SHA541 transcripts

  SHA541:
 Price
 and
 Inventory
 Controls
 
School
 of
 Hotel
 Administration,
 Cornell
 University
 


 S HA541

 

 

 


 

Transcripts

Transcript: Course Introduction

 
Welcome
 to
 Price
 and
 Inventory
 Control.
 I
 am
 Chris
 Anderson,
 I'm
 the
 author
 of
 this
 course
 and
 
a
 professor
 at
 Cornell
 University
 School
 of
 Hotel
 Administration.
 My
 teaching

 and
 research
 
focus
 is
 largely
 on
 revenue
 management
 and
 pricing
 with
 an
 app,
 application
 specifically
 in
 
service
 industries.
 
 

 
This
 course
 focuses
 on
 one
 of

 the
 core
 concepts
 of
 revenue
 management.
 That
 being
 marginal
 
analysis.
 We're
 gonna
 look
 at
 how
 firms
 can
 estimate
 the
 marginal
 value
 of
 the
 last
 room
 they
 
sell,
 the

 seat
 on
 the
 plane.
 Or
 the
 last
 rental
 car
 in
 the
 parking
 lot.
 And
 then
 they
 use
 this
 
marginal
 value
 then
 to
 control
 inventory,.
 Or
 to
 set
 prices
 going

 forward.
 
 

 
This
 course
 serves
 as
 a
 solid
 foundation
 in
 revenue
 management
 for
 those
 of
 you
 who
 are
 
relatively
 new
 to
 the
 area
 and
 as
 more

 of
 a
 reinforcement
 of
 the
 core
 concepts
 for
 those
 of
 you
 
with
 prior
 RM
 experience.
 Thanks,
 and
 welcome
 and
 I
 hope
 you
 find
 the
 course
 impactful.
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
1
 
© 2015 eCornell. All rights reserved. All other copyrights, trademarks, trade names, and logos are the sole property of their respective owners.
 


 



  SHA541:
 Price
 and
 Inventory
 Controls
 
School
 of
 Hotel
 Administration,
 Cornell
 University
 

 

 

Transcript: Price and Duration Controls
Successful
 revenue
 management
 has
 effective
 control
 of
 price
 and
 duration
 of
 stay—the
 two
 
strategic
 revenue
 management
 levers.
 Consider
 this
 matrix
 that
 plots
 firms
 along

 the
 dual
 axes
 
of
 duration
 and
 price,
 where
 duration
 is
 controlled
 or
 uncontrolled
 and
 price
 is
 relatively
 fixed
 
or
 variable.
 This
 chart
 provides
 an
 introduction
 to
 the
 revenue

 management
 perspective.
 


 
Firms
 in
 industries
 traditionally
 associated
 with
 revenue
 management
 (hotels,
 airlines,
 rental
 
car
 firms,
 and
 casinos)
 are
 able
 to
 apply
 variable
 pricing
 for
 a

 service
 that
 has
 a
 specified
 or
 
predictable
 duration.
 These
 firms
 are
 in
 quadrant
 2.
 To
 obtain
 the
 benefits
 associated
 with
 
revenue
 management,
 industries
 should
 attempt
 to
 move
 to

 quadrant
 2
 by
 implementing
 the
 
appropriate
 strategic
 levers.
 Most
 hospitality
 firms
 find
 that
 the
 more
 their
 firm
 operates
 in
 
quadrant
 2,
 the
 higher
 their
 revenue
 per
 available
 time-­‐based

 unit.
 
Not
 all
 firms
 within
 quadrant
 2
 industries
 practice
 revenue
 management
 or
 practice
 revenue
 
management
 well.
 For
 example,
 a
 luxury
 hotel
 that
 is
 not
 implementing
 strict
 length-­‐of-­‐stay
 

controls
 across
 its
 limited
 set
 of
 prices
 effectively
 operates
 in
 quadrant
 3
 due
 to
 the
 type
 of
 
guests
 to
 whom
 it
 caters.
 
2
 
© 2015 eCornell. All rights reserved. All other copyrights, trademarks, trade names, and logos are the sole property of their respective owners.
 

 



  SHA541:
 Price
 and
 Inventory
 Controls
 
School
 of
 Hotel
 Administration,
 Cornell
 University
 
Assume
 you
 want
 to
 move
 your
 firm
 to
 quadrant
 2;
 what
 are
 some

 of
 the
 things
 you
 should
 
consider?
 If
 you
 have
 one
 price,
 you
 can
 institute
 multiple
 prices.
 A
 variable-­‐price
 approach
 
moves
 the
 firm
 from
 quadrant
 3
 (with
 few
 prices)

 to
 quadrant
 4
 (with
 many
 prices).
 In
 quadrant
 
4,
 you
 have
 several
 prices
 but
 uncontrolled
 duration.
 To
 add
 duration
 controls,
 you
 may
 use
 
advance
 reservations
 to
 forecast
 demand,

 preferably
 by
 rate
 class
 and
 by
 length
 of
 stay.
 Now
 if
 
you
 are
 able
 to
 incorporate
 length-­‐of-­‐stay
 controls
 as
 well
 as
 multiple
 prices,
 the
 firm
 is
 better
 
positioned

 to
 move
 to
 quadrant
 2.
 

 

Transcript: Customer Segmentation and Demand Controls
Using
 customer
 segmentation
 and
 inventory
 controls
 to
 manage
 revenue
 is
 commonplace
 in
 
many
 industries.
 But
 this
 wasn’t
 always
 the

 case.
 The
 airline
 industry
 has
 a
 strong
 influence
 in
 
their
 use.
 Today
 you
 find
 a
 lot
 of
 volatility
 in
 airfares,
 but
 this
 is
 a
 relatively
 new
 phenomenon.
 

 
In
 the
 early
 years
 of
 air
 travel
 U.S.
 airlines
 were
 subjected
 to
 government
 regulations
 that
 
consistently
 kept
 fares
 high
 and
 made
 air
 travel
 a
 luxury
 item.
 But
 eventually

 the
 demand
 for
 
more
 affordable
 air
 travel
 led
 to
 the
 passing
 of
 the
 Airline
 Deregulation
 Act
 in
 1979.
 The
 result
 
of
 this
 act
 was
 complete
 elimination
 of
 fare

 restrictions,
 leaving
 the
 airline
 industry
 in
 a
 free
 
market.
 Almost
 immediately,
 a
 number
 of
 new
 airlines
 arose
 to
 compete
 with
 the
 existing
 
carriers
 and
 the
 number
 of
 passengers

 dramatically
 increased.
 A
 new
 way
 of
 pricing
 was
 
introduced
 as
 existing
 carriers
 (serving
 guests
 willing
 to
 pay
 higher
 prices)
 now
 also
 had
 to
 offer
 
lower
 prices
 to
 compete

 with
 new
 entrant
 airlines.
 

 
So
 how
 did
 they
 price?
 They
 began
 with
 segmenting
 customers.
 If
 we
 oversimplify
 we
 could
 
assume
 there
 are
 only
 two
 types
 of

 customers
 seeking
 to
 travel—business
 customers
 travelling
 
for
 work-­‐related
 issues
 and
 leisure
 travelers.
 The
 typical
 business
 traveler
 is
 willing
 to
 pay
 a
 
higher
 price
 in
 exchange
 for
 flexibility
 of

 being
 able
 to
 book
 a
 seat
 at
 the
 last
 minute
 (or
 cancel
 
his
 ticket
 if
 his
 plan
 changes)
 while
 the
 vacation
 traveler
 is
 willing
 to
 give
 up
 some
 flexibility

 for
 
the
 sake
 of
 a
 more
 inexpensive
 seat.
 The
 demand
 from
 the
 price-­‐sensitive
 customer
 tends
 to
 
come
 before
 the
 demand
 from
 business
 customer.
 But
 with
 multiple
 price
 points

 and
 demand
 
for
 more
 expensive
 seats
 arriving
 after
 price-­‐sensitive
 demand
 the
 airlines
 had
 to
 determine
 
how
 many
 seats
 they
 should
 sell
 to
 the
 early
 price-­‐sensitive
 customers
 and
 how

 many
 they
 
should
 protect
 for
 late,
 full-­‐fare
 customers.
 If
 too
 few
 seats
 are
 protected,
 the
 airline
 will
 lose
 
the
 full-­‐fare
 revenue.
 If
 too
 many
 are
 protected,
 flights
 will

 leave
 with
 empty
 seats.
 

