Revenue management without demand forecasting: a data-driven approach for bid price generation

Abstract

Traditional revenue management relies on long and stable historical data and predictable demand patterns. However, meeting those requirements is not always possible. Many industries face demand volatility on an ongoing basis, an example would be air cargo which has much shorter booking horizon with highly variable batch arrivals. Even for passenger airlines where revenue management (RM) is well-established, reacting to external shocks is a well-known challenge that requires user monitoring and manual intervention. Moreover, traditional RM comes with strict data requirements including historical bookings (or transactions) and pricing (or availability) even in the absence of any bookings, spanning multiple years. For companies that have not established a practice in RM, that type of extensive data is usually not available. We present a data-driven approach to RM which eliminates the need for demand forecasting and optimization techniques. We develop a methodology to generate bid prices using historical booking data only. Our approach is an ex-post greedy heuristic to estimate proxies for marginal opportunity costs as a function of remaining capacity and time-to-departure solely based on historical booking data. We utilize a neural network algorithm to project bid price estimations into the future. We conduct an extensive simulation study where we measure our methodology’s performance compared to that of an optimally generated bid price using dynamic programming (DP) and compare results in terms of both revenue and load factor. We also extend our simulations to measure performance of both data-driven and DP generated bid prices under the presence of demand misspecification. Our results show that our data-driven methodology stays near a theoretical optimum (< 1% revenue gap) for a wide-range of settings, whereas DP deviates more significantly from the optimal as the magnitude of misspecification is increased. This highlights the robustness of our data-driven approach.

Appendices

Appendix 1: Optimal price under exponential demand assumption

Continuing from “DP generated bid price” section, as an illustrative example, under exponentially distributed WTP, the purchase probability at a price, $P_{w} \left( {p,t} \right)$, is given by

$$P_{w} \left( {p,t} \right) = e^{{ - \frac{{\left( {p - p_{0} \left( t \right)} \right)}}{\alpha \left( t \right)}}} ,$$

(4)

where the mean willingness-to-pay is given by $\alpha \left( t \right)$. From the DP formulation in Eq. (2), the optimal price equation is given by

$$p^{*} \left( {x,t} \right) = \mathop {{\text{argmax}}}\limits_{p} \lambda \left( t \right)\delta t \cdot P_{w} \left( {p,t} \right) \cdot \left( {p - b\left( {x,t - 1} \right)} \right)$$

(5)

Therefore, under the exponential demand assumption given by Eq. (4), this turns into

$$p^{*} \left( {x,t} \right) = \max \left[ {p_{0} \left( t \right),\alpha \left( t \right) + b\left( {x,t - 1} \right)} \right].$$

(6)

In this case, generation of $b\left( {x,t} \right)$ and $p^{*} \left( {x,t} \right)$ both require the estimation of the demand model parameters $\lambda \left( t \right), \alpha \left( t \right),$ and $p_{0} \left( t \right).$

Appendix 2: Numerical example for relation of data-driven approach to EMSR

Let us look at an example comparing EMSR results to those of the data-driven approach with no consideration of booking times and using a simple average for estimation.

Let us denote the total demand for fare class 1 by $D_{1}$ and assume it is normally distributed, $D_{1} \sim N\left( {3,2} \right),$ with a fare of $f_{1} = 400.$ The corresponding EMSRs for class 1 calculated by $f_{1} P\left( {D_{1} > s} \right)$ for each remaining capacity $s = \left\{ {1, \ldots ,10} \right\}$ as described in “Expected marginal seat revenue (EMSR)” section are provided in Table 2.

Table 2 EMSRs calculated for $D_{1} \sim N\left( {3,2} \right)\, and\, f_{1} = 400$

Let us now look into our data-driven methodology under the same assumptions. Sampling from $D\sim N\left( {3,2} \right)$ to represent 5 flights (departure dates), applying Algorithm 1 to pad with zeroes for any surplus capacity, and then using average for estimation of bid price $b^{DD} \left( {x,t} \right)$ yield results in Table 3. Results based on 100 samples are also provided in the same table.

Table 3 EMSRs calculated for$D_{1} \sim N\left( {3,2} \right) and f_{1} = 400$, with corresponding data-driven bid prices generated from sampled data

As seen by the results, $b^{DD} \left( {x,t} \right)$ approach EMSR values as the sample size increases.