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Robert Hernandez, Hotel Data Science

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1 Robert Hernandez, Hotel Data Science
Mathematical Hotel Revenue Optimization Robert Hernandez, Hotel Data Science Origin World Labs Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

2 Mathematical Reasoning for Hotel Revenue Management Decision Making
Robert Hernandez, Hotel Data Science Origin World Labs Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

3 Randomness in RM Every problem in RM involves uncertainty.
Uncertainty means that a process is random. Website visits Conversions Calls to reservations Booking a room Group sales Restaurant visits Check-in No shows Cancellations We need to count how often we can expect a random event to occur. How often an event occurs if the FREQUENCY. Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

4 Counting Frequency 5 8 9 10 1 2 3 4 5 6 7 10 8 5 8 9 8 5 Day Reserv
Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

5 Probability 5 8 9 10 Count Freq Chance Prob 5 2 2/7 .29 100% 8 3 3/7
.43 71% 9 1 1/7 .14 28% 10 14% 1.00 Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

6 How spread out is the data
Two Parameters Average Standard Deviation Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

7 Normal Distribution Prepared by Origin World Labs
Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

8 Normal Distribution Excel
Given an average and a standard deviation, you can get the probability that any # of rooms will be sold. 1 - NORM.DIST(number of rooms, average, standard deviation, TRUE) Given an average and a standard deviation, you can get the # of rooms that will be sold with a certain probability. NORM.INV(1-specific probability, average, standard deviation) Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

9 How we describe our data file
Two Parameters Average Standard Deviation Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

10 Segment (i.e. Slice and Dice)
by Month by Period by Market by Channel by Days Out Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

11 Core Assumption of all Decision Sciences
Expected Value If the scenario plays out many times. Reward x Chance of Reward = Rational, Long term Expected Value (Law of Very Large Numbers) Core Assumption of all Decision Sciences The Blue Pill Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

12 The Lottery Costs $2 to play ($150MM) * .000000578% = $.86
Powerball odds 1/173,000,000 = % chance of winning. Costs $2 to play ($150MM) * % = $.86 - $2 * % = - $2 -$1.14 Rational Expected Value Lottery – Tax on people that don’t know math. Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

13 History of Capacity Control
Inherited from Airline Yielding. Accommodate business people. Fill up with economy. Marketing delivered the rates Operations Research calculated controls. Published on paper. Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

14 Capacity Control Top 30@$500 Frequent 20@$300
Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

15 > > Littlewood’s Rule Rate1 Prob1 Rate2 x
I will switch to selling to my better class when the EV for that rate is higher than my lower class rate. > Rate1 x Prob1 Rate2 > Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

16 Expected Marginal Seat Revenue
> Rate1 Prob1 Rate(w.avg lower classes) x > Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

17 Expected Marginal Seat Revenue
> Rate2 Prob2 Rate(w.avg lower classes) x > Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

18 Fundamental Model of Demand
How many units can I sell at each price point? High We’d like to put this relationship into a mathematical model. Demand Curve Quantity (Q) Low Prices (P) Low High Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

19 Fundamental Model of RM
How many rooms can I sell at each rate? High Hotel Demand Curve Rooms (Q) Low Rate (P) Low High Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

20 Fundamental Model of RM
Data Point 1. How many rooms sold when we charge a low rate? (L,H) Data Point 2. How many rooms sold when we charge a high rate? (H,L) High (L,H) Data Point 1 Rooms (Q) (H,L) Data Point 2 Low Low Rate (P) High Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

21 Core Assumption of Demand
Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

22 Core Assumption of Demand
Those that paid a higher price will pay a lower price. The Blue Pill Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

23 Core Assumption of Demand
8 5 3 1 Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

24 Demand Estimate Prepared by Origin World Labs
Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

25 Equation of a Line Y = SLOPE . X + INTERCEPT
Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

26 Equation of a Line Y = SLOPE . X + INTERCEPT INTERCEPT SLOPE
Rooms = SLOPE . Rate + INTERCEPT Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

27 The SLOPE Prepared by Origin World Labs
Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

28 The SLOPE High Rooms Sold – Low Rooms Sold Slope =
Low Rate – High Rate © Origin World Labs 2013 Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

29 Intercept Rooms = SLOPE . Rate + INTERCEPT
Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

30 Demand Example 8 5 3 1 Prepared by Origin World Labs
Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

31 Demand Formula Rooms = SLOPE . Rate + INTERCEPT
(1,400) , (8,100) Rooms = Rate Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

32 Revenue Formula Rooms = SLOPE . Rate + INTERCEPT
Revenue = Rate . Rooms Revenue = Rate . (SLOPE . Rate + INTERCEPT) Revenue = SLOPE . Rate2 + Rate . INTERCEPT Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

33 Revenue = Rate . (-.023 . Rate + 10.33)
Revenue Formula Revenue = Rate . ( Rate ) Revenue = Rate2 + Rate Revenue = Revenue = , Revenue = , = 800 Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

34 Revenue Formula Graph Revenue = -.023 . Rate2 + Rate . 10.33
Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

35 Derivative of Revenue Formula
Der of Revenue = SLOPE . Rate2 + Rate . INTERCEPT Der of Revenue = 2 . SLOPE . Rate + INTERCEPT Marginal Revenue = 2 . SLOPE . Rate + INTERCEPT Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

36 Marginal Revenue Formula
Mar Revenue = Rate2 + Rate Mar Revenue = Rate Mar Revenue = Rate Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

37 Derivative of Revenue Graph
Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

38 Optimal Rate Mar Revenue = -.046 . Rate + 10.3 0= -.046 . Rate + 10.3
= Opt Rate Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

39 Rate Formula Rooms = SLOPE . Rate + INTERCEPT Rooms - INTERCEPT = Rate
Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

40 Event | Market | Room Type | Source | VIP | Package | Promo
Micro Optimization Recognition of Multiple Simultaneous Demand Patterns. Isolate data for each demand. Utilize Dimensions to Micro-Segment Event | Market | Room Type | Source | VIP | Package | Promo Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

41 Micro Optimization Market Channel Room Type Bed Type Period Date
Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

42 Thank You robert@originworld.com 786.704.2277
Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

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