1. History and Theory of Revenue Management
Block 1 - Elias Kärle -
Slides by Christian Junker, Copyright STI2, 2016 1

2. Single Resource Capacity Control Customer Choice Behaviour
Agenda
Motivation
Single Resource Capacity Control
Customer Choice Behaviour
Not so high you put off potential buyers and not so low that you lose out on potential profits!
Supply Chain Management looks to minimize production and delivery cost.

3. 1. Motivation

4. Definition
Revenue Management is a collection of methods, strategies and tactics that companies utilize to scientifically manage demand for their products.
It helps you to sell the...
right product, at the
right time, at the
right price, to the
right customer
Synonyms (with slightly different meanings):
yield management, pricing and revenue management, pricing and revenue optimization, revenue process optimization, demand management, demand chain management
Not so high you put off potential buyers and not so low that you lose out on potential profits!
Supply Chain Management looks to minimize production and delivery cost.

5. Business Decisions
Revenue management helps with structural (segmentation), price building and quantitative decisions.
Key questions
How can customers be segmented based on their willingness to pay?
How to design products in order to prevent cannibalization between these segments?
Which price to charge these segments?
Should you charge different prices for different channels?
Adjust the prices over time? (seasonal factors, historical data about demand, …)
There is a bottleneck; sell to which segments and channels?
How to handle complements (seats on two connecting airline flights) and substitutes (different car categories for rentals)?
How can a firm segment buyers by providing different conditions and terms of trade that profitably exploit their different buying behavior or willingness to pay?
How can a firm design products to prevent cannibalization across segments and channels?
Once it segments customers, what prices should it charge each segment?
If the firm sells in different channels, should it use the same price in each channel?
How should prices be adjusted over time, based on seasonal factors and the observed demand to date for each product?
If a product is in short supply, to which segments and channels should it allocate the products?
How should a firm manage the pricing and allocation decisions for products that are complements (seats on two connecting airline flights) or substitutes (different car categories for rentals)?

6. And… how is this new?
Every seller in history had to make those decisions!
So… what gives?
Not the WHAT but the HOW
A technologically complex, detailed and intensely operational approach
Scientific advancements in economics, statistics and operational research
Massive advancements in electronic data processing. Most of them younger than 20 years!
Today: thousands of flights between hundred-thousands of source/destination pairs, each being booked at dozens of different prices… hundreds of days into the future.
However: humans NOT obsolete! Good systems are based on synergy between technology and humans.
First, scientific advances in economics, statistics, and operations research now make it possible to model demand and economic conditions, quantify the uncertainties faced by decision makers, estimate and forecast market response, and compute optimal solutions to complex decision problems
Second, advances in information technology provide the capability to automate transactions, capture and store vast amounts of data, quickly execute complex algorithms, and then implement and manage highly detailed demand- management decisions.
A modern large airline, for example, can have thousands of flights a day and provide service between hundreds of thousands of origin- destination pairs, each of which is sold at dozens of prices—and this entire problem is replicated for hundreds of days into the future!

7. Motivation Factors of a reservation
Price
Reservation
Product
Customer

8. Motivation
Product
The product to be sold (here touristic services) is at the core of the reservation.
Which aspect guides the revenue?
the hotel itself? (house with tradition?)
the destination? (party town at the Riviera?)
the experience? (become a monk for a week?)
the rooms?
the services? (24/7 massage service, Jet Ski?)
The product can be designed as soon as these main aspects are identified.
New types of rooms?
Additional price ranges?
etc.
Product
Customer
Price

9. Motivation
Customer
Der Kunde ist der wichtigste Aspekt in der Preisgestaltung!
Jeder Kunde hat seine eigene Motivation:
Verschiedene Motive
Verschiedene Erwartungen
Bereitschaft unterschiedliche Preise zu zahlen
Interesse an verschiedenen Produkten
Um dieses Umfeld zu verstehen und zu handhaben muss der Markt segmentiert werden. Für jedes dieser Segmente muss folgendes angepasst werden:
Interesse an verschiedenen Produktkategorien
Preisgestaltung
Reservierungsbestimmungen
Marketing
Product
Customer
Price

