Revenue Management Peter C. Bell 2005

Revenue Management
Vision 2020: Ahmedabad 2005

Peter C. Bell

Ws PBELL@IVEY.CA

1 w © 2005 by Peter C. Bell

My Objective

To introduce you to the practice and theory of
Revenue Management

Since this is a large and fast growing field, this will be a
broad-brush survey.


AGENDA:

• Introduction
• What is revenue management, who uses it
and what has been the impact?
• The five pillars of RM
– Pricing, discount allocation, overbooking, trading up
and re-planing
• Integrating the tools
• Conclusions


AGENDA:

• Introduction
and re-planing
• Conclusions


REVENUE MANAGEMENT: Definition

Revenue management (RM) is the
science and art of enhancing firm
revenues while selling essentially the
same amount of product.


REVENUE MANAGEMENT: History

The first reference to RM is:

Taylor, C.J. (1962) The determination of passenger
booking levels. Proceedings of the Second AGIFORS
Symposium, American Airlines, New York.

This work recognizes the value of selling more
airline seats than capacity in anticipation of
“no-shows.” We now call this “overbooking.”


REVENUE MANAGEMENT: History

The first major users of RM were
American Airlines and Delta Airlines
starting about 1985.

Both Tom Cook (American) and Robert
Cross (Delta) have been cited as the
“fathers” of corporate RM.


OR developments in “revenue
enhancement” since 1985 have led
to innovative new methods of pricing
and delivering products.

We call these methods “revenue
management” tools.


“MANAGEMENT SCIENTISTS
HAVE WRECKED THE AIRLINE
INDUSTRY”

Joseph F. Coates
(California futurist)


However the impact of revenue
management has been dramatic

… and the use of RM continues to
expand to new products.


“We estimate that yield management has
generated $1.4 billion in incremental revenue in
the last three years”
by
“creating a pricing structure that responds to
demand on a flight-by-flight basis”

R.L. Crandall, Chairman and CEO of AMR, 1992


“We have estimated that the yield management
system at American Airlines generates almost
$1 billion in annual incremental revenue”

Tom Cook, President
SABRE Decision Technologies,
June 1998


quot;Ford Motor Co. has quietly been enjoying a
huge surge in profitability... 1995 and 1999,
U.S. vehicle sales rose just 6 percent, from
3.9 million units to 4.1 million units. But
revenue was up 25 percent, and pretax
profits soared 250 percent, from about $3
billion to $7.5 billion. Of that $4.5 billion
growth, Ford's Lloyd Hansen, controller
for global marketing and sales, estimates
that about $3 billion came from a series of
revenue management initiatives.”
CFO Magazine, August, 2000


“(revenue management) basically saved National
Car Rental. And you can go from the CEO of
National on down, and they will all say: ‘just
applying these OR models made the life or death
difference for this company’”

Kevin Geraghty, Aeronomics Inc.


and .. on the other side:

RM used by the competition has bankrupted
several corporations .. the clearest example
being Peoples’ Express Airlines.


Donald Burr, Founder and CEO of People
Express

“believes that major carrier’s use of
sophisticated computer programs
to immediately match or undercut
his prices ultimately killed People
Express”


WHO USES RM?

• AIRLINES (All?)
• HOTELS (Hyatt, Marriott, Hilton, Sheraton, Forte, Disney ..)
• VACATIONS (Club Med, Princess Cruises, Norwegian ..)
• CAR RENTAL (National, Hertz, Avis, Europcar ..)
• WASHINGTON OPERA
• FREIGHT (Sea-Land, Yellow Freight, Cons. Freightways ..)
• TELEVISION ADS (CBC, ABC, NBC, TVNZ, Aus7 ..)
• UPS, SNCF
• RETAIL (Retek, Khimetrics)
• REAL ESTATE (Archstone)
• NATURAL GAS
• TEXAS CHILDREN’S HOSPITAL


AGENDA:

• Introduction
and re-planing
• Conclusions


THE 5 PILLARS OF RM

• New approaches to pricing
• Discount allocation
• Trading-up
• Overbooking
• Re-planing

• + markdown optimization, purchase loans, etc


NEW APPROACHES TO PRICING
PRODUCTS AND SERVICES


THE NEW PRICING CONCEPT

• Use product price as a management
control variable.
• Set this price “optimally” to various
customer groups or “clusters”.
• Be prepared to change prices often.


