Science of Hotel OptimizationRooms Revenue Workshop

Day 1: Data

Day 2: Analysis

Day 3: Optimization

SOHO Day 2 2

10 minute break every 50 minutes.

50 minute periods.

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http://www.forsmarthotels.com/sohodocs

SOHO Day 2 3

Ask every question.

Dozens of Books, Lectures, Courses in 4 hrs.

Contribute examples.

Give me a Pace.

I will go back.

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SOHO Day 2 4

Day 2 Objectives

Hour 1Add analysis columnsModels

Hour 2Let’s Count - FrequencyDemand Analysis – The Manual

Way

Hour 3-4Demand Analysis – The Math WayDynamic Optimization (if possible)

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SOHO Day 2 5

SOHODAY1.xlsx SOHODAY2.xlsx

Before Class

1. Joined tables from Day 1

2. Removed Cancel, No Shows, Comps.

3. Vlookup for COMPANY_NAME

4. Convert all to text.

5. Deleted columns

In-class

1. Gross up rates column

2. Days_out column

3. Month and Weekday column

4. Add month-weekday classification

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SOHO Day 2 6

BUILD FOR OTHERS

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SOHO Day 2 7

Nested Excel functions

• Function variable is another function.

• Combine two or more functions to deliver one answer.

• Innermost function first.

• Keeps worksheet clean.

• Hard to follow.

• May slow calculation speed.

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=ROUND(A4*Sum(A1:A3),0)

1. Sum cells.

2. Multiply by A4.

3. Round to the tenth place.

SOHO Day 2 8

Analysis Column: GROSS_RATE

1. Get the margin with vlookup.2. Markup the Net rate3. iferror then RATE_AMOUNT4. Roundup to nearest 10.

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When building nested Excel functions, go step-by-step.

=ROUNDUP(IFERROR(

[@[RATE_AMOUNT]]/VLOOKUP([@COMPANY],Margin[#All],2,FALSE)

,[@[RATE_AMOUNT]]),0)

GROSS RATE MARKUP

SOHO Day 2 9

Analysis Column: ARATE

1. Roundup to nearest multiple of 25.

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=CEILING([@[GROSS_RATE]],25)

Analysis RATE

SOHO Day 2 10

Analysis Column: DAYS_OUT, ADAYS_OUT

1. Subtract Insert from Reserv date.2. Round to the next whole number.

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Can’t use roundup because same day bookings will become -1.

=CEILING([@[RESERVATION_DATE]]-[@[INSERT_DATE]]

,25)

DAYS_OUT

1. Round to the next multiple of 30.

=CEILING([@[DAYS_OUT]],30)

Analysis DAYS_OUT

SOHO Day 2 11

MONTH & WEEKDAY

1. Get month number.

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=MONTH([@[RESERVATION_DATE]])

MONTH

1. Get weekday number (sun=1)

=WEEKDAY([@[RESERVATION_DATE]])

WEEKDAY

SOHO Day 2 12

WEEKPART

1. If weekday number is less than 6

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WEEKPART

=IF([@WEEKDAY]<6,"WEEK","END")

2. Then show “WEEK” for weekday

2. If not, show “END” for weekend

SOHO Day 2 13

PERIOD

1. Get month number from MONTH column.

2. Add a hyphen for easier reading.

3. Get weekpart from WEEKPART column.

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=[@MONTH]&"-"&[@WEEKPART]

MODEL PERIOD

SOHO Day 2 14

OWL’s vision for The Big RM Reset

Clerical RMDistribute the Right Rates and Manage Inventory.

Analytical RMTo take data, to be able to understand it, to process it, to extract value from it, to visualize it and to communicate it. 

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SOHO Day 2 15

Decision Models

Mental Models

Benefits• Fast • Simple• Inexpensive

Math Models

Benefits• Less biased• Complex• Rules-based• Reusable

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Problems• Bias• No Rules• Personal

Problems• Assumptions• Expensive

SOHO Day 2 16

The Model

“Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful.”

“The purpose of models is not to fit the data but to sharpen the questions.”

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George Edward Pelham Box, Empirical Model-Building and Response Surfaces (1987)

Samuel Karlin,Eleventh R. A. Fisher Memorial Lecture, Royal Society (April 1983)

“The approximate nature of the model must always be borne in mind…”

SOHO Day 2 17

The Fundamental Model of RM

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How 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

SOHO Day 2 18

The Fundamental Question of Hotel RM

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How many rooms can I sell at each rate?

Rate (P)

Rooms (Q)

High

High

Low

Low

Hotel Demand Curve

SOHO Day 2 19

Not that simple.

• Can’t you just go to your data table and count.• Unfortunately, it’s not that simple.• These data points have variation.

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Rate (P)

Rooms (Q)

High

Low

Low

(L,H)High

(H,L)

SOHO Day 2 20

Let’s Count - Random Events

• 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.