10. Motivation
Price
Obviously the price is the main control mechanism! WRONG!
price is determined according to demand
prices aren’t fixed, they rise and fall
they’re bound to seasonal flux
there are years with lots of demand and years with little
channels with hardly any demand
local, regional and international competition
However there are techniques to influence the price/revenue.
One of the topics of this course.
Product
Customer
Price

11. Motivation Reservation
The moment of reservation itself is a key moment in revenue management that often doesn’t get treated with the importance it deserves.
This moment is equally as important for the customer as it is for the hotel!
Both parties need to work efficiently together.
Many techniques exist for both parties. For example forecasts based on historical data can be very valuable.
Product
Customer
Reservation

12. History
Then

13. History
Now

14. ,,I’m willing to pay this price (or not)!”
Price building
,,I’m willing to pay this price (or not)!”
Multiple factors, sophisticated models, forecasting and estimation… all boils down to this simple truth

15. Key Performance Indicators
Important key performance indicators (KPIs) in hotel revenue management:
GOPPAR
RevPOST
RevPAR
RevPOR
They are used for specific targets based on:
timing
availability
quantity
marketplace demand
of a specific meeting space utilized by a group or overlapping groups.
Revenue Management strategies utilize GOPPAR, RevPOST, RevPAR, and RevPor metrics to
attain certain revenue goals in relationship to the timing, availability, quantity, and
marketplace demand of specific meeting space utilized by a group or overlapping groups.

16. Key Performance Indicators “Revenue Per Available Room”
Comparison of hotels of different size.
Calculate market share and year-to-year performance.
A rising RevPAR indicates a rising occupancy rate and/or price.
Price fluctuations have a much higher influence on the RevPAR.
However! Only an overview, can’t make statements about the real profitability of a hotel.
E.g. a RevPAR of €60.- can mean different things. Which hotel is working more profitable?
Hotel A: 50% occupancy at €120.- ADR
Hotel B: 100% occupancy at €60.- ADR
Ignores revenue from other sources, e.g. spa, seminar rooms, ...
“Erlös pro verfügbarer Zimmerkapazität”
Aus Revenue Management Sicht handelt Hotel B nicht profitabel. Der Blick in die Parameter zur Berechnung des RevPar spiegeln eine differenzierte Situation wider. Ein weiteres Problem für die Berechnung des RevPar liegt darin, dass keine Kosten für die Zimmernutzung und kein Erlös aus zusätzlichen Zimmerleistungen mit einfliessen.
Der Jahresvergleich (englischYear-over-year (YOY), Year-to-Year) vergleicht einen für ein bestimmtes Jahr ermittelten Wert mit dem entsprechenden Wert eines oder mehrerer Vorjahre.
RevPAR: Revenue Per Available Room, or RevPAR, is a metric commonly used to
measure financial performance in the hospitality industry. RevPAR is a function of
both room rates and occupancy, and is one of the most important gauges of
performance among hotel operators.
What: RevPAR is used by Hotel Management and analysts to determine the Market
share and Year-Over-Year performance of a hotel. Total revenue per available room
(Total RevPAR) is the product of (a) occupancy and (b) Total RevPOR.
Rising RevPAR is an indication that either occupancy is improving, or room rates are
rising -- or some combination of both. Of the two, rising room rates have a much more
dramatic impact on the bottom line than corresponding increases in occupancy. It is
not uncommon to see both figures rise together, though, as higher occupancy is
usually concurrent with a stronger pricing environment.
RevPAR evaluates the strength of only one type of revenue-generating stream, and it
is important to note that many hotels derive a substantial portion of their total
revenues from restaurants, spas, casinos, conferences, and other incremental
revenue streams.
RevPAST and RevPOST: Revenue Per Available Space-Time (RevPAST) and the associated
Revenue Per Occupied Space Time (RevPOST) are ratios designed to measure the efficiency of
Total Sales gained via the occupancy of a Hotel or Convention Center’s Meeting Space or
Function Space.
How: Revenue Management strategies can be designed to attain certain revenue goals in
relationship to the timing, availability, quantity, and marketplace demand of specific meeting
space utilized by a group or overlapping groups. For example, a baseline can be established by a
hotel or other venue to determine the historical market performance of a particular meeting room
or convention space and sales strategies (pricing, incentives, stipulations) can be implemented to
maximize revenues captured by the Hotel or venue for each particular Meeting room or the overall
hotel.

