Mathematical Hotel Revenue Optimization

Mathematical Hotel Revenue Optimization

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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

[email protected]

Robert Hernandez, Hotel Data Science 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.


Counting Frequency

5 8 9 10

Day

10 8 5 8 9 8 5

1 2 3 4 5 6 7

Reserv


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%


How spread out is the data

Two Parameters

Average

Standard Deviation


Normal Distribution


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)


How we describe our data file

Two Parameters

Average

Standard Deviation


Segment(i.e. Slice and Dice)

by Month

by Period

by Market

by Channel

by Days Out


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)


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.


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.


Capacity Control

Top30@$500

Frequent20@$300


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.


Rate1 Rate(w.avg lower classes)Prob1x >

>

Expected Marginal Seat Revenue


Rate2 Rate(w.avg lower classes)Prob2x >

>

Expected Marginal Seat Revenue


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


Fundamental Model of RMHow many rooms can I sell at each rate?

Rate (P)

Rooms (Q)

High

High

Low

Low

Hotel Demand Curve


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)


Core Assumption of Demand



Those that paid a higher price will pay a lower price.

The Blue Pill



1

3

5

8


Demand Estimate


Equation of a Line

Y = SLOPE . X + INTERCEPT


Equation of a LineY = SLOPE . X + INTERCEPT

Rooms = SLOPE . Rate + INTERCEPT

INTERCEPT

SLOPE


The SLOPE


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


Demand Example

1

3

5

8


Demand Formula

Rooms = SLOPE . Rate + INTERCEPT(1,400) , (8,100)

Rooms = -.023 . Rate + 10.33


Revenue Formula


Revenue = Rate . Rooms

Revenue = Rate . (SLOPE . Rate + INTERCEPT)

Revenue = SLOPE . Rate2 + Rate . INTERCEPT


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


Revenue Formula GraphRevenue = -.023 . Rate2 + Rate . 10.33


Derivative of Revenue Formula

Der of Revenue = SLOPE . Rate2 + Rate . INTERCEPT

Der of Revenue = 2 . SLOPE . Rate + INTERCEPT

Marginal Revenue = 2 . SLOPE . Rate + INTERCEPT


Marginal Revenue Formula

Mar Revenue = -.023 . Rate2 + Rate . 10.33

Mar Revenue = 2 . -.023 . Rate + 10.33

Mar Revenue = -.046 . Rate + 10.33


Derivative of Revenue Graph


Optimal Rate

Mar Revenue = -.046 . Rate + 10.3

0= -.046 . Rate + 10.310.3/ .046 = Rate

223.91 = Opt Rate


Rate Formula


Rooms - INTERCEPT = RateSLOPE


Micro Optimization

Room Type

Channel

Bed Type

Date

Market

Period


Thank [email protected]

786.704.2277

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

Mathematical Hotel Revenue Optimization

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