 
Littlewood
 (working
 for
 British
 Airways)
 proposed
 a
 way
 to
 make
 this
 determination.
 He
 
proposed
 that
 discount-­‐fare
 bookings
 should
 be
 accepted
 as
 long

 as
 their
 value
 exceeds
 that
 of
 
anticipated
 full-­‐fare
 bookings,
 assuming
 that
 customers
 can
 be
 segmented
 according
 to
 when
 
they
 purchase
 their
 tickets.
 This
 simple,
 inventory
 control
 system
 was

 the
 beginning
 of
 what
 
eventually
 lead
 to
 revenue
 management.
 
3
 
© 2015 eCornell. All rights reserved. All other copyrights, trademarks, trade names, and logos are the sole property of their respective owners.
 


 



  SHA541:
 Price
 and
 Inventory
 Controls
 
School
 of
 Hotel

 Administration,
 Cornell
 University
 

 
Using
 Littlewood’s
 approach
 we
 can
 designate
 two
 fare
 classes
 as
 having
 fares
 of
 R2
 and
 R1,
 
where
 R2
 is
 greater
 than
 R1.
 The

 demand
 for
 class
 R1—the
 lower
 fare—comes
 before
 demand
 
for
 class
 R2.
 The
 question
 now
 is
 how
 much
 demand
 for
 class
 R1
 should
 be
 accepted
 so
 that
 the
 
optimal

 mix
 of
 passengers
 is
 achieved
 and
 the
 highest
 revenue
 is
 obtained?
 Littlewood
 
suggested
 closing
 down
 class
 R1
 when
 the
 certain
 revenue
 from
 selling
 another
 low
 fare
 seat
 is
 

less
 than
 the
 expected
 revenue
 of
 selling
 that
 same
 seat
 at
 the
 higher
 fare.
 In
 other
 words,
 as
 
long
 as
 the
 probability
 of
 selling
 all
 remaining
 seats
 at
 the

 higher
 price
 is
 greater
 than
 the
 ratio
 
of
 the
 lower
 price
 over
 the
 higher
 price,
 we
 are
 better
 off
 not
 selling
 at
 the
 low
 price
 and
 
keeping
 it

 for
 the
 high
 price.
 This
 is
 our
 Target
 Probability.
 

 
Let’s
 look
 at
 an
 example.
 Grand
 Sky
 Airlines
 sells
 tickets
 on
 one
 of
 its
 85-­‐passenger
 planes
 for
 

€150
 (the
 discounted
 fare)
 and
 €250
 (the
 full-­‐fare).
 In
 general,
 their
 customers
 are
 aware
 of
 the
 
pricing
 and
 those
 seeking
 discounts
 tend
 to
 book
 early.
 Sean,
 one
 of
 the

 managers
 at
 Grand
 
Sky,
 knows
 that
 he
 can
 fill
 his
 entire
 plane
 at
 €50
 per
 seat
 if
 he
 so
 desires,
 but
 at
 some
 point
 it
 is
 
best
 to

 stop
 selling
 discounted
 seats
 and
 reserve
 some
 inventory
 for
 later
 arriving
 higher
 
yielding
 (€250)
 passengers.
 How
 does
 Sean
 calculate
 this
 target
 or
 the
 point
 at
 which
 to
 stop
 

selling
 €150
 seats
 and
 reserve
 the
 remaining
 seats
 for
 the
 €250
 customers?
 

 
Using
 Littlewood’s
 rule
 (R1
 divided
 by
 R2)
 we
 can
 calculate
 Sean’s
 target
 probability.
 In
 this

 case
 
it
 is
 .6
 or
 60%.
 As
 long
 as
 the
 probability
 of
 selling
 all
 remaining
 seats
 (“n”
 seats)
 at
 €250
 is
 
equal
 to
 or
 greater
 than
 60%
 then

 Grand
 Sky
 is
 better
 off
 selling
 seats
 at
 €250.
 
Now
 we
 need
 to
 calculate
 the
 probability
 of
 selling
 “n”
 or
 more
 seats.
 We
 use
 historical
 data
 to
 
help

 calculate
 the
 probability
 of
 future
 events.
 The
 graph
 shows
 the
 number
 of
 €250
 seats
 
Grand
 Sky
 Airlines
 sold
 each
 day
 for
 the
 last
 100
 days.
 

4
 

© 2015 eCornell. All rights reserved. All other copyrights, trademarks, trade names, and logos are the sole property of their respective owners.
 


 



  SHA541:
 Price
 and
 Inventory
 Controls
 
School
 of
 Hotel
 Administration,
 Cornell
 University
 


 
For
 example,
 24
 €250
 seats
 were

 sold
 on
 one
 of
 the
 days
 and
 33
 €250
 seats
 were
 sold
 on
 12
 of
 
the
 days.
 
Now
 we
 can
 calculate
 the
 probability
 of
 selling
 at
 least
 a

 certain
 number
 of
 seats
 at
 €250
 and
 
compare
 that
 number
 to
 our
 target
 of
 60%.
 
To
 calculate
 this
 probability,
 divide
 the
 number
 of
 days
 we
 sold
 “n”
 or

 more
 seats
 by
 the
 total
 
observations.
 We
 could
 start
 the
 calculations
 at
 any
 point
 (selling
 24
 or
 more
 seats,
 selling
 25
 or
 
more
 seats,
 etc.).
 But
 we
 can

 use
 our
 graph
 to
 select
 a
 reasonable
 starting
 point.
 

 
On
 the
 graph
 we
 see
 that
 the
 mid-­‐point
 is
 around
 34
 seats.
 This
 will
 make
 a
 good
 starting

 point
 
for
 our
 calculations.
 It
 may
 be
 easier
 to
 calculate
 these
 probabilities
 if
 we
 look
 at
 the
 data
 in
 a
 
table
 format.
 This
 table
 displays
 the
 same
 data

 that
 we
 just
 saw
 in
 the
 form
 of
 a
 graph.
 We
 
want
 to
 calculate
 the
 probability
 that
 there
 will
 be
 future
 demand
 for
 34
 or
 more
 seats.
 Start
 by

 
finding
 the
 number
 of
 days
 34
 or
 more
 seats
 were
 sold
 in
 
the
 past.
 To
 do
 this,
 add
 the
 frequencies
 when
 demand
 was
 34
 or
 more
 seats.
 We

 add
 the
 
frequency
 of
 demand
 at
 34,
 35,
 etc.
 up
 to
 41
 together
 to
 arrive
 at
 56
 days
 when
 demand
 was
 34
 
or
 more
 seats.
 Now
 divide
 56

 by
 the
 total
 observations
 (100).
 This
 gives
 us
 the
 probability
 that
 
demand
 will
 be
 greater
 or
 equal
 to
 34
 seats
 at
 €250
 as
 .56
 or
 56%.
 