17. Key Performance Indicators “Gross Operating Profit Per Available Room”
Similar to RevPAR.
Better indicator for the actual performance of the hotel.
In addition to the revenue it takes also the departmental and operating expenses into account.
However, also does not take the overall revenue mix of the hotel into account.
Nevertheless it is good indicator to gauge the overall profitability and the worth of a hotel.
GOP = Rohertrag, Rohgewinn, Bruttoertrag (engl. gross profit)
GOPPAR: GOPPAR, or Gross Operating Profit Per Available Room, is defined as total gross operating
profit (GOP) per available room per day, where GOP is equal to total revenue less the total
departmental and operating expenses.
GOP stands for: Gross Operating Profit
It is a KPI which refers to the Hotels profits after subtracting all of their operating expenses. It illustratetes the level of operational profitability of a hotel.

18. Key Performance Indicators “Revenue Per Occupied Room”
One of the most important parameters. It is used to gauge budget goals, forecasted demand and year-to-year performance.
Mostly used in addition or alternatively to RevPAR.
RevPAR can be calculated by multiplying RevPOR with the occupancy rate.
The “Total RevPOR” also takes extra services like room services, laundry, etc. into account.
RevPOR is independent of general and local economic fluctuations since it is independent of the occupancy rate.
It is used to gauge the overall potential of a hotel.
RevPOR: Revenue Per Occupied Room, or RevPOR, is one of the most important measures
used by Hotels to evaluate the Revenue Contribution of a Group. RevPOR is most often viewed by
Revenue Managers in comparison to budgeted targets, anticipated demand, and Year-Over-Year
figures in order to determine the rates, concessions, and contract terms offered to Meeting
Planners.
What: RevPOR is used in conjunction with, or in place of, the more standard revenue per available
room (RevPAR) statistic. RevPAR is calculated by taking the RevPOR value and multiplying it by
the occupancy rate. RevPOR may also be expressed as "total RevPOR", which includes not only
the room rate itself, but also any extra services such as group F&B, Audio-Visual rentals or
commissions, room service, laundry services and in-room movie viewing, among others.
RevPOR is used by analysts to determine the total revenue and profit potential of a company;
occupancy rates will rise and fall with the general and local economy, but RevPOR is a metric that
stands independent of how full the hotel is at any point in time.
How: Revenue per available room (RevPAR) is the product of (a) occupancy and (b) ADR. Total
revenue per occupied room (Total RevPOR) is calculated by dividing total resort revenue
(including revenue from rooms, food and beverage, and other amenities) by total occupied rooms.

19. Key Performance Indicators “Revenue Per Occupied Space Time”
RevPOST
...is a measure of the Revenue Efficiency of a Group or of a Hotel’s utilization of its Function Space
RevPOST may be used by Hotels, Meeting Planners, Revenue Managers, and
financial analysts to compare the Revenue performance of different hotels in
their markets.
What: Unlike Rooms vs. Space Ratio, which is an internal hotel measures of a
group’s usage of Hotel resources without respect to Revenues or Profitability,
RevPOST may be used by Hotels, Meeting Planners, Revenue Managers, and
financial analysts to compare the Revenue performance of different hotels in
their markets.
Why: RevPOST may be used by hotel salespeople and Revenue Managers to
determine the Revenue Efficiency of different groups that overlap similar or
identical dates, as well as to establish budgetary goals for preferred patterns
offered by a Hotel to groups. RevPOST can also be applied to most global
markets when expressed as RevPM2 (Revenue Per Meters Squared) or
RevPKSF (Revenue per Square Foot X 1,000). As the size, scope, and frequency
of conference and incentives continues to increase worldwide, RevPOST has
grown in importance as a fundamental metric used to monitor the Revenue
performance and booking efficiency of hotel salespeople.