THE “CONCEPTUAL LEAPS”

• “Products” do not have a value, rather the
value of a product depends on the point in
time of purchase.

• “Products” have different values to different
clusters of customers.


DEMAND AT A POINT IN TIME BY A
CUSTOMER CLUSTER DRIVES RM PRICING

MARKET SEGMENTATION IS THE KEY TO
ENHANCING REVENUES THROUGH RM
PRICING


A MARKET

Q = F(P,……..)
Price

Quantity Sold


SEGMENTING A MARKET

Q = F(P,……..)
becomes qi = Fi(pi,…..)
for i = 1,…N
Price

Market
Segmentation

Quantity Sold


MARKET SEGMENTATION: METHODS

• Time of purchase
• Customer characteristics (seniors, others)
• Sales channel (“clicks” and “bricks”)
• Offer a discount to large customers
• Offer a discount for slow delivery
++


Example of market segmentation

Coke price rises with heat
Vending machine that alters price with temperature
change is possible

NEW YORK (CNNfn) - It's not the New Coke, but it may
be the Smart Coke. Soft-drink giant Coca-Cola Co. is
working on a vending machine that automatically
raises the price of a soda whenever the weather grows
hot.
Coke chairman Doug Ivester said the machine was
designed to reconcile supply and demand by raising
the price when demand increased.
quot;Coca-Cola is a product whose utility varies from
moment to moment,quot; he was quoted as saying.


“CLUSTERING” CUSTOMERS

• Different groups of customers value a product
differently
– Example:
• “Business class” air customers value
convenience, comfort, flexibility
• “Economy class” customers value low
prices, (and perhaps longer stays,
advance reservations)
• “Clustering” means assigning customers to
“clusters” or “market segments”


An example of “clusters”

• E-Bivalent Newbies (5% of online shoppers)
– Newest to Net, somewhat older, spends least online, likes online
least
• Time Sensitive Materialists (17%)
– Most interested in convenience, less likely to read reviews or
compare prices
• Clicks and Mortar (23%)
– Browse online, prefers to buy offline, more likely female, has
privacy and security concerns, goes to malls often
• Hooked, Online and Single (16%)
– More likely young, single males with high incomes, have been
on Net longest, most likely to play games, download, bank
online
• Hunter-Gatherers (20%)
– Typically 30-49 years old, two kids, most likely to visit sites that
provide information and comparison
• Brand Loyalists (19%)
– Most likely to bypass search engines to go directly to sites they
know, most satisfied with shopping online, spend most online
-- Harris Interactive study of 3,000 Internet Shoppers, 2000


CHANGING PRODUCT VALUE
OVER TIME (“time segmentation”)

• Perishable products that age,
• Seasonality,
• Some customers will pay for the security of
early purchase, or for the flexibility of late
purchase,
• Suppliers may attach value to the security of
early sales……….


CHANGING DEMAND OVER TIME
Example: PERISHABLE PRODUCTS
Demand

Segment 1 S2 S3

Time

Example: EVENT or TRIP TICKETS
Demand

Time Event Date


Common Demand Models

Q = Quantity sold
p = price/unit

Linear demand:
Q=A–Bp
Usually maximum and minimum prices are specified

Constant elasticity demand:
Q = A p-e
where e is the price elasticity of demand


LINEAR APPROXIMATION OF DEMAND
CURVE

Demand Curve
Price

Linear Approximation

Quantity Sold


MODEL CHOICE MAY NOT BE OBVIOUS

DEMAND EQUATION ESTIMATION

70
60
50
Quantity

40

30
20
10
0
$100.00 $150.00 $200.00 $250.00
Price

Q = 92.1 - .37 P R2 = 0.95 Q= 2170037377 P-3.59 R2 = 0.95

General Demand Function

In general, for any time period and cluster:

Q = F(P, Ps, Pc, X1, X2, ….)