 

If
 we
 do
 the
 same
 calculation
 for
 the
 sale
 of
 33
 or
 more
 seats
 we
 arrive
 at
 a
 probability
 of
 68%.
 
Now
 we
 can
 compare
 these
 probabilities
 to
 our

 target
 probability.
 Remember,
 as
 long
 as
 the
 
probability
 of
 selling
 all
 remaining
 seats
 at
 €250
 is
 ≥
 60%
 then
 Grand
 Sky
 is
 better
 off
 selling
 
seats
 at
 €250

 rather
 than
 €150.
 The
 probability
 of
 selling
 the
 33rd
 seat
 at
 €250
 is
 68%
 thus
 
greater
 than
 60%
 and
 the
 probability
 of
 selling
 the
 34th
 seat
 at
 €250
 is

 56%,
 less
 than
 60%.
 
5
 
© 2015 eCornell. All rights reserved. All other copyrights, trademarks, trade names, and logos are the sole property of their respective owners.
 


 



  SHA541:
 Price
 and
 Inventory
 Controls
 
School
 of
 Hotel
 Administration,
 Cornell
 University
 

 

We
 can
 also
 look
 at
 this
 from
 a
 monetary
 viewpoint.
 The
 probability
 of
 selling
 34
 or
 more
 seats
 
at
 €250
 is
 56%.
 To
 find
 the
 expected
 revenue
 of
 the

 last
 seat
 we
 sell
 multiple
 .56
 by
 €250
 which
 
equals
 €140.
 Given
 the
 expected
 revenue
 of
 the
 34th
 seat
 is
 €140,
 less
 than
 the
 €150
 we
 obtain
 
for

 certain
 if
 sold
 as
 a
 discounted
 seat,
 34
 seats
 is
 not
 our
 threshold.
 

 
Let’s
 look
 at
 selling
 33
 or
 more
 seats.
 This
 probability
 is
 68%,
 giving
 us

 an
 expected
 revenue
 
from
 selling
 the
 33rd
 seat
 at
 €250
 of
 €170.
 We
 can
 go
 back
 to
 our
 original
 question:
 What
 is
 the
 
point
 at
 which
 to
 stop

 selling
 €150
 seats
 and
 reserve
 the
 remaining
 seats
 for
 the
 €250
 
customers?
 Assume
 that
 on
 our
 85
 seat
 plane
 the
 85th
 seat
 is
 sold
 first
 and
 the
 1st
 seat

 is
 sold
 
last.
 Thus
 the
 airline
 is
 better
 off
 selling
 up
 to
 52
 seats
 (85
 total
 minus
 33)
 at
 €150
 and
 reserving
 
the
 remaining
 33
 seats
 for
 the

 €250
 paying
 customers.
 In
 essence
 we
 are
 calculating
 the
 
expected
 marginal
 revenue
 of
 keeping
 a
 seat
 (or
 room)
 for
 later
 arriving
 higher
 yielding
 guests.
 
We
 should
 continue
 to

 sell
 at
 lower
 discounted
 rates
 as
 long
 as
 these
 rates
 exceed
 the
 expected
 
marginal
 revenue
 of
 selling
 at
 higher
 rates.
 

 
Littlewood,
 K.
 (1972).
 Forecasting
 and
 control

 of
 passenger
 bookings.
 Proceedings
 from
 the
 
Twelfth
 Annual
 AGIFORS
 Symposium,
 Nathanya,
 Israel.
 

 

Transcript: Class Protection
We’re
 going
 to
 continue
 our
 discussion
 on
 using
 Littlewood’s
 rule.
 Now
 our

 focus
 is
 going
 to
 
change
 from
 controlling
 rates
 to
 actually
 controlling
 segments.
 We’ll
 have
 a
 quick
 recap
 of
 
Littlewood’s
 rule
 and
 then
 we
 will
 move
 to
 how
 we

 use
 that
 technique
 to
 control
 segments.
 
Remember,
 Littlewood’s
 rule
 is
 about
 allocating
 inventory
 to
 certain
 price
 classes.
 Now
 we’re
 
going
 to
 think
 about
 allocating
 inventory
 to
 certain
 types

 of
 business,
 whether
 that’s
 a
 transient
 
late-­‐arriving
 customer
 or
 a
 group
 traveler
 who's
 making
 that
 request
 one
 or
 two
 years
 in
 
advance
 of
 check-­‐in.
 
As
 a
 quick

 sort
 of
 review,
 suppose
 we
 have
 two
 prices,
 €200
 and
 €250.
 And
 just
 for
 argument's
 
sake
 let’s
 say
 today
 is
 Wednesday
 the
 20th
 and
 we’re
 looking
 at
 controlling
 inventory

 for
 next
 
Wednesday.
 
As
 of
 today
 we
 have
 15
 rooms
 available
 for
 next
 Wednesday.
 The
 decisions
 we
 need
 to
 make
 
today
 are
 about
 those
 15
 rooms:
 Should

 we
 continue
 to
 sell
 some
 of
 those
 at
 €200
 or
 should
 
we
 keep
 them
 all
 for
 €250-­‐paying
 customers?
 Euro
 paying
 customers.
 Right,
 so
 what
 stage
 is
 a
 
function,

 of
 how
 many
 rooms
 we
 have
 left
 as
 well
 as
 days
 before
 arrival.
 When
 do
 we
 want
 to
 
stop
 selling
 at
 200?
 
6
 
© 2015 eCornell. All rights reserved. All other copyrights, trademarks, trade names, and logos are the sole property of their respective owners.
 

 



  SHA541:
 Price
 and
 Inventory
 Controls
 
School
 of
 Hotel
 Administration,
 Cornell
 University
 

 
We’ve
 collected
 some
 data
 to
 help
 us
 assess
 those
 potential
 outcomes.

 Basically,
 this
 data
 
would
 be
 the
 number
 of
 requests
 for
 €250-­‐paying
 customers
 in
 this
 last
 week
 prior
 to
 arrival.
 
We’re
 focused
 on
 demand
 for
 the
 higher-­‐yielding
 class
 versus

 demand
 for
 the
 lower-­‐yielding
 
class.
 
Let’s
 assume
 we’ve
 collected
 data
 for
 over
 say
 the
 last
 100
 Wednesdays
 and
 during
 those
 100
 
Wednesdays,
 in
 that
 last
 week
 before

 arrival,
 the
 average
 demand
 is
 15.
 That
 demand
 has
 a
 
standard
 deviation
 of
 5
 to
 represent
 its
 uncertainty.
 Remembering
 back
 to
 Littlewood’s
 rule,
 we
 
want
 to
 keep
 selling

 at
 €200
 as
 long
 as
 that
 200
 exceeds
 the
 potential
 revenue
 from
 selling
 at
 
€250.
 And
 the
 potential
 revenue
 from
 selling
 at
 €250
 is
 the
 probability
 that
 we
 would

 sell
 all
 
those
 remaining
 rooms
 at
 250
 times
 250.
 
So
 given
 that
 demand
 has
 a
 mean
 of
 15
 and
 a
 standard
 deviation
 of
 5,
 let’s
 assume
 some
 

distributional
 form
 for
 that
 demand.
 For
 ease,
 let’s
 assume
 that
 it
 follows
 a
 normal
 
distribution,
 so
 a
 nice
 sort
 of
 symmetric-­‐about-­‐the-­‐mean,
 sort
 of
 bell-­‐shaped
 distribution.
 
We
 can
 use

 some
 built-­‐in
 functionality
 in
 Excel
 to
 help
 us
 estimate
 how
 many
 rooms
 to
 keep
 for
 
the
 €250-­‐paying
 customers.
 