20. 2. Single Resource Capacity Control

21. Introduction Single resource capacity control
We will now look at models for revenue management that are based on single resources and how to optimally allocate its capacity to different classes of demand.
That means: the same product is sold to different classes with different conditions. E.g. sale of hotel rooms for a given date at different rate classes or rebates.
In reality many RM problems show network characteristics. I.e. they consist of bundles of resources. However they are still mostly implemented using a collection of single resource models. Furthermore single resource models are the base for many heuristics.
Assumptions
distinct classes of same resource, (in the beginning) distinct and mutually exclusive market segments, units of capacity homogenous, consumer demands single unit of resource.
Key question
How to optimally allocate resource capacity to the various classes?
The units of capacity are assumed to be homogeneous, and customers demand a single unit of capacity for the resource.
This allocation must be done dynamically as demand materializes and with considerable uncertainty about the quantity
or composition of future demand. The remainder of the section focuses on various models
and methods for making these capacity-allocation decisions.

22. Control Types Booking limits
Limit the capacity that will be sold in a specific class.
If the capacity for a specific class is used up it will be closed.
Either partitioned or nested classes.
Partitioning
Split capacity into buckets that can be exclusively sold in a specific class. Is a more valuable class sold out it will be closed regardless whether there is capacity left or not.
Nested
Hierarchical overlap between the classes. Higher valued classes can access the capacity of lower valued classes.
Usually nested strategies are used to prevent the situation where in which high value classes are closed although there is still capacity left.
In the travel industry, reservation systems provide different mechanisms for controlling availability.
Therefore, the control mechanisms chosen for a given implementation are often dictated by the reservation system.
For example, with 30 units to sell, a partitioned booking limit may set a booking limit of 12 units for class 1, 10 units for class 2, and 8 units for class 3.
If the 12 units of class 1 capacity are used up, class 1 would be closed regardless of how much capacity is available in the remaining buckets.
This could be undesirable if class 1 has higher revenues than do classes 2 and 3 and the units allocated to class 1 are sold out.
the nested booking limit on class 1 and lower (all classes) would be b 1 = 30 (the entire capacity), the nested booking limit on classes 2 and 3 combined would be b 2 = 18, and the nested booking limit on class 3 alone would be b 3 = 8.
We would accept at most 30 bookings for classes 1, 2, and 3; at most 18 for classes 2 and 3 combined; and at most 8 for class 3 customers.

23. Control Types Protection Levels
Different point of view compared to booking limits. Not “how much capacity to sell up to”, but “how much capacity to protect”.
Again two versions, partitioned and nested.
Partitioned
Identical to partitioned booking limits. Booking limit of 20 units is equivalent to protection of 20 units.
Nested
Again defined for sets of classes, ordered in a hierarchical manner. The protection level is defined as the amount of capacity to save for the respective classes and lower valued ones combined.
Connection between y and booking limit b for a class j:
A protection level specifies an amount of capacity to reserve (protect) for a particular class or set of classes. Again, protection levels can be nested or partitioned. A partitioned protection level is trivially equivalent to a partitioned bookinglimit; a booking limit of 18 on class 2 sales is equivalent to protecting 18 units of capacity for class 2.
In the nested case, protection levels are again defined for sets of classes—ordered in a hierarchical manner according to class order. Suppose class 1 is the highest class, class 2 the second highest, and so on. Then the protection level j, denoted yj , is defined as the amount of capacity to save for classes j, j − 1,..., 1 combined—that is, for classes j and higher (in terms of class order). Continuing our example, we might set a protection level of 12 for class 1 (meaning 12 units of capacity would be protected for sale only to class 1), a protection level of 22 for classes 1 and 2 combined, and a protection level of 30 for classes 1, 2, and 3 combined (although frequently no protection level is specified for this last case because it is clear that all the capacity is available to at least one of the classes).
Figure 1 shows the relationship between protection levels and booking limits. The booking limit for class j, bj is simply the capacity minus the protection level for classes j − 1 and higher. That is,bj = C − yj−1, j = 2,..., n,where C is the capacity. For convenience, we define b1 = C (the highest class has a booking limit equal to the capacity) and yn = C (all classes combined have a protection level equal to capacity).

