Kimuraa, Kimitoshi Satob a Data Management & Planning Oﬃce, Recruit Co., Ltd. b Facluty of Engineering, Kanagawa University 33rd European Conference on Operational Research 30th June – 3rd July 2024, Copenhagen, Denmark

hotels 📗 # Aim of research Paper 1 Create high accuracy cancellation prediction model Dolores Romero Morales, Jingbo Wang, Forecasting cancellation rates for services booking revenue management using data mining, European Journal of Operational Research 202 (2010) 554–562 [Paper] Nuno Antonio, Ana de Almeida, Luis Nunes, Predicting hotel booking cancellations to decrease uncertainty and increase revenue, Tourism & Management Studies, 13(2), 2017 [Paper] 2 A/B testing of the eﬀect of contacting customers based on cancellation prediction Nuno Antonio, Ana de Almeida, Luis Nunes, Predicting Hotel Bookings Cancellation With a Machine Learning Classiﬁcation Model, 2017 16th IEEE Conference on Machine Learning and Applications, 2017 [Paper] 3 Data article - describing two hotel datasets Nuno Antonio, Ana de Almeida, Luis Nunes, Hotel booking demand datasets, Data in Brief Volume 22, February 2019, Pages 41-49 [Paper, Kaggle, Kaggle Notebook]

not answered yet 🤔 Question 1 Question 2 How much impact does improving the accuracy of cancellation prediction have on revenue growth?💰 In what situations does improving the accuracy of cancellation prediction have an impact on revenue growth?📈 To answer these questions, we conducted simulations using estimated parameters derived from real data of the hotel in Japan 🏨

C units of perishable room over [0, T] 2. Selling price at time t : p t ∈ [p min , p max ] 3. Assumptions: a. The hotel has only one room type and one meal plan. b. At time t, only one reservation is accepted (no multiple or group bookings is accepted). Example of #1: The hotel has only double room with dinner and breakfast included. +

dynamic pricing is extended by adding cancellations based on Bitran and Mondschein (1997). 1. Consumer arrives at arrival rate at time t : λ t 2. Consumer reserve the room with probability of Pr(X > p t ) 3. Cancellation rate at time t : γ t 4. Cancellation and its timing t + τ are determined at time t , where τ ∼ Pr(τ | t) 5. Cancellation refund percentage at time t + τ : r t + τ λ t reserve not reserve cancel not cancel Pr(X > p t ) Pr(X < p t ) γ t 1 - γ t arrive gain revenue at t : p t gain revenue at t + τ : p t (1-r t+τ )

simulation 💻 1. Cancellation is predicted at time of reservation. 2. If a cancellation is predicted, reduce the inventory count by one. 3. If cancellation is predicted, keep the inventory unchanged. 4. A reservation determined to be canceled will result in an increase of one in inventory at time t + τ. λ t reserve not reserve cancel predicted cancel not predicted Pr(X > p t ) Pr(X < p t ) arrive reduce the inventory keep the inventory unchanged a t 1 - a t if reservation is determined to be canceled, increase one in inventory at time t + τ Probability that the cancel is predicted at time t

cancel not predicted Pr(X > p t ) Pr(X < p t ) arrive reduce the inventory keep the inventory unchanged a t 1 - a t if reservation is determined to be canceled, increase one in inventory at time t + τ Probability that the cancel is predicted at time t How to calculate a t 1. a t is calculated based on the following components. - accuracy of the cancellation prediction model: acc - actual cancellation rate: γ a

Numerical example. - if acc = 80% and γ a = 30%, a t 1 = 67%, a t 0 = 14%. - 1 in superscript of a t represents the occurrence of an actual cancellation, while 0 represents no actual cancellation. λ t reserve not reserve cancel predicted cancel not predicted Pr(X > p t ) Pr(X < p t ) arrive reduce the inventory keep the inventory unchanged a t 1 = 67% 1 - a t 1 = 33% if reservation is determined to be canceled, increase one in inventory at time t + τ

Numerical example. - if acc = 80% and γ a = 30%, a t 1 = 67%, a t 0 = 14%. - 1 in superscript of a t represents the occurrence of an actual cancellation, while 0 represents no actual cancellation. λ t reserve not reserve cancel predicted cancel not predicted Pr(X > p t ) Pr(X < p t ) arrive reduce the inventory keep the inventory unchanged a t 0 = 14% 1 - a t 0 = 86% if reservation is determined to be canceled, increase one in inventory at time t + τ

Numerical example. - if acc = 80% and γ a = 30%, a t 1 = 67%, a t 0 = 14%. - 1 in superscript of a t represents the occurrence of a cancellation, while 0 represents no cancellation. 3. We can derive a t based on confusion matrix of cancellation prediction model. - a t 1 = n TP / (n TP + n FN ) - a t 0 = n FP / (n FP + n TN ) Prediction Cancel Not Cancel Actual Cancel n TP n FN Not Cancel n FP n TN We need to calculate n TP , n FN , n FP , n TN in order to derive a t