Excel
 always
 calculates
 probabilities
 from
 the
 left
 hand
 side.
 Basically

 the
 probability
 that
 
demand
 is
 less
 than
 or
 equal
 to
 some
 critical
 level,
 we
 want
 probability
 the
 demand
 is
 greater
 
than
 or
 equal
 to
 our
 critical
 level
 being

 €200
 over
 €250.
 

7
 
© 2015 eCornell. All rights reserved. All other copyrights, trademarks, trade names, and logos are the sole property of their respective owners.
 


 



  SHA541:
 Price
 and
 Inventory
 Controls
 
School
 of
 Hotel
 Administration,
 Cornell
 University
 

 
Excel
 has
 a
 function
 called
 NormInv
 and
 what
 NormInv
 does,
 or
 Norm
 Inverse
 for
 the
 full
 
version
 of
 that
 formula-­‐-­‐we
 provide
 a
 probability
 and
 some
 description
 of
 that

 demand,
 in
 our
 
case
 the
 mean
 of
 15
 and
 the
 standard
 deviation
 of
 5,
 and
 it
 tells
 us
 the
 number
 that
 
corresponds
 to
 that
 probability.
 
So
 in

 Excel
 we
 would
 simply
 use
 Norm
 Inverse
 of
 1
 minus
 200
 over
 250,
 15,
 and
 5,
 and
 that
 
would
 return
 to
 us
 10.8.
 That
 basically
 means
 that
 the
 probability

 of
 us
 selling
 10.8
 or
 more
 
rooms
 is
 200
 over
 250.
 So
 if
 we
 kept
 exactly
 10.8
 rooms
 for
 the
 €250-­‐paying
 customers,
 we
 
would
 be
 indifferent
 between
 that

 10.8th
 room
 as
 a
 €250
 room
 versus
 it
 as
 a
 €200
 room.
 

8
 
© 2015 eCornell. All rights reserved. All other copyrights, trademarks, trade names, and logos are the sole property of their respective owners.
 


 



  SHA541:
 Price
 and
 Inventory
 Controls
 

School
 of
 Hotel
 Administration,
 Cornell
 University
 


 
Given
 we
 can’t
 sell
 partial
 rooms,
 and
 then
 we’re
 going
 to
 keep
 10
 rooms.
 So
 basically
 the
 
probability
 of

 selling
 10
 rooms
 is
 a
 little
 more
 than
 200
 over
 250,
 but
 keep
 in
 mind
 that
 if
 we
 
were
 to
 keep
 11,
 the
 probability
 would
 be
 less
 than
 200

 over
 250.
 So
 our
 logic
 here
 is
 to
 keep
 
10
 rooms
 and
 allow
 us
 to
 keep
 selling
 up
 to
 5
 more
 rooms
 at
 €200.
 
Now
 that
 we
 can

 have
 a
 solid
 idea
 of
 how
 we
 might
 use
 Littlewood’s
 rule
 to
 calculate
 how
 
many
 rooms
 to
 keep,
 we
 can
 extend
 that
 now
 to
 segments.
 Keep
 in
 mind
 that

 group
 requests
 
typically
 are
 made
 one,
 two,
 even
 three
 years
 prior
 to
 check-­‐in.
 These
 are
 large
 conferences
 
looking
 for
 large
 blocks
 of
 rooms,
 typically
 at
 very
 big
 discounts.

 
And
 so
 one
 of
 the
 questions
 that
 you
 have
 to
 face
 is
 what
 part
 of
 my
 hotel
 or
 what
 segment
 of
 
my
 rooms
 do
 I
 want
 to
 keep

 for
 these
 low-­‐yielding,
 early-­‐arriving
 customers.
 Obviously,
 they’re
 
very
 valuable
 customers,
 but
 you
 don’t
 want
 to
 sell
 all
 your
 rooms
 to
 these
 customers
 because
 
you
 have
 later-­‐arriving,
 higher-­‐yielding
 customers.

 
Right,
 so
 we
 could
 use
 the
 same
 Littlewood
 logic
 to
 look
 at
 this.
 I'm
 going
 to
 sell
 X
 rooms
 to
 
groups,
 given
 the
 probability
 of
 selling
 capacity
 minus

 X
 to
 higher-­‐yielding
 people
 as
 the
 same
 
rate
 as
 that
 group
 class.
 
Obviously,
 we’d
 like
 to
 keep
 all
 our
 rooms
 for
 these
 people
 if
 we
 could
 stock
 out.

 We
 estimate
 
that
 probability
 of
 stock
 out
 using
 our
 Norm
 Inverse
 function,
 given
 the
 ADR
 for
 the
 transients
 
9
 
© 2015 eCornell. All rights reserved. All other copyrights, trademarks, trade names, and logos are the sole property of their respective owners.
 


 

  SHA541:
 Price
 and
 Inventory
 Controls
 
School
 of
 Hotel
 Administration,
 Cornell
 University
 
versus
 the
 ADR
 for
 the
 corporate
 and
 government
 versus
 the
 ADR
 for
 the
 group.
 This
 way
 we’re

 
calculating
 those
 allocations
 across
 those
 segments,
 and
 in
 essence
 determining
 what
 our
 mix
 is
 
for
 our
 property
 

 

Transcript: Ideal Car Rental—Types of Cars
Peter
 Carter,
 at
 Ideal
 Car,
 has

 100
 days
 of
 data
 showing
 daily
 rentals.
 We
 can
 use
 this
 
information
 to
 help
 Peter
 determine
 how
 many
 cars
 he
 should
 stock,
 striking
 a
 reasonable
 
balance
 between
 utilization

 rates
 and
 the
 possibility
 of
 running
 out
 of
 cars
 with
 the
 subsequent
 
loss
 of
 revenue.
 

 
The
 chart
 shows
 the
 monthly
 revenue
 and
 costs
 for
 the
 three

 types
 of
 cars
 in
 Ideal’s
 fleet.
 


 
The
 first
 step
 in
 solving
 our
 problem
 is
 to
 find
 how
 many
 times
 a
 car
 must
 rent
 to
 cover
 its

 fixed
 
costs.
 We’ll
 demonstrate
 with
 the
 economy
 class
 car.
 The
 economy
 cars
 have
 monthly
 fixed
 
costs
 of
 €336
 (€256
 in
 lease
 plus
 €80
 in
 insurance).
 Given
 that
 each

 economy
 car
 nets
 €24
 per
 
rental
 (€26
 rental
 rate
 minus
 €2
 in
 variable
 cleaning
 costs)
 that
 means
 a
 car
 needs
 to
 rent
 at
 
least
 14
 times
 per
 month

 to
 cover
 its
 fixed
 costs
 (i.e.
 needs
 to
 rent
 14
 times
 to
 break
 even)
 as
 
€336
 divided
 by
 €24
 equals
 14.
 We’ll
 assume
 that
 each
 month
 has
 30
 days.

 That
 means
 on
 any
 
given
 day
 for
 a
 car
 to
 be
 profitable
 it
 needs
 to
 have
 a
 probability
 of
 renting
 of
 14/30
 or
 46%.
 

 
Now
 instead

 of
 30
 days,
 let’s
 look
 at
 100
 days
 of
 data
 for
 economy
 cars.
 The
 chart
 shows
 the
 
frequency
 of
 the
 number
 of
 cars
 rented
 during
 the
 last
 100
 days.

 On
 2
 of
 the
 100
 days
 only
 10
 
economy
 cars
 were
 rented.
 There
 is
 also
 two
 days
 when
 11
 cars
 were
 rented.
 On
 7
 days
 12
 cars
 
were

 rented
 and
 so
 on.
 If
 Ideal
 had
 stocked
 10
 cars
 then
 they
 would
 have
 rented
 all
 10
 cars
 on
 
10
 
© 2015 eCornell. All rights reserved. All other copyrights, trademarks, trade names, and logos are the sole property of their respective owners.
 