24. Bookign Limit VS Protection Levels

25. Control Types Standard and Theft Nesting
Standard Nesting
Very simple. If demand is incoming, satisfy as long as the booking limit (or protection level) allows it (or no capacity is left).
Theft Nesting
In this variant satisfying a request not only lowers the capacity of the class but also steals capacity of the less valuable classes. This means the protection level for this class remains the same as long as units are available in lower classes.
Standard nesting has a forecasting aspect. Bookings in a class lower the probability of a future booking in it. Theft nesting on the other hand ignore this aspect, each booking is equally as likely.
Standard Verschachtelung
(1) there is capacity remaining and (2) the total number of requests accepted for class j to date is less than the booking limit b j (equivalently, the current capacity remaining is more than the protection level y j−1 for classes higher than j).
Another alternative, which is less prevalent although still encountered occasionally in practice, is called theft nesting. In theft nesting, a booking in class j not only reduces the allocation for class j, but also “steals” from the allocation of all lower classes. Therefore, when we accept a request for class j, not only is the class j allocation reduced by one, but so are the allocations for classes j + 1, j + 2, , n. This is equivalent to keeping y j units of capacity protected for future demand from class j and higher. In other words, even though we just accepted a request for class j, under theft nesting we continue to reserve y j units for class j and higher, and to do so requires reducing the allocation for classes j + 1, j + 2, , n. Under standard nesting, in contrast, when we accept a request from class j we effectively reduce by one the capacity we protect for future demand from class j and higher.
The two forms of nesting are in fact equivalent if demand arrives strictly in low-to-high class order; that is, the demand for class n arrives first, followed by the demand for class n−1, and so on. 4 This is what the standard (static) single-resource models assume, so for these static models, the distinction is not important. However, in practice demand rarely arrives in low-to-high order, and the choice of standard versus theft nesting matters. With mixed order of arrivals, theft nesting protects more capacity for higher classes (equivalently, allocates less capacity to lower classes). Again, however, standard nesting is the norm in RM practice.

26. Control Types Bid Price
Revenue-based instead of class-based controls.
Accept/reject purchase based on a threshold price (depend on capacity and/or time)
Simpler, only one threshold price at a point in time instead of capacity numbers for each class.
BUT must be updated after each sale! A function depending on the capacity. Otherwise whole capacity potentially sold to any class succeeding current threshold. With update it can model the same segmentation policies as booking limits or protection levels.
If revenue information is available at time of purchase allows fine grained control of acceptance for individual purchases. Class based controls can only accept/reject whole class.
a bid-price control sets a threshold price (which may depend on variables such as the remaining capacity or time)
for updating Store table of bid prices indexed by available capacity and/or time.
However, if actual revenue information is available for each request, then a bid-price control can selectively accept only the higher revenue requests in a class, whereas a control based on class designation alone can only accept or reject all requests of a class. Of course, if the exact revenue is not observable at the time of reservation, then this advantage is lost.

27. Displacement Cost
While the mathematics of optimal capacity controls can become complex, the overriding logic is simple.
fulfill request if and only if revenue is greater than the value of the capacity required
the value of capacity should be measured by its (expected) displacement cost (aka opportunity cost), i.e. expected loss in future revenue from using the capacity now
Value Function
Measures the optimal expected revenue as a function (depends on method) of the remaining capacity. The displacement cost then is the difference between the value function at a capacity and the value function at a capacity - 1.
The logic is simply to compare revenues to displacement costs to make the accept or deny decision.

