RM LESSON 8

Revenue Management is the practice of optimizing financial outcomes by managing the availability and pricing of products or services in order to maximize revenue.

Agenda

  1. Nested Reservation System

  2. Optimizing Rate Mix

  3. Expected Marginal Room Revenue

Nested Reservation System

  • Objective of Rate Mix Control:

    • Determine how many rooms to protect for each rate class in a hotel.

    • Aims to save rooms for the highest-paying guests, typically the last booking guests.

  • Protection Level:

    • The number of rooms a hotel chooses to save for specific rates.

    • Implemented by limiting availability of rooms in cheaper rate classes for early-booking guests with a lower willingness to pay.

    • Booking limits are set for these classes.

  • Nested Protection Level:

    • Protects capacity for a given rate and all higher rate classes, rather than protecting only a single class.

  • Nested Booking Control Policy:

    • Allows higher-value products to access capacity allocated to lower-value products.

  • Demand Analysis:

    • Based on knowledge about the average unconstrained demand, determine the minimum allocation and maximum booking limit for each rate class.

    • Ensures that the highest rate class is always available if rooms are left to sell.

Booking Limitations

  • Nested Booking Limit:

    • When total bookings for a rate class and its lower classes reach the nested booking limit, that rate class becomes unavailable for purchase.

    • Guests can only purchase higher rate classes.

  • Example of Rate Class Availability:

    • Current availability for a hotel with a capacity of 100 rooms:

    • Rate Class A: $240 - Current Booking: 100 - Nested Booking Limit: 1 (Available)

    • Rate Class B: $190 - Current Booking: 91 - Nested Booking Limit: 4 (Available)

    • Rate Class C: $150 - Current Booking: 85 - Nested Booking Limit: 30 (Not Available)

    • Rate Class D: $100 - Current Booking: 55 - Nested Booking Limit: 55 (Not Available)

Sell-Up Process

  • Definition:

    • Sell-up occurs when a guest whose first choice rate class is not available opts to pay more for a higher available rate class, provided the price remains below their maximum willingness to pay.

  • Revenue Generation:

    • Enhancing guest sell-ups can significantly increase hotel revenues.

  • Sophistication of RM Systems:

    • More sophisticated Revenue Management (RM) systems are better at capturing guests with high willingness to pay and improving competitiveness against methods generating sell-ups.

Basic Assumptions

  • General Reservations:

    1. Reservations for the lowest rates come in earlier than those for higher rates.

    2. Demand for each rate class is independent.

    3. Initial capacity allocation is made well before the day of arrival.

  • Optimization Challenges:

    • Dynamics of demand elasticity

    • Actual sales dynamics vs. timing of forecasting

    • Application of probabilities

    • Length-of-stay effects

    • Ancillary revenue considerations

    • Marginal cost considerations

Optimizing Rate Mix

  • Core Objective of RM:

    • Allocate rooms among different rate classes to maximize total expected revenue or profits amid uncertain demand levels.

  • Expected Value Calculation Example:

    • If a hotel room is reserved for a customer with a 70% probability of booking at a price of $100 per night,

    • Therefore, Expected Value (EV) for that room:
      (EV=70%∗100)=70(EV = 70\% * 100) = 70

  • Bottom Line Insight:

    • $70 is the lowest price that should be accepted from a customer present at the moment.

    • If someone offers more than $70, the room can potentially be sold; otherwise, it should not be sold.

  • Key to Effective RM:

    • Accurate estimation of the expected revenue of each room in the hotel.

Re-Introduction to Probabilities

  • Example Case - Bed-and-Breakfast with 10 Rooms:

    • Management needs to assess the probability of a certain number of rooms booked any given night.

  • Booking Options:

    • Options range from 0 rooms booked to 10 rooms booked.

Probability Functions

  • Probability Mass Function (PMF):

    • Gives the probability that a discrete random variable equals a specific value.

  • Cumulative Distribution Function (CDF):

    • Gives the probability that a random variable is less than or equal to a specific value.

