Mathematical Hotel Revenue Optimization
Robert Hernandez, Hotel Data Science Origin World Labs
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
Mathematical Reasoning for Hotel Revenue Management Decision Making
Robert Hernandez, Hotel Data Science Origin World Labs
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
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.
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
Counting Frequency
5 8 9 10
Day
10 8 5 8 9 8 5
1 2 3 4 5 6 7
Reserv
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
Probability
5 8 9 10
Count Freq Chance Freq Prob
5 2 2/7 .29 100%
8 3 3/7 .43 71%
9 1 1/7 .14 28%
10 1 1/7 .14 14%
1.00 100%
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
How spread out is the data
Two Parameters
Average
Standard Deviation
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
Normal Distribution
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
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)
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
How we describe our data file
Two Parameters
Average
Standard Deviation
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
Segment(i.e. Slice and Dice)
by Month
by Period
by Market
by Channel
by Days Out
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
Expected ValueIf the scenario plays out many times.
Core Assumption of all Decision SciencesThe Blue Pill
Reward x
Chance of Reward =Rational, Long term Expected Value
(Law of Very Large Numbers)
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
The LotteryPowerball odds 1/173,000,000 = .000000578% chance of winning.
Costs $2 to play
($150MM) * .000000578% = $.86
- $2 * 99.9999994% = - $2 -$1.14Rational Expected Value
Lottery – Tax on people that don’t know math.
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
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.
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
Capacity Control
Top30@$500
Frequent20@$300
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
Littlewood’s Rule
Rate1 Rate2Prob1x >
>
I will switch to selling to my better class when the EV for that rate is higher than my lower class rate.
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
Rate1 Rate(w.avg lower classes)Prob1x >
>
Expected Marginal Seat Revenue
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
Rate2 Rate(w.avg lower classes)Prob2x >
>
Expected Marginal Seat Revenue
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
Fundamental Model of DemandHow many units can I sell at each price point?
Prices (P)
Quantity (Q)
High
High
Low
Low
We’d like to put this relationship into a mathematical model.
Demand Curve
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
Fundamental Model of RMHow many rooms can I sell at each rate?
Rate (P)
Rooms (Q)
High
High
Low
Low
Hotel Demand Curve
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
Fundamental Model of RMData Point 1. How many rooms sold when we charge a low rate? (L,H)
Rate (P)
Rooms (Q)
High
Low
Low
(L,H) Data Point 1High
(H,L) Data Point 2
Data Point 2. How many rooms sold when we charge a high rate? (H,L)
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
Core Assumption of Demand
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
Core Assumption of Demand
Those that paid a higher price will pay a lower price.
The Blue Pill
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
Core Assumption of Demand
1
3
5
8
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
Demand Estimate
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
Equation of a Line
Y = SLOPE . X + INTERCEPT
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
Equation of a LineY = SLOPE . X + INTERCEPT
Rooms = SLOPE . Rate + INTERCEPT
INTERCEPT
SLOPE
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
The SLOPE
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
The SLOPE
© Origin World Labs 2013
Slope =Low Rate – High Rate
High Rooms Sold – Low Rooms Sold
Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization
Intercept
Rooms = SLOPE . Rate + INTERCEPT
Rooms - SLOPE . Rate = INTERCEPT
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
Demand Example
1
3
5
8
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
Demand Formula
Rooms = SLOPE . Rate + INTERCEPT(1,400) , (8,100)
Rooms = -.023 . Rate + 10.33
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
Revenue Formula
Rooms = SLOPE . Rate + INTERCEPT
Revenue = Rate . Rooms
Revenue = Rate . (SLOPE . Rate + INTERCEPT)
Revenue = SLOPE . Rate2 + Rate . INTERCEPT
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
Revenue Formula
Revenue = Rate . (-.023 . Rate + 10.33)
Revenue = -.023 . Rate2 + Rate . 10.33
Revenue = -.023 . 1002 + 100 . 10.33Revenue = -.023 . 10,000 + 100 . 10.3
Revenue = -.023 . 10,000 + 1030 = 800
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
Revenue Formula GraphRevenue = -.023 . Rate2 + Rate . 10.33
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
Derivative of Revenue Formula
Der of Revenue = SLOPE . Rate2 + Rate . INTERCEPT
Der of Revenue = 2 . SLOPE . Rate + INTERCEPT
Marginal Revenue = 2 . SLOPE . Rate + INTERCEPT
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
Marginal Revenue Formula
Mar Revenue = -.023 . Rate2 + Rate . 10.33
Mar Revenue = 2 . -.023 . Rate + 10.33
Mar Revenue = -.046 . Rate + 10.33
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
Derivative of Revenue Graph
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
Optimal Rate
Mar Revenue = -.046 . Rate + 10.3
0= -.046 . Rate + 10.310.3/ .046 = Rate
223.91 = Opt Rate
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
Rate Formula
Rooms = SLOPE . Rate + INTERCEPT
Rooms - INTERCEPT = RateSLOPE
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
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
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
Micro Optimization
Room Type
Channel
Bed Type
Date
Market
Period
Belmond RM Conference 2014 : Mathematical Hotel Revenue OptimizationPrepared by Origin World Labs
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Prepared by Origin World Labs Belmond RM Conference 2014 : Mathematical Hotel Revenue Optimization