28. Models: Static Assumptions
One of the first and simplest models. Makes following assumptions:
demand for the different classes arrives in nonoverlapping intervals in the order of increasing prices of the classes
demands for different classes are independent random variables
perfect segmentation between classes, i.e. demand for a given class, does not depend on the capacity controls (esp. availability of other classes)
no continuous time, i.e. aggregate quantity of demand arrives in a single stage and the decision is simply how much of this demand to accept
no, or partially acceptable groups
risk neutrality
@1 In reality, demand for the different classes may overlap in time. However, the nonoverlapping-intervals assumption is a reasonable approximation (for example, advance-purchase discount demand typically arrives before full-fare coach demand in the airline case). Moreover, the optimal controls that emerge from the model can be applied—at least heuristically—even where demand comes in arbitrary order (using either bid prices or the nesting policies, for example). As for the strict low-before-high assumption, this represents something of a worst-case scenario; for instance, if high-revenue demand arrives before low-revenue demand, the problem is trivial because we simply accept demand first come, first serve.
@2 to deal with dependence in the demand structure would require introducing complex state variables on the history of observed demand.
We can make some justification for the assumption by appealing to the forecast inputs to the model. That is, to the extent that there are systematic factors affecting all demand classes (such as seasonalities), these are often reflected in the forecast and become part of the explained variation in demand in the forecasting model (for example, as the differences in the forecasted means and variance on different days). The randomness in the single-resource model is then only the residual, unexplained variation in demand. So, for example, the fact that demand for all classes may increase on peak flights does not in itself cause problems, provided the increase is predicted by the forecasting method.
Still, one has to worry about possible residual dependence in the unexplained variation in demand, and this is a potential weakness of the independence assumption.
@3 There is considerable porousness (imperfect segmentation) in the design of the restrictions, and the price differences between the classes are rarely that dispersed. The assumption that demand does not depend on the capacity controls is therefore a weakness
@4 However, in a real reservation system, we typically observe demand sequentially over time, or it may come in batch downloads. The control decision has to be made knowing only the demand observed to date
However the optimal controls used are very robust and can handle this very robustly
@6 In economics and finance, risk neutral preferences are neither risk averse nor risk seeking. A risk neutral party's decisions are not affected by the degree of uncertainty in a set of outcomes, so a risk neutral party is indifferent between choices with equal expected payoffs even if one choice is riskier. RM typically makes such decisions for a large number of products sold repeatedly (for example, daily flights, daily hotel room stays, and so on)

29. Models: Static 2-Class Model
Oldest and simplest single-resource model for quantity based RM. Only uses 2 classes with different prices.
Question: how much to accept for class 2 before only accepting class 1.
Similar to “newsvendor problem” and solved using simple marginal analysis. Should we accept request for class 2? Only as long as price 2 is bigger than price 1 adjusted for risk, i.e. probability that it will get sold.
This formula can be used directly as a bid price control
Or define an optimal protection level and Littlewood’s Rule
two product classes, with associated prices p 1 > p 2 . The capacity is C, and we assume there are no cancellations or overbooking.
Suppose that we have x units of capacity remaining and we receive a request from class 2. If we accept the request, we collect revenues of p 2 . If we do not accept it, we will sell unit x (the
marginal unit) at p 1 if and only if demand for class 1 is x or higher. That is, if and only if D 1 ≥ x. Thus, the expected gain from reserving the xth unit for class 1 (the expected marginal value) is p 1 P (D 1 ≥ x)
Note that the right-hand side of (1) is decreasing in x. Therefore, there will be an optimal
protection level, denoted y 1 ∗ , such that we accept class 2 if the remaining capacity exceeds
y 1 ∗ and reject it if the remaining capacity is y 1 ∗ or less.
If a continuous distribution F 1 (x) is used to model demand (as is often the case), then the
optimal protection level y 1 ∗ is given by the simpler expressions

30. Models: Static n-Class Model I
Generalized version of the 2-class problem, now with n classes. Demand arrives in n stages, one for each class, with classes arriving in increasing order of their revenue values.
Dynamic Programming
A method for solving a complex problem by breaking it down into a collection of simpler subproblems, solving each of those subproblems just once, and storing their solutions.
Assumed sequence of events
realization of demand for class occurs and value observed
decide on quantity to accept. It must be less than remaining capacity. There is an optimum based on class, capacity and demand.
collect the revenue for this constellation and proceed to the next class.
Assumes demand is known beforehand for analytical convenience. In reality arrives over time. Model not dependent on it however.
(1) The realization of the demand D j occurs, and we observe its value.
(2) We decide on a quantity u of this demand to accept. The amount accepted must be less than the capacity remaining, so u ≤ x. The optimal control u ∗ is therefore a function of the stage j, the capacity x, and the demand D j , u ∗ = u ∗ (j, x, D j ), although we often suppress this explicit dependence on j, x, and D j in what follows.
(3) The revenue p j u is collected, and we proceed to the start of stage j − 1 with a remaining capacity of x − u.
This sequence of events is assumed for analytical convenience; we derive the optimal control u ∗ “as if” the decision on the amount to accept is made after knowing the value of demand D j . In reality, of course, demand arrives sequentially over time, and the control decision has to be made before observing all the demand D j . However, it turns out that optimal decisions do not use the prior knowledge of D j as we show below. Hence, the assumption that D j is known is not restrictive.