Numerical example. - if acc = 80% and γ a = 30%, a t 1 = 67%, a t 0 = 33%. - 1 in superscript of a t represents the occurrence of a cancellation, while 0 represents no cancellation. 3. We can derive a t based on confusion matrix of cancellation prediction model. - a t 1 = n TP / (n TP + n FN ) - a t 0 = n FP / (n FP + n TN ) Prediction Cancel Not Cancel Actual Cancel n TP n FN Not Cancel n FP n TN We need to calculate n TP , n FN , n FP , n TN in order to derive a t

How to calculate n TP , n FP , n FN , n TN from acc - We assume that the actual cancellation rate γ a equals to the predicted cancellation rate γ p - n FP = n FN = N × (1 - acc) / 2 - γ a = γ p ⇒ (n TP + n FN ) / N = (n TP + n FP ) / N ⇒ n FN = n FP - n TP = N × (γ a - (1 - acc) / 2) - γ a = (n TP + n FN ) / N ⇒ n TP = N × γ a - n FN - n TN = N × ((1 - γ a ) - (1 - acc) / 2) - 1 - γ a = (n FP + n TN ) / N ⇒ n TN = N × (1 - γ a ) - n FP

given an initial inventory of c 💰 v(t, c) = λ t Pr(X > p t ) (1 - γ t ) (p t (1 - ρ t )+ V(t + 1, c - 1)) When the customer arrives, makes a purchase, and does not cancel. + λ t Pr(X > p t ) γ t (p t + V(t + 1, c - 1)) When the customer arrives, makes a purchase, and cancels. + λ t Pr(X < p t )V(t + 1, c) When the customer arrives and does not make a purchase. + (1 - λ t )V(t + 1, c) When the customer does not arrive. where ρ t is expected refund ratio.

the optimal price: V(t, c) = max v(t, c), c ∈ { 0, … , C }, t = 1, … , T where the boundary conditions are ... V(t, 0) = 0 When the inventory level reaches zero, the total expected revenue is zero. V(T+1, c) = 0 If there is remaining stock at the end of the sales period, the total expected revenue is zero. p t ∈ [p min , p max ]

the time interval [0, 1] into L = 60 periods. 2. Customer’s willingness to pay. a. Purchase probability: Pr(X > p t ) b. Probability distribution follows nonparametric distribution estimated from actual data. 3. Capacity: C = 7 4. Number of potential customers: 20 5. Cancellation rate γ t is calculated based on 7-period moving average of actual cancellation rate. 6. Cancellation timing of reservation at time t + τ follows nonparametric distribution estimated from actual data. 7. Cancellation refund percentage r t is determined by the cancellation policy of the actual property. 8. Simulate 10,000 sample paths and calculate their means. 9. Revenue is simulated at cancellation prediction accuracy ranging from [0.5, 1.0] in increments of 0.1

Question 1 Answer How much impact does improving the accuracy of cancellation prediction have on revenue growth? Accuracy of the cancellation prediction model improves by 10%, it will lead to an average revenue increase of 2%.

Question 2 Answer 2 In what situations does improving the accuracy of cancellation prediction have an impact on revenue growth? The higher the arrival rate, the greater the impact on improving accuracy.

multiplying the estimated arrival rates by values ranging from 0.1 to 3.0 and checked for variations in accuracy💡 The values multiplied by arrival rates 0.1 0.2 0.5 1.0 1.5 2.0 3.0 Accuracy 0.5 0.6 0.7 0.8 +X% 0.9 1.0 Revenue improvement ratio

the revenue increase from improving the accuracy of cancellation prediction model. 2. We found that accuracy improvement has a signiﬁcant impact, especially for hotels with high arrival rates. High arrival rates

impact of accuracy improvements on revenue increase in relation to implementation of overbooking, and the presence of group reservation, and the diﬀerence in cancel policies, and the frequency of cancellations. 2. Evaluating the revenue increase from improving the estimation of arrival rates and willingness to pay function. Willingness to pay function Arrival rates

uncertainty of reservations and cancellations. Although dynamic pricing provides appropriate discounts for last-minute cancellations, it is not always possible to ﬁll vacancies unless there is suﬃcient demand. Therefore, it is important to know how the accuracy of cancellation forecasts aﬀects the results of dynamic pricing in practice. In this study, we analyze the relationship between forecast accuracy and expected returns using actual data on room reservations and cancellations in a region in Japan. The results show that a 10% improvement in forecast accuracy results in a 2% improvement in revenue. We also show that this improvement simultaneously improves consumer surplus by lowering the average sales price and improves the load factor. Furthermore, the improvement is more eﬀective during the peak season when the number of potential customers is higher.