• where:
• P = price of product
• Ps = price of substitute products
• Pc = price of complement products
• Xi are exogenous variables (weather,
economic factors, advertising…etc)


Estimating Demand

Demand estimation is a craft: firms tend to keep
this part of their RM confidential.

Two steps are required:

1. Build a demand model (off-line). Common
techniques include regression, curve fitting,
and cluster analysis.
2. Develop an on-line demand model updating
procedure to respond immediately to
unexpected observed demand.


“LEAKAGE”

• Demand “leakage” (from a high priced
segment to a low priced segment)
occurs when segmentation is not
perfect.
Q1 = F1(p1…) – L(p1 – p2)
Q2 = F2(p2…) + L(p1 – p2) where p1 > p2


“FENCES”

• Revenue will disappear unless market
segments are kept separate to limit “leakage”
from high priced segments to low priced
segments.
• Tools to maintain segment separation are
called “fences”.
Examples of fences:
– The fee airlines charge to modify a low fare ticket
(usually $150-200).
– The requirement for a Saturday night stopover for a
low fare ticket.
– Booking and paying 90 (or 60, or 30) days in
advance.
Look for examples of creative fences!


Pricing

Approaches to Revenue Maximization
– Traditional fixed pricing
– Variable pricing
– Optimum dynamic pricing
• Computing optimum prices


Single price: 2 market segments

Revenue = p (Q1 + Q2)
There is usually a p* that
Price
optimizes revenue.
p

Q1 Q2 Quantity Sold


Two prices: 2 market segments

Revenue = p1Q1 + p2Q2
Price If p1* and p2* maximize revenue
then:
p1
p1*Q1 + p2*Q2 ≥ p*(Q1 + Q2)
p2

Q1 Q2 Quantity Sold


Formal statement of deterministic ODP
problem (time segments)

Let: pi be the product price in period i,
qi be the quantity sold in period i,
qi = fi (pi) be the demand curve for period i,
and
I be the inventory to be sold over N pricing
periods.
then:
∑
N
Max Z = pi qi
i =1
Subject to:
qi = fi (pi) for i = 1, ......N
∑
N
qi = I
i =1


Deterministic ODP problem with forecast
errors

Let: pi be the product price in period i,
qi be the quantity sold in period i,
qi = fi (pi) be the demand curve for period i, and
I be the inventory to be sold over N pricing periods.
then:
For each period, k, k = 1,2,...N

∑
N
Z= piqi
Max i=k

Subject to:
qi = fi (pi) + error for i = k, k+1, ......N

∑ ∑
k −1
N
qi = I − qi
i= k i =1


ACCEPT/REJECT DECISION MAKING

RM algorithms are mostly “accept/reject” rules.

If a customer appears and offers to buy a unit
for $P, do you accept (in which case you give
up the opportunity to sell the same unit to a
later arriving customer who may pay more
than $P), or do you reject (in which case you
give up $P in the hope of selling the unit later
>$P but may not sell the unit).

The issue is one of balancing “yield loss” and
“spoilage”.


Revenue optimization drove the entry of RM into
services.
- non-replenishable inventories,
- low (zero?) variable cost of providing product.

For restockable items, contribution optimization
can be more difficult.
- role of inventory and replacement policies,
- need for “profitable market share”.


The Single-Period Stochastic Optimum
Pricing Problem
Define:
• p - the price (a decision variable),
• c - the variable production cost (c < p),
• I - the quantity available for sale (which may be a decision
variable),
• h - holding cost per unit of inventory unsold at the end of the
period,
• u - shortage cost per unit of unsatisfied demand,
• q = D(p, ξ) be the demand function where ξ is a random
variable with density function f(ξ).