31. Models: Static n-Class Model II
In plain English
we observe demand, and try to come up with the protection level u that generates the best value for this class j while considering the value of lower classes j-1 as well. u lies between 0 and either remaining demand or remaining capacity.
This is an optimization problem, we need to find the optimal parameters. Use smart software or create a table and look at the numbers.
Find the levels for the class j that brings that still has a bigger marginal value (delta value) according to the following formula. Booking limit and bid price can be calculated from this protection level

32. Models Heuristics
Although optimal controls are pretty straight forward, not used widely. In practice several heuristics are used.
They are very simple to implement and run. Usually good enough and it’s better to be “approximately right” than “precisely wrong”.They predate optimal controls actually by more than a decade.
EMSR-a and EMSR-b (expected marginal seat revenue) based on the n-class, static, single resource model. Most popular heuristics.
Although EMSR-a is more publicized it’s close cousin EMSR-b provides the better results and is more popular in practice.

33. Models Heuristics: EMSR-a
EMSR-a is based on the idea of adding the protection levels produced by applying Littlewood’s rule to successive pairs of classes.
Consider stage j + 1, in which demand of class j + 1 arrives with price p j+1. We are interested in computing how much capacity to reserve
for the remaining classes, j, j − 1, , 1; that is, the protection level, y j , for classes j and higher.
To do so, let us consider a single class k among the remaining classes j, j − 1, , 1 and compare k and j + 1 in isolation. Considering only these two classes, we would use Littlewood’s rule (2) and reserve capacity y k j+1 for class k, where
EMSR-a is certainly simple and has an intuitive appeal. For a short while it was even believed to be optimal, but this notion was quickly dispelled once the published work on optimal controls appeared.

34. Models Heuristics: EMSR-b
EMSR-b is again based on an approximation that reduces the problem at each stage to two classes, but in contrast to EMSR-a, the approximation is based on aggregating demand rather than aggregating protection levels.
Specifically, the demand from future classes is aggregated and treated as one class with a revenue equal to the weighted-average revenue.
In practice EMSR-b is more popular and generally seems to perform better than EMSR-a.

35. 3. Customer Choice Behaviour

36. Introduction Key assumption until now
Demand for each of the classes is completely independent of the capacity controls being applied by the seller.
Very unrealistic
Will customer rent full price room if discounted room is available?
Heuristic and exact methods to manage this exist.
Some Terminology
Buy-up… customer buys higher fare when discount is closed
Diversion… customer takes another flight
These factors are important and should be included in the models!

37. Models Buy-Up Factors I
Up until now we expected customer not to buy anything if his class of choice is closed. However, realistically there is a chance she will buy up to the higher class.
There are different approaches, however in current applications of the model, they are often simply made-up, reasonable-sounding numbers. A good rough-cut approach for incorporating choice behavior.
Easiest model is based on Littlewood and works for two classes (only).
It introduces a probability q that a customer of class 2 buys up to class 1.
This model is more eager to close class 2. This makes intuitive sense because there is a chance that the customer will buy up.