 

  SHA541:
 Price
 and
 Inventory
 Controls
 
School
 of
 Hotel
 Administration,
 Cornell
 University
 
all
 100
 days
 (because
 demand
 is
 never
 less
 than
 10).
 Each
 of
 these
 10
 cars
 is
 very

 profitable.
 If
 
they
 stocked
 11
 cars
 then
 the
 11th
 car
 would
 have
 rented
 on
 all
 days
 except
 the
 two
 days
 
where
 demand
 was
 only
 10.
 The
 probability
 of

 demand
 for
 the
 11th
 car
 is
 98/100
 or
 98%
 


 

 
Remember,
 for
 a
 car
 to
 be
 profitable
 it
 needs
 to
 have
 a
 probability
 of
 renting

 of
 ≥
 46%.
 After
 
calculating
 all
 the
 probabilities
 we
 see
 that
 19th
 car
 rents
 enough
 to
 cover
 fixed
 costs
 and
 
generates
 a
 little
 profit.
 Whereas
 if
 we
 stocked

 20
 cars
 the
 20th
 car
 would
 not
 rent
 often
 
enough
 to
 cover
 its
 fixed
 costs.
 In
 the
 100-­‐day
 period
 we
 rent
 20
 or
 more
 cars
 only
 43
 times,
 

thus
 the
 probability
 of
 renting
 the
 20th
 car
 is
 43%,
 less
 than
 the
 46%
 we
 need.
 

 
Another
 way
 to
 look
 at
 this
 is
 by
 the
 number
 of

 times
 the
 car
 rents.
 Remember,
 in
 any
 given
 
month
 a
 car
 must
 rent
 at
 least
 14
 times
 to
 generate
 enough
 contribution
 to
 cover
 fixed
 costs.
 
Because
 we
 are

 now
 considering
 a
 little
 more
 than
 3
 months
 worth
 of
 data
 a
 car
 must
 rent
 
100/30
 X
 14
 or
 46
 times
 to
 be
 profitable—more
 than
 the
 20th
 car
 but

 less
 the
 19th
 car.
 
11
 
© 2015 eCornell. All rights reserved. All other copyrights, trademarks, trade names, and logos are the sole property of their respective owners.
 


 



  SHA541:
 Price
 and
 Inventory
 Controls
 
School
 of
 Hotel
 Administration,
 Cornell
 University
 

 

 

Transcript: Ask The Expert: Upgrading/Upselling Opportunities
When
 are
 upgrades
 and
 upsells
 useful?
 

Upgrades
 are
 especially
 useful
 when
 there
 is
 a
 mismatch
 between
 supply
 and
 demand.
 There
 
are
 several
 reasons

 why
 capacity
 mismatches
 may
 occur
 in
 practice,
 including
 forecast
 errors
 
and
 strategic
 supply
 limits
 that
 aim
 to
 skim
 revenues
 from
 customers
 with
 high
 willingness
 to
 
pay.
 Upgrades
 become

 a
 key
 managerial
 lever
 in
 the
 case
 of
 travel
 and
 service
 industries
 in
 
general
 when
 capacity
 is
 relatively
 fixed
 and
 difficult
 to
 change
 in
 the
 short
 run
 as
 demand

 
fluctuates
 over
 time.
 
How
 are
 upgrades
 useful?
 

Upgrades
 help
 balance
 demand
 and
 supply
 by
 shifting
 excess
 capacity
 of
 high-­‐grade
 products
 to
 
low-­‐grade
 products
 with
 excess

 demand.
 Upgrading
 allows
 firms
 to
 get
 consumers
 to
 commit
 to
 
purchases
 at
 lower
 prices
 and
 then
 extract
 additional
 revenues
 with
 the
 upgrade/upsell.
 
What
 are
 some
 of
 the
 main

 concerns
 with
 upgrading?
 

In
 addition
 to
 potentially
 not
 having
 enough
 high-­‐valued
 inventories
 available,
 upgrading
 can
 
create
 strategic
 consumer
 issues
 especially
 for
 those
 receiving
 free
 upgrades.
 Consumers
 tend

 
to
 expect
 upgrades
 and
 may
 become
 dissatisfied
 if
 usual
 upgrades
 become
 unavailable.
 
What
 type
 of
 data
 do
 you
 need
 to
 determine
 if
 and
 when
 you
 should
 upgrade?
 

The
 key
 to
 proper
 management
 of
 upgrades
 is
 a
 solid
 understanding
 of
 total
 demand
 for
 
higher-­‐valued
 inventory
 and
 when
 this
 demand
 materializes.
 Essentially
 you
 must
 be
 able
 to

 
estimate
 the
 likelihood
 that
 you
 won't
 need
 that
 high-­‐valued
 room
 once
 you've
 upgraded
 it
 and
 
made
 it
 available
 to
 a
 lower-­‐valued
 customer.
 

 

Transcript: Simultaneous Decision Making
Up

 until
 this
 stage,
 we’ve
 been
 focusing
 on
 a
 single
 constraining
 resource.
 Right,
 how
 many
 
rooms
 should
 I
 allocate
 to
 which
 different
 prices,
 how
 should
 I
 manage
 the
 seats
 on

 my
 
particular
 flight?
 Going
 forward,
 going
 to
 add
 some
 complexity
 basically,
 so
 we’re
 going
 to
 focus
 
on
 not
 just
 one
 resource
 but
 multiple
 resources,
 so
 you
 can
 think

 of
 this
 as
 guests
 staying
 
multiple
 nights
 at
 your
 property
 or
 individuals
 flying
 with
 your
 airline
 but
 stopping
 at
 
interconnected
 cities
 and
 moving
 on
 to
 subsequent
 cities.
 Under

 this
 context
 of
 guests
 staying
 
12
 
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  SHA541:
 Price
 and
 Inventory
 Controls
 
School
 of
 Hotel
 Administration,
 Cornell
 University
 
more

 than
 one
 night
 or
 flyers
 having
 interconnecting
 traffic,
 it
 results
 in
 consumers
 purchasing
 
different
 products
 using
 the
 same
 resource.
 
So
 I
 might
 have
 a
 guest
 who
 checks
 in

 today
 for
 a
 one-­‐night
 stay.
 I
 might
 have
 another
 guest
 
who
 checks
 in
 today
 for
 a
 two-­‐night
 stay.
 Both
 of
 those
 guests
 are
 staying
 tonight,
 but
 they
 
each

 bought
 a
 different
 product.
 One
 bought
 a
 one-­‐night
 stay,
 one
 bought
 a
 two-­‐night
 stay,
 but
 
they’re
 both
 using
 rooms
 tonight.
 So
 when
 I
 decide
 how
 many
 rooms
 to
 allocate

 to
 each
 of
 
those
 two
 different
 product
 classes,
 I
 need
 to
 realize
 that
 they’re
 both
 using
 inventory
 tonight.
 


 
So
 going
 forward,
 we’re
 going
 to
 think

 about
 how
 to
 incorporate
 that
 complexity
 in
 my
 
allocation
 decisions.
 This
 might
 be
 clarified
 with
 a
 simple
 example.
 So
 let’s
 look
 at
 our
 property
 
for
 the
 upcoming
 week.

 We
 have
 a
 very
 simple
 structure
 here.
 We
 have
 two
 prices,
 150
 and
 
200
 Euros,
 and
 guests
 stay
 one
 or
 two
 nights.
 


 
13
 
© 2015 eCornell. All rights reserved. All other copyrights, trademarks, trade names, and logos are the sole property of their respective owners.