The contribution, π, depends on the random demand:
qp − cI − h ( I − q ) q<I
π ( p, I ) = 
 I ( p − c) − u (q − I ) q≥I

The firm must chose values for the decision variables (p and I)
based on expected contribution, E(π), which depends on the
forecast of the random demand q:


Inventory/SC models vs. RM models

• Most inventory and supply chain models
assume demand (Q) is given.
• RM models replace given demand (Q) with a
given demand curve [F(p)]. The firm must
optimize p (and hence determine Q) and
simultaneously optimize inventory.
• Many research opportunities.


THE 5 PILLARS OF RM

• Optimum dynamic pricing
• Discount allocation
• Trading-up (or planned upgrades)
• Overbooking
• Re-planing (or short selling)

• + markdown optimization, purchase loans, etc


Discount allocation

• Multiple prices for the same units
– Multi-day packages (hotels, rental cars)
– Singles and 10-packs
– A ski hill had 22 different packages
covering the same ski session
• Issue: how many units to allocate to each
discount package price (the “reservation
level”)?


Discount allocation: Solver example


Discount allocation: hotel example


DYNAMICS OF MULTIPLE DISCOUNT
PACKAGES AND PRICE CATEGORIES

Issue: If a customer appears and demands the
low fare or discount package, when do you
say “No” in order to preserve product for the
higher paying customers?

Example: How many “full fare economy” seats
on the plane?


Reservation rule (Littlewood 1972)

Issue: How many units (seats) to reserve for
low price sale?

Continue to sell discount product at time t until:
r ≥ (1 - Pt) R or (1 - Pt) ≤ r / R

Where: r = low price (marginal revenue)
R = high price (marginal revenue)
Pt = probability of selling at least
the remaining number of units.


EMSR Heuristic (Expected Marginal Seat
Revenue) Belobaba 1987

Apply Littlewood’s rule sequentially to fare classes in
increasing fare order.

Let µi ,σi be the estimates of mean and std. deviation of demand
for product class i with price pi
Set a reservation (or protection) level of Li so that
pi+1 = Pi P(Xi > Li)

Where Pi is the weighted average fare for classes 1,2,,,,,I
And Xi is a normal random variable convoluting demand for
classes 1,2,….i


Protection levels: Expected MR curves


Overbooking (aka overselling)

Issue: Should you take more orders than you
have product in the expectation that some
customers who have ordered will not collect
the product?

• If so, how many extra orders should you take
and when?
– P{cancel order} declines as delivery date
approaches


OVERBOOKING: EXAMPLES

• airline seats, and passenger train seats, are usually
booked in advance of the date of travel,
• rental cars can be reserved ahead of the day of rental,
• hotel rooms and campsite spaces, seats for stage
shows, sports events, and concerts are sold in
advance,
• fresh turkeys can be ordered for delivery at
thanksgiving,
• package vacations and cruises are usually booked in
advance,
• tuxedos, cut flowers, some baked goods, etc. are
commonly booked for future delivery


Managing the overbooked customer

A key cost in all the models
• Airlines offer cash or travel coupons to
ticketed customers in order to persuade them
to take an alternate flight when space is
needed for overbooked passengers.
• Hotels will trade up overbooked customers to
rooms on the executive floor,
• Rental car companies will substitute a higher
class of car at no extra charge.

In all these cases, the cost is well know.


Minimizing the “no show” rate

If all customers with reservations showed up,
there would be no benefit from overbooking
• Require payment at the time the booking is made,
perhaps offering an early payment price reduction.
• Require payment in full at some prearranged time in
advance of the delivery date. If payment is not
received, the supplier cancels the booking.
• Fees may be charged if a booking is changed.