  • Survival Function:

    • Gives the probability that a random variable is greater than a certain value.

Probability Analysis Example

  • Room Booking Probabilities:

    • Probability of selling exactly 0 rooms: 5%

    • Probability of selling exactly 1 room: 10%

    • Probability of selling exactly 2 rooms: 15%

    • Probability of selling exactly 3 rooms: 20%

    • Probability of selling exactly 4 rooms: 15%

    • Probability of selling exactly 5 rooms: 10%

    • Probability of selling exactly 6 rooms: 5%

    • Probability of selling exactly 7 rooms: 5%

    • Probability of selling exactly 8 rooms: 5%

    • Probability of selling exactly 9 rooms: 5%

    • Probability of selling exactly 10 rooms: 5%

Cumulative Probability Example

  • Probability of Certain Rooms or Fewer Booked:

    • Cumulative probability that exactly 0 rooms booked is 5%

    • Cumulative probability that exactly 0 or 1 rooms booked is 15% (5% + 10%)

    • Cumulative probability for exactly 0, 1, or 2 rooms booked is 30% (5% + 10% + 15%)

  • Cumulative Results:

    • Probability of 0 or fewer rooms is 5%

    • Probability of 1 or fewer rooms is 15%

    • Probability of 2 or fewer rooms is 30%

    • Probability of 3 or fewer rooms is 50%

    • Probability of 4 or fewer rooms is 65%

    • Probability of 5 or fewer rooms is 75%

    • Probability of 6 or fewer rooms is 80%

    • Probability of 7 or fewer rooms is 85%

    • Probability of 8 or fewer rooms is 90%

    • Probability of 9 or fewer rooms is 95%

    • Probability of 10 or fewer rooms is 100%

Survival Function Analysis

  • Understanding Booking Beyond a Certain Threshold:

    • If an 80% chance exists that 6 or fewer rooms will be booked, then:

    • There is a 20% probability of booking 7, 8, 9, or 10 rooms.

  • Probability Beyond Certain Rooms:

    • Probability of selling more than 0 rooms: 95%

    • Probability of selling more than 1 room: 85%

    • Probability of selling more than 2 rooms: 70%

    • Probability of selling more than 3 rooms: 50%

    • Probability of selling more than 4 rooms: 35%

    • Probability of selling more than 5 rooms: 25%

    • Probability of selling more than 6 rooms: 20%

    • Probability of selling more than 7 rooms: 15%

    • Probability of selling more than 8 rooms: 10%

    • Probability of selling more than 9 rooms: 5%

    • Probability of selling more than 10 rooms: 0%

Probability Summation

  • Combined Analysis of Different Probability Functions:

    • Listing combined probabilities for specific room bookings

Rooms

PMF (%)

CDF (%)

Survival (%)

0

5%

5%

95%

1

10%

15%

85%

2

15%

30%

70%

3

20%

50%

50%

4

15%

65%

35%

5

10%

75%

25%

6

5%

80%

20%

7

5%

85%

15%

8

5%

90%

10%

9

5%

95%

5%

10

5%

100%

0%

Expected Marginal Room Revenue (EMRR)

  • Definition

    • EMRR is the room revenue a hotel expects from selling one more room (the marginal room) based on the probability that it will be available to sell, derived from average unconstrained demand.

  • Probability Context:

    • Based on historical booking data and forecasts, consider:

    • If historically 74 rooms are sold on a given date, what is the probability of selling the 75th room?

  • Survival Function:

    • The survival probability of selling more than 74 rooms informs the availability for the 75th room.