 


 



  SHA541:
 Price
 and
 Inventory
 Controls
 
School
 of
 Hotel
 Administration,
 Cornell
 University
 
In
 this
 particular
 example,
 we
 forecasted
 demand
 for
 the
 upcoming

 week,
 and
 it
 turns
 out
 that
 
only
 Wednesday
 is
 booming
 with
 us
 and
 on
 Wednesday
 we
 have
 demand
 in
 excess
 of
 capacity.
 
So
 managing
 inventory
 on
 Wednesday
 is

 relatively
 straightforward.
 We
 want
 to
 make
 sure
 we
 
accept
 requests
 that
 bring
 in
 as
 much
 revenue
 as
 possible
 and
 reject
 those
 requests
 that
 bring
 
in
 less
 revenue.
 So

 in
 this
 context
 we’d
 accept
 two-­‐night
 stays
 at
 200,
 we’d
 accept
 two-­‐night
 
stays
 at
 150,
 but
 we
 may
 reject
 some
 one-­‐night
 stays
 at
 150
 given
 their
 lower
 revenue.
 

 
Now
 we
 extend
 this
 example
 to
 not
 just
 Wednesday
 having
 demand
 in
 excess
 of
 capacity
 but
 
also
 Thursday.
 So
 now
 we
 have
 two
 constraining
 resources
 and

 while
 it
 seems
 still
 
straightforward,
 if
 we
 were
 to
 maximize
 revenue
 on
 Wednesday
 by
 accepting
 two-­‐night
 stays
 
and
 rejecting
 some
 one-­‐night
 stays,
 and
 then
 move
 on
 to
 Thursday

 and
 maximize
 revenue
 on
 
Thursday
 by
 accepting
 some
 two-­‐night
 stays
 and
 rejecting
 some
 one-­‐night
 stays,
 we
 quickly
 
realize
 that
 the
 decisions
 I
 made
 on
 Wednesday,
 i.e.
 the
 two-­‐night

 stays
 I
 accepted
 on
 
Wednesday,
 well,
 those
 people
 are
 now
 staying
 on
 my
 property
 on
 Thursday,
 and
 those
 

14
 
© 2015 eCornell. All rights reserved. All other copyrights, trademarks, trade names, and logos are the sole property of their respective owners.
 


 

  SHA541:
 Price
 and
 Inventory
 Controls
 
School
 of
 Hotel
 Administration,
 Cornell
 University
 
decisions
 I
 made
 on
 Wednesday
 impact
 the
 decisions
 I
 can
 make
 on
 Thursday.
 
 

 
So
 I
 can’t
 just
 make
 my
 Wednesday
 decisions
 first
 and
 then
 my
 Thursday
 decisions,
 I
 really
 need
 
to
 make
 my
 Wednesday
 and
 Thursday
 decision
 simultaneously
 and
 not

 just
 Wednesday
 and
 
Thursday,
 but
 because
 the
 guests
 who
 stayed
 two
 nights
 on
 Tuesday
 are
 going
 to
 be
 on
 my
 
property
 on
 Wednesday
 and
 impact
 my
 Wednesday
 decisions

 and
 then
 impact
 my
 Thursday
 
decisions,
 I
 really
 need
 to
 make
 my
 decisions
 for
 that
 whole
 week
 simultaneously
 versus
 one
 at
 
a
 time.
 This
 moves
 us
 to
 this

 framework
 of
 simultaneous
 decision-­‐making.
 


 
One
 of
 the
 common
 aspects
 of
 this
 simultaneous
 decision-­‐making
 framework
 is
 that
 most
 of
 
these
 settings
 have
 some
 sort
 of
 limited

 resource.
 This
 limited
 resource
 might
 be,
 as
 in
 our
 
earlier
 example,
 how
 many
 rooms
 we
 have
 available
 on
 Wednesday
 and
 Thursday
 or
 it
 might
 
15
 
© 2015 eCornell. All rights reserved. All other copyrights, trademarks, trade names, and logos are the sole property of their respective owners.
 

 



  SHA541:
 Price
 and
 Inventory
 Controls
 
School
 of
 Hotel
 Administration,
 Cornell
 University
 
be
 how
 much
 cash
 you
 have
 on
 hand
 to
 purchase
 items

 or
 it
 might
 be
 how
 many
 items
 you
 
have
 in
 stock
 which
 you
 can
 use
 to
 manufacture
 goods
 and
 sell
 to
 consumers.
 The
 thing
 that’s
 
common
 across
 this

 framework
 is
 this
 constrained
 or
 limited
 resource.
 

 
Our
 goal
 is
 to
 mathematically
 model
 these
 and
 as
 a
 function
 of
 that
 we
 need
 to
 be
 able
 to
 

evaluate
 performance.
 And
 the
 easiest
 way
 to
 evaluate
 performance
 is
 to
 have
 some
 sort
 of
 
single
 unifying
 objective.
 So
 from
 our
 context
 we’re
 going
 to
 maximize
 revenue
 or
 maximize

 
profit,
 but
 in
 other
 contexts
 you
 might
 want
 to
 minimize
 cost,
 right?
 We
 have
 to
 be
 able
 to
 map
 
this
 performance
 metric,
 revenue,
 to
 our
 decisions,
 how
 many

 rooms
 to
 accept
 across
 each
 of
 
the
 rate
 classes
 and
 lengths
 of
 stays.
 


 

 
In
 addition
 to
 having
 both
 this
 sort
 of
 unifying
 objective,

 which
 is
 a
 function
 of
 these
 decision
 
variables,
 we’re
 also
 going
 to
 have
 these
 constraints,
 right?
 I
 only
 have
 100
 rooms
 available
 on
 
Wednesday
 and
 100
 rooms
 available

 on
 Thursday.
 We’re
 going
 to
 add
 some
 other
 sort
 of
 
logical
 constraints;
 those
 logical
 constraints
 are
 things
 like,
 I
 can’t
 accept
 negative
 reservations,
 
right?
 So
 that’s
 pretty
 easy

 for
 you
 to
 think
 logically,
 but
 again
 we’re
 going
 to
 do
 this
 
computationally
 so
 we
 have
 to
 define
 those
 things
 as
 well.
 

 

Transcript: Optimization at Snap Électrique
Excel
 Solver

 is
 a
 tool
 that
 we
 can
 use
 in
 our
 simultaneous
 decision
 making
 process.
 To
 use
 
Solver,
 we
 must
 build
 a
 model
 that
 specifies:
 
•

The
 decisions
 we

 need
 to
 make;
 we
 refer
 to
 these
 as
 decision
 variables
 
 
16
 

© 2015 eCornell. All rights reserved. All other copyrights, trademarks, trade names, and logos are the sole property of their respective owners.
 


 



  SHA541:
 Price
 and
 Inventory
 Controls
 
School

 of
 Hotel
 Administration,
 Cornell
 University
 
•
•

The
 measure
 to
 optimize,
 called
 the
 objective—for
 example,
 maximize
 profit
 or
 
minimize
 costs
 
 
Limitations
 on
 how
 we
 make

 decisions,
 called
 constraints—for
 example,
 limited
 
resources
 

Solver
 will
 find
 values
 for
 the
 decision
 variables
 that
 satisfy
 the
 constraints
 while
 optimizing
 
(maximizing
 or
 minimizing)
 the
 objective.
 We

 will
 use
 Snap
 Électrique
 to
 help
 describe
 how
 to
 
use
 Solver.
 