Overbooking: the basic model

M = the amount of product
B = the booking limit (B ≥ M)
RN = the value of sale of unit N with RN+1 ≤ RN,
Ci = cost of satisfying the ith overbooked customer if no product is
available, Ci+1 ≥ Ci
P[Q|B] = probability that Q customers will show up if we sell B units.

The expected cost of unsold product is:
{(RQ+1 + RQ+2 +...+ RM) P[Q|B] } summed over all values of Q < M
The expected cost of handling oversold customers is:
{(C1 + C2 +...+ CQ-M) P[Q|B] } summed over all values of Q > M

Find B that minimizes the sum of these two expected costs.


Overbooking: Determining the optimal level


Trading up (planned upgrades)

Issue: If a customer appears demanding a
product that is sold out, should you trade the
customer up to a higher valued product (at
your expense)?
Issue B. If you adopt this as policy, what does
this do to your inventory management?


Re-planing

Issue: If a plane is sold out several days before
flight date and a customer appears prepared
to pay a “high” price for that flight, can you
profitably “incentivize” a low-fare paid
customer to change flights?

2001 McKinsey, CALEB Technologies,
American Airlines


Other RM tools

• “Markdown optimization” is common in retail
(Retek, Manugistics, Spotlight): This is really
price optimization with non-increasing prices.
– The benefits are claimed to be very
substantial
• “Bottleneck optimization” (Maxager Tech.) is
price optimization where “inventory” is
production time on the scarce production unit.
• There are others but all seem to be variations
on the 5 basic tools.


AGENDA:

• Introduction
and re-planing
• Conclusions


Integration

• Although these tools are almost always
discussed separately, they all function within
a highly integrated system


PRICES

RESERVATION LEVELS


CAPACITY

PRICES

RESERVATION LEVELS


CAPACITY
OVERBOOKING LEVEL

PRICES

RESERVATION LEVELS


CAPACITY
OVERBOOKING LEVEL

PRICES

RESERVATION LEVELS

PLANNED UPGRADES


CAPACITY
OVERBOOKING LEVEL

PRICES REPLANE
LEVEL

RESERVATION LEVELS

PLANNED UPGRADES


Update
Real time
Database
Historical Data Product Sales
Sales Data
Revise Demand
Model

Current
Inventory
Build The
Demand
Levels
Demand Model Market
Forecasts

Off-line Support Activities
Pricing
Posted Prices
System
Revenue Management
System


REQUIREMENTS FOR SUCCESS

• SUPERIOR INFORMATION TECHNOLOGY,

• SUPERIOR OPERATIONS RESEARCH SKILLS,
and

• THE ABILITY TO MANAGE DYNAMIC PRICES.


AGENDA:

• Introduction
and re-planing
• Conclusions


BUSINESS OPPORTUNITIES

A great number of products seem ripe for RM.

Some examples:
Cinemas, golf courses, electricity, taxis, public
transit, newspapers and magazines,
advertising, fashion clothing, blue jeans,
vegetables, fast food, supermarkets, sports
events, theatre, pop concerts,……


RESEARCH OPPORTUNITIES

Academic
Almost every “inventory” model can be extended
to include a demand curve (some already
have been!)
Accept/reject decision heuristics (Bayesian)
Application
The merger of SC optimization and RM (“EPO”)
Clustering
New and improved “fencing”
Demand modeling (how good does it need to
be?)


CONCLUSIONS

RM tools have become very important for both
business and OR
There are opportunities for many new revenue
maximizing models and pricing/inventory
models
Heuristics to aid implementation are a priority
Competitive models provide an opportunity
The competitive customer
Competition among RM firms


CONCLUSIONS

RM techniques raise many business issues:
winning firms will be able to implement these
ideas while keeping customers (and
regulators) happy.
Everyone gains from the efficiencies that RM
produces, but some individuals lose.
Successful implementation usually requires
taking good care of the few who lose.


Revenue Management Peter C. Bell 2005

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