC experimental design methods, the orthogonal design has been most widely used since it is easy to understand and construct. However, in recent years, a stream of research has put emphasis on the so-called efficient experimental designs rather than keeping the orthogonality of the experiment, as the former is capable of producing more efficient data in the sense that more reliable parameter estimates can be achieved with an equal or lower sample size. This paper provides two state-of-the-art methods called optimal orthogonal choice (OOC) andD-efficient design. More statistically efficient data is expected to be obtained by either maximizing attribute level differences, or minimizing theD-error, a statistic corresponding to the asymptotic variance-covariance (AVC) matrix of the discrete choice model, when using these two methods, respectively. Since comparison and validation in the field of these methods are rarely seen, an empirical study is presented.D-error is chosen as the measure of efficiency. The result shows that both OOC andD-efficient design are more efficient. At last, strength and weakness of orthogonal, OOC, andD-efficient design are summarized.

The Impact of Zoning and Built Environment Characteristics on Transit, Biking, and Walking

2019 ◽  
Vol 11 (1) ◽  
pp. 108-129
Author(s):  
Andrew G. Mueller ◽  
Daniel J. Trujillo
Keyword(s):  
Land Use ◽  
Built Environment ◽  
Discrete Choice ◽  
Travel Behavior ◽  
Choice Model ◽  
Mode Choice ◽  
Land Use Regulation ◽  
Policy Action ◽  
Development Goals ◽  
The Impact

This study furthers existing research on the link between the built environment and travel behavior, particularly mode choice (auto, transit, biking, walking). While researchers have studied built environment characteristics and their impact on mode choice, none have attempted to measure the impact of zoning on travel behavior. By testing the impact of land use regulation in the form of zoning restrictions on travel behavior, this study expands the literature by incorporating an additional variable that can be changed through public policy action and may help cities promote sustainable real estate development goals. Using a unique, high-resolution travel survey dataset from Denver, Colorado, we develop a multinomial discrete choice model that addresses unobserved travel preferences by incorporating sociodemographic, built environment, and land use restriction variables. The results suggest that zoning can be tailored by cities to encourage reductions in auto usage, furthering sustainability goals in transportation.

Air Passengers’ Preferences for Aviation Voluntary Carbon Offsetting: A Co-benefits Perspective

2021 ◽  
pp. 004728752110303
Author(s):  
Beile Zhang ◽  
Brent W. Ritchie ◽  
Judith Mair ◽  
Sally Driml
Keyword(s):  
Discrete Choice ◽  
Latent Class ◽  
Choice Model ◽  
Choice Modeling ◽  
Positive Outcomes ◽  
Market Segments ◽  
Discrete Choice Modeling ◽  
Educational Benefits ◽  
Carbon Offsetting ◽  
Simple Reduction

Co-benefits are positive outcomes from voluntary carbon offsetting (VCO) programs beyond simple reduction in carbon emissions, which include biodiversity, air quality, economic, health, and educational benefits. Given the rates of aviation VCOs remain at less than 10%, this study investigated air passengers’ preferences for co-benefits as well as certification, location, and cost of VCO programs. Using discrete choice modeling, this study shows that aviation VCO programs with higher levels of co-benefits, particularly biodiversity and health benefits, are preferred by air passengers and confirms a preference for domestically based and certified VCO programs. The latent class choice model identified three classes with different preferences for VCO program attributes and demographic characteristics. The results of this study contribute to the knowledge of VCO co-benefits and imply that airlines should take note of this preference for biodiversity and health co-benefits when designing VCO programs and differentiate between market segments to increase the uptake of VCOs.

scholarly journals Pre-calibration of a Discrete Choice Model and Evaluation of Cycling Mobility for Île-de-France

2021 ◽  
Vol 184 ◽  
pp. 172-177
Author(s):  
Guoxi Feng ◽  
Maxime Jean ◽  
Alexandre Chasse ◽  
Sebastian Hörl
Keyword(s):  
Discrete Choice ◽  
Choice Model ◽  
Discrete Choice Model

scholarly journals Self-Regulating Demand and Supply Equilibrium in Joint Simulation of Travel Demand and a Ride-Pooling Service

2021 ◽  
pp. 036119812199714
Author(s):  
Gabriel Wilkes ◽  
Roman Engelhardt ◽  
Lars Briem ◽  
Florian Dandl ◽  
Peter Vortisch ◽  
...  
Keyword(s):  
Real Time ◽  
Travel Demand ◽  
State Of The Art ◽  
Choice Model ◽  
Mode Choice ◽  
Attractive Alternative ◽  
Full Potential ◽  
Demand Model ◽  
Modeling Framework ◽  
Demand And Supply

This paper presents the coupling of a state-of-the-art ride-pooling fleet simulation package with the mobiTopp travel demand modeling framework. The coupling of both models enables a detailed agent- and activity-based demand model, in which travelers have the option to use ride-pooling based on real-time offers of an optimized ride-pooling operation. On the one hand, this approach allows the application of detailed mode-choice models based on agent-level attributes coming from mobiTopp functionalities. On the other hand, existing state-of-the-art ride-pooling optimization can be applied to utilize the full potential of ride-pooling. The introduced interface allows mode choice based on real-time fleet information and thereby does not require multiple iterations per simulated day to achieve a balance of ride-pooling demand and supply. The introduced methodology is applied to a case study of an example model where in total approximately 70,000 trips are performed. Simulations with a simplified mode-choice model with varying fleet size (0–150 vehicles), fares, and further fleet operators’ settings show that (i) ride-pooling can be a very attractive alternative to existing modes and (ii) the fare model can affect the mode shifts to ride-pooling. Depending on the scenario, the mode share of ride-pooling is between 7.6% and 16.8% and the average distance-weighed occupancy of the ride-pooling fleet varies between 0.75 and 1.17.

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