We
 begin
 with
 the
 decision
 variables.
 They
 usually
 measure
 the
 amounts
 of
 resources
 to
 be
 
allocated

 to
 some
 purpose,
 or
 the
 level
 of
 some
 activity,
 such
 as
 the
 number
 of
 products
 to
 be
 
manufactured.
 For
 Snap
 Électrique,
 we
 need
 to
 decide
 how
 many
 of
 each

 of
 the
 four
 products
 
to
 make.
 
Once
 we
 define
 the
 decision
 variables,
 the
 next
 step
 is
 to
 define
 the
 objective,
 which
 is
 
normally
 some
 function
 that
 depends

 on
 the
 decision
 variables.
 For
 Snap,
 the
 objective
 is
 to
 
maximize
 profit.
 


 
We
 know
 that
 each
 LCD
 touch
 screen
 yields
 a
 profit
 of
 €29,
 each

 integrated
 audio
 system
 €32,
 
each
 voice
 and
 audio
 processor
 €72,
 and
 each
 custom
 kiosk
 €54.
 Then
 our
 objective
 function
 
might
 be:
 
(€29
 times
 the
 number
 of
 LCDs)

 +
 (€32
 times
 the
 number
 of
 integrated
 audio
 systems)
 +
 (€72
 
times
 the
 number
 of
 voice
 and
 audio
 processors)
 +
 (€54
 times
 the
 number
 of
 custom
 kiosks).
 
We’d

 be
 finished
 at
 this
 point,
 if
 the
 model
 did
 not
 require
 any
 constraints.
 In
 most
 models
 
constraints
 play
 a
 key
 role
 in
 determining
 what
 values
 can
 be
 assumed
 by

 the
 decision
 variables
 
and
 what
 sort
 of
 objective
 value
 can
 be
 attained.
 It
 is
 the
 constraints
 that
 require
 us
 to
 use
 
optimization
 models
 like
 Solver.
 
17
 

© 2015 eCornell. All rights reserved. All other copyrights, trademarks, trade names, and logos are the sole property of their respective owners.
 


 



  SHA541:
 Price
 and
 Inventory
 Controls
 
School
 of
 Hotel
 Administration,
 Cornell
 University
 
Constraints
 reflect
 real-­‐world
 limits
 on
 production
 capacity,
 market
 demand,

 available
 funds,
 
and
 so
 on.
 To
 define
 a
 constraint,
 you
 first
 compute
 a
 value
 based
 on
 the
 decision
 variables.
 
Then
 you
 place
 a
 limit
 (≤,
 =,
 or
 ≥)

 on
 this
 computed
 value.
 
Many
 constraints
 are
 determined
 by
 the
 physical
 nature
 of
 the
 problem.
 For
 example,
 if
 our
 
decision
 variables
 measure
 the
 number
 of
 products
 of
 different

 types
 that
 we
 plan
 to
 
manufacture,
 producing
 a
 negative
 number
 of
 products
 would
 make
 no
 sense.
 This
 type
 of
 non-­‐
negativity
 constraint
 is
 very
 common.
 
Often
 we
 have

 constraints
 that
 require
 decision
 variables
 to
 assume
 only
 integer
 (whole
 
number)
 values
 at
 the
 solution.
 Integer
 constraints
 normally
 can
 be
 applied
 only
 to
 decision
 
variables,
 not
 to
 the

 quantities
 calculated
 from
 them.
 
For
 Snap,
 we
 cannot
 allocate
 more
 resources
 to
 production
 than
 we
 have
 in
 inventory.
 Also
 we
 
cannot
 produce
 negative
 or
 partial
 products.
 
Now

 let’s
 look
 at
 the
 model
 we
 created
 for
 Snap
 Électrique.
 
In
 the
 worksheet,
 we
 have
 reserved
 cells
 B4
 though
 E4
 to
 represent
 our
 decision
 variables—the
 
optimal
 mix
 of

 products
 to
 produce.
 Solver
 will
 determine
 the
 optimal
 values
 for
 these
 cells.
 
The
 profits
 for
 each
 product
 (€29,
 €32,
 €72,
 and
 €54)
 are
 entered
 in
 cells
 B5,
 C5,
 D5,

 and
 E5.
 
This
 allows
 us
 to
 compute
 the
 objective
 in
 cell
 F5.
 Remember,
 our
 objective
 is
 the
 sum
 of
 the
 
number
 of
 products
 made
 times
 the
 profit
 margin.

 
In
 cells
 B8:E10,
 we've
 entered
 the
 amount
 of
 resources
 needed
 to
 produce
 each
 type
 of
 
product.
 With
 these
 values,
 we
 can
 enter
 a
 formula
 in
 cells
 F8
 to

 F11
 that
 computes
 the
 total
 
amount
 of
 resource
 used
 for
 any
 number
 of
 products
 produced.
 
Now
 open
 Solver.
 This
 may
 be
 under
 the
 Tools
 menu
 or
 the
 Data

 menu
 depending
 on
 what
 
version
 of
 Excel
 you
 are
 using.
 

18
 
© 2015 eCornell. All rights reserved. All other copyrights, trademarks, trade names, and logos are the sole property of their respective owners.
 


 



  SHA541:
 Price
 and
 Inventory
 Controls
 
School

 of
 Hotel
 Administration,
 Cornell
 University
 


 
We
 must
 let
 Solver
 know
 which
 cells
 on
 the
 worksheet
 represent
 the
 decision
 variables,
 
constraints,
 and
 objective
 function.
 
In

 the
 Set
 Objective
 box,
 type
 or
 click
 on
 cell
 F5,
 the
 objective
 function.
 
In
 the
 By
 Changing
 Variable
 Cells
 edit
 box,
 type
 B4:E4
 or
 select
 these
 cells
 with
 the

 mouse.
 
To
 add
 the
 constraints,
 click
 the
 Add
 button
 and
 select
 cells
 F8:F10
 in
 the
 Cell
 Reference
 edit
 
box
 (this
 will
 show
 the
 number
 of
 units
 or
 hours

 needed),
 and
 select
 cells
 G8:G10
 in
 the
 
Constraint
 edit
 box
 (the
 number
 of
 units
 or
 hours
 available).
 We
 can
 only
 use
 equal
 to
 or
 less
 
than
 the
 amount

 of
 units
 or
 hours
 we
 have
 in
 stock.
 The
 constraint
 is
 set
 to
 ≤.
 
Define
 the
 non-­‐negativity
 constraint
 on
 the
 decision
 variables.
 Depending
 on
 the
 version
 of
 
Excel,

 we
 do
 this
 by
 making
 sure
 the
 Make
 Unconstrained
 Variables
 Non-­‐Negative
 box
 is
 
checked
 or
 click
 Options
 then
 Assume
 Non-­‐Negative.
 
19
 
© 2015 eCornell. All rights reserved. All other copyrights, trademarks, trade names, and logos are the sole property of their respective owners.
 


 

  SHA541:
 Price
 and
 Inventory
 Controls
 
School
 of
 Hotel
 Administration,
 Cornell
 University
 
Also
 click
 on
 Assume
 Linear
 Model
 or
 use
 Simplex
 LP,
 depending
 on
 your
 version
 of

 Solver.
 
To
 find
 the
 optimal
 solution
 click
 Solve.
 When
 the
 next
 window
 appears
 click
 OK.
 
After
 a
 moment,
 the
 Solver
 returns
 the
 optimal
 solution
 in
 cells
 B4
 through

 E4
 and
 a
 new
 
window
 appears.
 Here
 are
 the
 results.
 


 
This
 shows
 that
 we
 should
 build
 zero
 LCD
 Touch
 Screens.
 