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SOHO Day 2 21

Frequency Table

SQL CodeSELECT PERIOD, ARATE, RESERVATION_DATE, Count(ROOM) AS COUNT_ROOMFROM SOHODAY2.ElementsWHERE MARKET_CODE='TRANSIENT'GROUP BY PERIOD, ARATE, RESERVATION_DATE

MSQuery Modified VersionSELECT `Elements$`.PERIOD, `Elements$`.ARATE, `Elements$`.RESERVATION_DATE, Count(`Elements$`.ROOM) AS ‘COUNT_ROOM’FROM `C:\SOHODAY2.xlsx`.`Elements$` `Elements$`WHERE (`Elements$`.MARKET_CODE='TRANSIENT')GROUP BY `Elements$`.PERIOD, `Elements$`.ARATE, `Elements$`.RESERVATION_DATE

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SOHO Day 2 22

Tip: Put calculations on Manual

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SOHO Day 2 23

Let’s count – Expected Rooms Sold

Frequency – How often an event happens.

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For each Period:1. Sum the number of times each rate was paid.

SUMIFS(Frequency[''COUNT_ROOM''],Frequency[ARATE],$A3,Frequency[PERIOD],B$2)

2. Divide each count by total # of days that the rate appeared.COUNTIFS(Frequency[ARATE],$A3,Frequency[PERIOD],B$2)

3. Rounddown to the ones place and clean the errors.=+IFERROR(

ROUNDDOWN(SUMIFS(Frequency[''COUNT_ROOM''],Frequency[ARATE],$A3,Frequency[PERIOD],B$2)/COUNTIFS(Frequency[ARATE],$A3,Frequency[PERIOD],B$2),0)

,0)

SOHO Day 2 24

Demand Curve – The Manual Way

Core Assumption – Those that paid a higher price will pay a lower price.

Start from the highest rate and add the pickup to the next highest rate.

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SOHO Day 2 25

Pivot Chart

Always try to graph your data.

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SOHO Day 2 26

INDEX(MATCH)

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INDEX($A$133:$A$195,MATCH(B197,B$133:B$195,0))

1. Find the row where this is

2. In this column

3. Get the info in this row

4. In this column

SOHO Day 2 27

WARNING

We are going to make a huge modeling mistake on purpose.

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SOHO Day 2 28

Demand Estimate – The Math Way

Using the equation for a line, we can create an equation for demand.

y = mx + b

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Rooms Sold Slope Rate Intercept

A measure of steepness.

Where the line crosses the y-axis or the number of rooms sold when the rate is $0.

SOHO Day 2 29

We need to extract two points from the data

1. How many rooms sold when we charge a low rate? (L,H)

2. How many rooms sold when we charge a high rate? (H,L)

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Rate (P)

Rooms (Q)

High

Low

Low

(L,H)High

(H,L)

SOHO Day 2 30

Defining an Equation for a Demand Line

1. Find the two points.

2. Find the Slope.

3. Use the slope and one data point to find the intercept.

4. Rework the equation to find the Price curve.

5. Use both equations to find the Revenue curve.

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SOHO Day 2 31

ARRAY FORMULAS

Turn any function into a criteria function.

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MIN(IF(FREQ[PERIOD]=B$2,FREQ[ARATE],""))

1. If a row in the ARATE column is related to this PERIOD.

2. Then include it in the search for finding the minimum.

SOHO Day 2 32

Find the Slope.

• Change in Rate divided by the change in Rooms Sold• Always constant, always negative.

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Change in Rooms Sold

Change in Rate

Slope =Low Rate – High Rate

High Rooms Sold – Low Rooms Sold

SOHO Day 2 33

Use the slope to find the intercept

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For 1-Week, Slope = -.0824

102 = -.0824(100) + b

Data Point (100, 102)

102 + 8.244898= b

110.25 = b

Rooms = -.0824*Rate+110.25

SOHO Day 2 34

Graph “1-Week” Demand Equation

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Now I can analyze any rate.

SOHO Day 2 35

Revenue Curve, 1-Week

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Revenue = Rate * Rooms

Revenue = Rate * (-.0824*Rate + 102.27)

Revenue = Rate * (-.0824*Rate + 102.27)Distribute

Revenue = -.0824*Rate2 + 102.27*Rate

Rooms = -.0824*Rate+110.25

SOHO Day 2 36

Price Curve, 1-Week

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Rate = Rooms - Intercept

Rate = Rooms - 102.27

Rooms = Slope * Rate + Intercept

Slope

-.0824

SOHO Day 2 37

Revenue Graph

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SOHO Day 2 38

Derivative of Revenue Curve, 1-Week

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Revenue = -.0824*Rate2 + 102.27*Rate

The derivative of the revenue curve basically helps us calculate where the curve reaches its highest value.

Step 1 Multiply -.0824 by 2 and drop the second power on Rate

Revenue = -.1649 * Rate + 102.27 * Rate

Step 2 Drop the second Rate Revenue = -.1649 * Rate + 102.27

Revenue Change = -.1649*Rate + 102.27

SOHO Day 2 39

Optimal Rate

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Solve for Revenue Change = 0

-.1649*Rate = -110.24

Rate = $668.56

SOHO Day 2 40

The math is great, but the model is USELESS.

• Aggregating data increases errors.• Break down the model even further.

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