Revenue Management and Survival Analysis in the Automobile Industry (eBook)

Dr. André Jerenz promovierte extern bei Prof. Dr. Ulrich Tüshaus am Lehrstuhl Operations Research an der Universität der Bundeswehr, Hamburg. Er ist als Offizier im Bundesamt für Informationsmanagement und Informationstechnik der Bundeswehr in Koblenz tätig.

Foreword 6
Acknowledgements 8
Contents 10
List of Figures 14
List of Tables 16
Nomenclature 18
Introduction 20
1.1 Motivation 20
1.2 Outline and Research Contribution 21
Revenue Management and the Automobile Industry 24
2.1 Concept of Revenue Management 24
2.2 The Automobile Industry 33
2.3 Revenue Management in the Automobile Industry 38
2.4 Price-Based Revenue Management in the Used Car Sector 42
2.5 Summary 49
Modeling the Price-Based Revenue Management Problem 50
3.1 Introduction 50
3.2 Basic Continuous-Time Model 54
3.3 Stochastic Discrete-Time Model 63
3.4 Finite Price Sets 67
3.5 Extensions of the Basic Problem 73
3.6 The Complete Model 78
3.7 Summary 80
Survival Analysis: Estimation of the Price- Response Function 82
4.1 Reservation Price and Price Response Function 83
4.2 Survival Analysis 89
4.3 Parametric Regression Modeling 100
4.4 Estimation of the Price Response Function 109
4.5 Summary 115
Validation of the Survival Analysis Approach: a Case Study within the Used Car Market 116
5.1 Introduction 116
5.2 Used Car Study 118
5.3 Cox Model 123
5.4 Accelerated Failure Time Model 135
5.5 Spline Regression Extended Model 142
5.6 Presentation of the Extended Log-Logistic Model 149
5.7 Summary 152
Computational Analysis: Proof of Concept 154
6.1 General Description of the Revenue Management Program 154
6.2 Case Study for a Selected Used Vehicle 157
6.3 Assessment of Potential for Profit Enhancement 166
6.4 Summary 171
Conclusions and Further Directions 172
7.1 Directions for Future Research 172
7.2 Summary 174
References 176
Index 186

Chapter 5 Validation of the Survival Analysis Approach: a Case Study within the Used Car Market (S. 114-115)

There is hardly anything in the world that someone cannot make a little worse and sell a little cheaper, and the people who consider price alone are that person’s lawful prey.
JOHN RUSKIN (1819–1919)

The objective of the present chapter involves applying survival analysis for estimating individual price response functions. Based on an extensive market study concerning the German used car sector, several models introduced in the previous chapter are fitted to the datasets and their applicability on predicting survival is determined, thereby estimating individual sales probabilities of used vehicles.

5.1 Introduction

In the previous chapter, survival analysis was used to estimate individual price response functions for used vehicles. Hypothesizing that the sale of a used vehicle is in.uenced by internal factors such as the asking price as well as external factors like the market conditions, one way to determine these relationships is to assume a vehicle’s time on the market until a sale occurs as the dependent variable. Then, the in.uence of explanatory variables such as the asking price can be assessed using survival analysis regression. Different models were introduced, including Cox proportional hazards models and accelerated failure time models as two categories of parametric regression modeling.

In this chapter, methods and models stated in the previous chapter are applied on a dataset from a study conducted in the German used car market with the scope of determining explanatory variables and their effect on the failure time of used vehicles. Here, the failure of a used car on the market translates to a sale of the vehicle. Then, based on a .tted model, survival of a speci.c used vehicle, or the probability of its sale, can be estimated with regard to its characteristics and the given market conditions. Furthermore, the survival regression model can be used to determine optimal pricing strategies of a used car retailer, if the asking price has a significant influence on the survival of a used car.

In section 5.2, the market study regarding the German used car market is described and the process of model building is illustrated. Section 5.3 selects and .ts a Cox proportional hazards model on the dataset including an assessment of its adequacy. Afterward, an accelerated failure time model is identi.ed, and the .tted model assessed and validated. In section 5.5, the model that best .ts the data is extended by restricted regression splines to incorporate possible non-linearity in the covariates. The chapter is concluded in section 5.6 by a presentation and discussion of the .nal extended survival model that best .ts the data from the market study. The calculations and plots in this chapter were performed with the R software (R Development Core Team 2006), using the Design and Hmisc library, written by Frank E. Harrell (Harrell 2005, 2007) as well as the Survival library, written by Terry Therneau (Therneau and Lumley 2006).