38. Models Buy-Up Factors II
More classes?
No more binary choice but multinomial. Littlewood not possible but EMSR-a and EMSR-b approximate multi class. Can be extended.
Modified EMSR-b
where q is the probability that a customer of a class buys up to one of the higher valued classes. p̂ > p is an estimate of the average revenue received given that a customer buys up to one of the higher valued classes (e.g. p̂j+1 = pj if customers are assumed to buy up to the next-highest price class).
Net result of this change is to increase the protection level and close down class j + 1 earlier than one would do under normal EMSR-b.
Grain of salt… it’s an ad-hoc adjustment to an already heuristic approach!
While this modification to EMSR-b provides a simple heuristic way to incorporate choice behavior, it is a somewhat ad hoc adjustment to an already heuristic approach to the problem. Beyond the limitations of the model and its assumptions, there are some serious difficulties involved in estimating the buy-up factors.
That it increases the protection level about the usual EMSR-b value can be seen by noting that p j+1 = R̄ j P (S j > y j ) in the usual EMSR-b case and p̂ j+1 > p j+1 ; thus, y j has to increase to satisfy the equality (20).

39. Models Discrete Choice Modelling I
Modeling with general discrete-choice model, a more theoretically sound approach to incorporating choice behavior than heuristics.
provides insight into how choice behavior affects the optimal availability controls.
Time is discrete
In each period there is at most one arrival. The probability of arrival is denoted by λ assumed to be same for each period.
N = {1, , n} denote the entire set of classes
In each period t, the seller chooses a subset S t ⊆ N of classes to offer. When the set of classes S t is offered in period t, the probability that a customer chooses class j ∈ S t is denoted P j (S t ). P 0 (S t ) denotes the no- purchase probability.

40. Models Discrete Choice Modelling II
Simplified Example
For example, some psychologists have shown that customers can be overwhelmed by more choices, and they may become more reluctant to purchase as more options are offered. Such cases would be covered by a suitable choice of P j (S) that results in the total probability of purchase,
j∈S P j (S), being decreasing in S.
To see how the probabilities in Table 3 are derived, consider the set S = {Y, K}. If S = {Y, K} is offered,
segments Business 1 and Business 2 buy the Y fare because they cannot qualify for both the SA stay and
21-day advance-purchase restrictions on K, so P Y = = 0.3. Similarly, Leisure 1 cannot qualify for the
SA stay restriction of K and is not willing to purchase Y , so these customers do not purchase at all. Segments
Leisure 2 and 3, however, qualify for both restrictions on K and purchase K. Hence, P K = = 0.5.
Class M is not offered, so P M = 0. The other rows of Table 3 are filled out similarly.

41. History and Theory of Revenue Management
Hands on Exercises 41

42. Exercise 1 Status Quo: Revenue management in your business
Form groups of up to four people and discuss the mentioned points. Write down your names and answers in a document (txt, doc, Google Doc …) and send it to by the end of today. Subject: Status Quo. Prepare a short presentation (no slides, just orally) of your thought and present it after the preparation phase.
Identify your business:
What: what do you (want to) sell?
To whom: (potential) customers, target group(s)?
Price(s) and Classes?
Times: Is there a temporal change in your sales strategy? Daily, Weekly, Monthly, Saesonally, Annually?
Do you practice Revenue Management?
Yes! What and how?
No! Where do you see potential?
What can you apply from the just learned?
Make a RM plan
Estimate the change in revenue after applying 3.a

43. In what areas does RM make sense?
Exercise 2
Questionnaire
Form groups of up to four people and discuss the mentioned questions. Write down your names and answers in a document (txt, doc, Google Doc …) and send it to by the end of today. Subject: Questionnaire.
In what areas does RM make sense?
Besides rooms, to what else can you apply RM in hotels?
How do you know if you are selling at prices that are too low?
How do you know if you are selling at prices that are too high?
How to act during high demand?
How to act during low demand?

44. Preliminaries
You will use Excel to solve the following example.
(LibreOffice, or Google Sheets works fine as well)
The can be found on the course website (KPIs.xls)
Please build groups of three or four
Each group will solve the problem and can volunteer to present their results.
Volunteering will positively influence your grade!

45. Exercise 3: Basic Measures GOPPAR, RevPOST, RevPAR, RevPor, ...
This exercise is about calculating basic measures and KPIs for your hotel.
You’ll find some toy data for an example hotel, namely its supply, demand, revenue and operational cost.
Open the provided “KPIs” excel file
Fill in the missing measures for the toy hotel
(optional calculate average monthly change)
Create a diagram for your data
Volunteer group will present their findings to the rest of the group. How did your hotel perform?