Mental accounting is a far-reaching concept, which is often used to explain various kinds of irrational behaviors in human decision making process. This paper investigates dynamic pricing problems for single-flight and multiple flights settings, respectively, where passengers may be affected by mental accounting. We analyze dynamic pricing problems by means of the dynamic programming method and obtain the optimal pricing strategies. Further, we analytically show that the passenger mental accounting depth has a positive effect on the flight’s expected revenue for the single flight and numerically illustrate that the passenger mental accounting depth has a positive effect on the optimal prices for the multiple flights.
In airline revenue management, revenue maximization could be attained by dynamic pricing and capacity control [
Most classical dynamic pricing models suppose that passenger behavior is rational [
In recent years, as the customer behavior issue has been introduced into the operations management field, modeling customer behavior increasingly attracts extensive attention in the area of dynamic pricing and revenue management [
In the customer choice behavior model, dynamic pricing of multiple products is studied extensively. Zhang and Cooper [
In the strategic customer model, dynamic pricing problems are still under development. Aviv and Pazgal [
The concept of customer mental accounting has been widely studied in the operations management literature. Liao and Chu [
In this paper, we investigate the multiperiod dynamic pricing problems for a single flight and multiple flights in the case of a monopoly airline selling the ticket to passengers who could be affected by mental accounting. We explicitly model the passenger dynamic choice process by MNL choice model, in which the probability of purchasing a ticket is specified as a function of mental accounting depth. At each decision period, airline dynamically determines the flight price in order to maximize the expected revenue over the booking horizon. Given the passenger choice model, we formulate the dynamic pricing problems using the dynamic programming method for a single flight and multiple flights in the presence of passenger mental accounting. Then we obtain the optimal pricing strategies. The optimal prices are significantly affected by the depth of mental accounting. Furthermore, we numerically demonstrate the positive effect of passenger mental accounting on airline’s dynamic pricing strategies.
The model of passenger mental accounting in this paper complements the related research on behavioral operations, and the aim of this paper is to establish a manageable modeling framework that embodies mental accounting. The remainder of this paper is organized as follows. In Section
In this section, we investigate a single-flight dynamic pricing problem. The model can be regarded as a building block of the multiple-flight case. Consider a single-leg flight with capacity
We first present a single-flight decision framework to capture passenger’s mental accounting. Consider a potential passenger deciding whether to purchase a flight ticket or not to buy at all. Suppose that payment of purchasing the flight ticket is classified in mental accounting, such as travel mental accounting. Let
Assume that the utility from passenger’s purchasing is
Let
Given the remaining seat level
Let
In the following section, we describe the optimal pricing strategy. Before obtaining the optimal price and expected revenue, we first rewrite
Function
Because
From Theorem
For a given remaining seat level
From Theorem
Let
Theorem
Theorem
Let
To prove this theorem, we need to show that, for all
First, let us consider
Next, we consider
Similarly, we can deduce that all
Consider
Consider
In this section, we deal with a multiple-flight dynamic pricing problem. The airline’s goal is to maximize the expected revenue from the booking horizon by setting the appropriate price for each flight in each period; in other words, in every period
There are
Passengers choose among the substitutable flights or choose nothing; the probability that a passenger chooses flight
Let
For the expected revenue function
We next investigate the optimal pricing strategy. Before obtaining the optimal price, we first rewrite the price of each flight as a function of passenger’s choice probability. From
To facilitate description of structural properties, we define
Function
Taking the second derivatives of
Next, we show that the Hessian matrix
If
Similarly, we can conclude that
Here we show that
For a given remaining seat level
Furthermore, the optimal expected revenue is given by
From Theorem
Let
Substituting (
In this section, we numerically illustrate the effect of passenger mental accounting on the optimal pricing of flights. We examine sets of examples with two substitutable flights in which
Figure
Optimal prices of both flights in time remaining
Figure
Optimal prices of both flights in the remaining seat level of flight 1.
Next, we examine how the mental accounting depth affects the optimal prices of both flights. Specifically, we want to depict the change in the optimal prices of both flights over mental accounting depth when
Effect of mental accounting on the optimal prices.
In this paper, we study the dynamic pricing problems for a single flight and multiple flights over finite booking horizon in the presence of mental accounting. We use Bellman equation to obtain the optimal prices. Furthermore, we present the numerical simulation to investigate how mental accounting depth affects the optimal prices. According to the numerical example, we derive that passenger’s mental accounting has a positive impact on the optimal prices.
In the future study, we can incorporate the batch demand into dynamic pricing instead of unit purchase. Of course, it is also useful to incorporate competition into the dynamic pricing problem or consider demand learning in our model.
The authors declare that there is no conflict of interests about the named companies regarding the publication of this paper.
This work was supported by the National Natural Science Foundation of China (nos. 71172172 and 71272058), Specialized Research Fund for Doctoral Program of Higher Education of China (no. 20121101110054), Special Program for International Science, and Technology Cooperation of Beijing Institute of Technology (no. GZ2014215101).