Robert Hernandez, Hotel Data Science Mathematical Hotel Revenue Optimization Robert Hernandez, Hotel Data Science Origin World Labs robert@originworld.com Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

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

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

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

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 5 8 9 10 Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

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

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

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

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

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

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

The Lottery Costs $2 to play ($150MM) * .000000578% = $.86 Powerball odds 1/173,000,000 = .000000578% chance of winning. Costs $2 to play ($150MM) * .000000578% = $.86 - $2 * 99.9999994% = - $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

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

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

> > 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Demand Formula Rooms = SLOPE . Rate + INTERCEPT (1,400) , (8,100) Rooms = -.023 . Rate + 10.33 Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

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

Revenue = Rate . (-.023 . Rate + 10.33) Revenue Formula Revenue = Rate . (-.023 . Rate + 10.33) Revenue = -.023 . Rate2 + Rate . 10.33 Revenue = -.023 . 1002 + 100 . 10.33 Revenue = -.023 . 10,000 + 100 . 10.3 Revenue = -.023 . 10,000 + 1030 = 800 Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

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

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

Marginal Revenue Formula Mar Revenue = -.023 . Rate2 + Rate . 10.33 Mar Revenue = 2 . -.023 . Rate + 10.33 Mar Revenue = -.046 . Rate + 10.33 Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

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

Optimal Rate Mar Revenue = -.046 . Rate + 10.3 0= -.046 . Rate + 10.3 223.91 = Opt Rate Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization

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

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

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

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