EMRR Calculation Example

  • Hotel Case Study (100 Rooms):

    • Probability for the 81st room (marginal room):

    • Cumulative Probability (rooms ≤ 80): P(X ≤ 80) = 86.0 ext{%}

    • Survival Probability (more than 80): P(X > 80) = 14.0 ext{%}

    • EMRR is calculated as follows:
      EMRRxth=R∗P(X>x)EMRR_{xth} = R * P(X > x)

  • For the 81st room:

    • EMRR_{81st} = $100 * 16.0 ext{%} = $16.00

  • For the 20th room:

    • EMRR_{20th} = $100 * 98.20 ext{%} = $98.20

EMRR Insights

  • Revenue Dynamics:

    • As available capacity increases, expected marginal revenue from each additional room declines.

    • High probability of selling only one room means lower chance of discounting necessary, leading to higher expected revenue.

  • Cumulative Sales Dynamics:

    • As each additional room is offered, the probability of it being sold decreases slightly, reflecting decreasing marginal revenue.

Rate Mix Optimization

  • Guiding Principles:

    • The exact shape of the EMRR curve derives from probabilities associated with each level of demand and the rate structure.

  • Incremental Room Reservations Strategy:

    • Rooms are reserved for customers in the highest rate class until the EMRR for the next room equals or dips below that of the next lower rate class.

  • Illustrative Example:

    • If the Best Available Rate (BAR) is $100 and the discount rate is $70, reserve rooms exclusively for $100 customers until the probability of selling one more to them drops to 70%.

    • This indicates that the protection level for the full-rate class has been met once 25 rooms are reserved.

Visualization and Capacity Allocation Example

  • Graphical Representation:

    • Consider three rates of $150, $100, $75:

    • Analyze the graphical solution for capacity allocation.

  • Consideration in More Complex Rate Structures:

    • For four rates of $240, $190, $150, $100, calculations apply similarly, involving nested protection levels, minimum allocation, and booking limits.

Rate Class

Nested Protection Level

Minimum Allocation

Booking Limit

$240

9

9

100

$190

15

6

91

$150

45

30

85

$100

NA

NA

55

Note: For the $100 rate class, since it's the lowest, there is no applicable nested protection level or minimum allocation.

Conclusion

  • Understanding and applying these principles in revenue management will enable effective room pricing strategies and maximize overall hotel revenue.

Excel File Mentioned for Calculations:

  • Follow along with raw data, EMRR for different rates, and goal-seeking functionalities within the provided Excel file.


Nested Reservation System

  • Objective: Protect rooms for high-rate guests by limiting availability for lower-rate classes (Booking Limits).

  • Nested Protection Level: Reserves capacity for a specific rate and all classes above it, ensuring higher-value products can access capacity allocated to lower-value ones.

  • Sell-Up Process: Occurs when guests buy a higher rate because their preferred lower rate is unavailable.

Optimization & Expected Value

  • Objective: Allocate rooms across classes to maximize total expected revenue.

  • Expected Value (EV): The lowest price a hotel should accept for a room today based on future booking probability.

    • Example: If there is a 70%70\% probability of booking at $100, the EVEV is $70.

Probability Functions

  • Probability Mass Function (PMF): Probability of selling an exact number of rooms.

  • Cumulative Distribution Function (CDF): Probability of selling a specific number of rooms or fewer (P(X≤x)P(X \le x)).

  • Survival Function: Probability of selling more than a certain number of rooms (P(X>x)P(X > x)).

Expected Marginal Room Revenue (EMRR)

  • Definition: The revenue a hotel expects from selling one additional (marginal) room.

  • Calculation Formula:
    EMRRxth=R×P(X>x)EMRR_{xth} = R \times P(X > x)

  • Dynamics: As more rooms are sold, the probability (P(X>x)P(X > x)) of selling the next room decreases, reducing the EMRR.

Rate Mix Strategy

  • Allocation Rule: Reserve rooms for a higher rate class until the EMRR of the next room drops below the value of the next lower rate class.

  • Example: If the full rate is $100 and the discount is $70, the hotel protects rooms for the $100 class until the survival probability of selling an additional room at that rate is less than 70%70\%.

  • Calculation Tools: Advanced systems use these principles to set nested protection levels and booking limits for complex rate structures.