 

Transcript: Marginal Value of Last Room Sold

What
 happens
 when
 I
 accept
 a
 reservation?
 When
 I
 accept
 a
 reservation,
 assuming
 the
 guest
 
shows,
 I
 receive
 the
 revenue
 from
 that
 individual.
 I
 also
 decrease
 my
 capacity
 to

 sell
 to
 
subsequent
 consumers
 by
 that
 reservation.
 The
 act
 of
 accepting
 a
 reservation
 really
 decreases
 
the
 available
 capacity
 to
 your
 hotel.
 Thinking
 about
 this
 from
 a
 marginal
 value

 standpoint,
 I
 
don’t
 want
 to
 accept
 a
 reservation
 unless
 it's
 at
 least
 as
 high
 as
 the
 marginal
 value
 of
 that
 room.
 
Here
 we
 determine
 how
 many
 reservations
 to

 accept
 across
 our
 two
 rate
 classes
 of
 €350
 and
 
€250
 where
 guests
 can
 stay
 one,
 two,
 or
 three
 nights.
 

20
 
© 2015 eCornell. All rights reserved. All other copyrights, trademarks, trade names, and logos are the sole property of their respective owners.
 


 

  SHA541:
 Price
 and
 Inventory
 Controls
 
School
 of
 Hotel
 Administration,
 Cornell
 University
 


 
We
 decided
 which
 reservations
 to
 accept
 with
 the
 goal
 of
 maximizing
 revenue.

 In
 that
 context
 
we
 made
 almost
 €515,000
 (€514,850).
 Now
 let’s
 step
 back
 and
 say
 Well,
 what
 if
 I
 had
 one
 more
 
room
 on
 the
 14th?
 On
 the
 very

 first
 day,
 if
 I
 had
 179
 rooms,
 what
 if
 I
 had
 180
 rooms?
 We’ll
 just
 
simply
 change
 the
 rooms
 that
 we
 have
 available
 from
 179
 to
 180
 and
 rerun

 our
 optimization
 
mode.
 If
 we
 rerun
 our
 optimization
 model,
 it
 turns
 out
 that
 our
 revenue
 now
 is
 €515,000.
 
So
 by
 having
 one
 more
 room
 we
 can
 make
 €515,000

 versus
 earlier
 we
 were
 making
 €514,850.
 
So,
 in
 essence,
 that
 one
 incremental
 room
 generated
 €150
 incremental
 Euros.
 
Our
 goal
 now
 is
 to
 take
 that
 idea
 from
 179
 to

 180
 and
 sort
 of
 automate
 that.
 It
 turns
 out,
 given
 
we’re
 doing
 things
 computationally,
 that’s
 relatively
 easy.
 When
 our
 results
 come
 back,
 we
 
simply
 click
 on
 the
 sensitivity

 report
 on
 the
 right
 side,
 and
 by
 doing
 that
 we
 generate
 what
 is
 
referred
 to
 as
 the
 shadow
 prices.
 What
 we
 see
 here
 in
 the
 very
 first
 row
 of

 that
 shadow
 price
 
table
 is
 €150.
 So,
 corresponding
 to
 cell
 H4,
 was
 the
 rooms
 that
 were
 available
 on
 December
 
14th,
 we
 have
 a
 shadow
 price
 of
 €150,
 which

 before
 we
 calculated
 manually.
 

21
 
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  SHA541:
 Price
 and
 Inventory
 Controls
 
School
 of
 Hotel
 Administration,
 Cornell
 University
 

 
So
 if
 you
 think
 about
 things
 on
 the
 14th,
 if
 I
 had
 180
 rooms
 versus
 179
 rooms
 I
 would
 have
 
made
 €150
 more.
 If
 I
 had
 178

 rooms
 versus
 179
 rooms,
 I
 would
 lose
 €150.
 
If
 we
 go
 back
 and
 compare
 the
 solutions
 to
 having
 179
 versus
 180
 rooms,
 we
 see
 some
 very
 
interesting
 results.

 When
 we
 had
 179
 rooms
 available
 on
 the
 14th,
 we
 accepted
 44
 reservations
 
for
 three-­‐night
 stays
 at
 €250.
 When
 we
 had
 180
 rooms
 on
 the
 14th,
 we
 actually
 accepted

 45
 of
 
those
 three-­‐night-­‐stay
 €250
 requests.
 Because
 those
 are
 three-­‐night
 requests,
 those
 individuals
 
are
 now
 going
 to
 stay
 into
 the
 15th
 and
 into
 the
 16th.
 Because
 of
 that,

 if
 I
 accept
 that
 three-­‐
night
 stay
 on
 the
 14th,
 I
 have
 to
 accept
 less
 stays
 on
 subsequent
 days.
 It
 turns
 out
 on
 the
 15th
 I
 
accept
 one
 less

 €350
 one-­‐night
 stay.
 If
 you
 look
 at
 the
 16th,
 on
 the
 16th
 before
 I
 accepted
 one
 
three-­‐night
 stay
 at
 €250,
 now
 I
 accept
 no
 three-­‐night
 stays
 at
 €250.On
 the

 17th
 before
 I
 
accepted
 19
 two-­‐night
 stays
 at
 €250;
 now
 on
 the
 17th
 I’ve
 accepted
 20
 of
 those
 two-­‐night
 stays
 
at
 €250.
 

22
 
© 2015 eCornell. All rights reserved. All other copyrights, trademarks, trade names, and logos are the sole property of their respective owners.
 

 



  SHA541:
 Price
 and
 Inventory
 Controls
 
School
 of
 Hotel
 Administration,
 Cornell
 University
 


 
You
 see,
 the
 simple
 act
 of
 having
 one

 more
 room
 available
 on
 the
 14th
 has
 this
 massive
 chain
 
reaction
 on
 subsequent
 stay
 days.
 It’s
 this
 chain
 reaction
 that
 creates
 this
 odd
 marginal
 value.
 
We
 see,
 then,

 that
 we
 can
 generate
 those
 shadow
 prices
 for
 all
 subsequent
 days.
 It
 turns
 out
 
for
 the
 subsequent
 days
 the
 shadow
 prices
 are
 much
 more
 straightforward,
 either
 €350
 or
 

€250.
 
The
 next
 part
 is
 how
 we
 use
 these
 shadow
 prices.
 Just
 like
 having
 one
 more
 room
 on
 the
 14th
 
we
 generate
 €150.
 Having
 one
 less
 room
 would

 decrement
 us
 by
 €150.
 The
 same
 thing
 on
 the
 
15th-­‐If
 I
 had
 one
 more
 room
 I
 could
 increase
 my
 revenue
 by
 €350.
 If
 I
 had
 one
 less
 room
 I

 
would
 lose
 €350.
 
My
 focus
 is
 now
 is
 back
 to
 our
 marginal
 analysis,
 thinking
 about
 accepting
 our
 reservation.
 If
 I
 
accept
 a
 reservation
 for
 the
 14th
 that

 means
 instead
 of
 having
 179
 rooms
 I
 have
 178
 rooms.
 If
 I
 
only
 have
 178
 rooms,
 I’m
 going
 to
 lose
 €150.
 Logically,
 I
 would
 not
 accept
 any
 reservation
 

unless
 it
 brought
 in
 at
 least
 €150.
 
23
 
© 2015 eCornell. All rights reserved. All other copyrights, trademarks, trade names, and logos are the sole property of their respective owners.
 


 



  SHA541:
 Price
 and
 Inventory
 Controls
 
School
 of
 Hotel
 Administration,
 Cornell
 University

 
That’s
 fairly
 straightforward
 for
 us—it
 means
 we’re
 going
 to
 accept
 reservations
 at
 €250
 and
 
€350.
 If
 you
 look
 at
 the
 15th,
 now
 it
 says
 if
 we
 had
 one

 less
 room
 on
 the
 15th,
 our
 revenue
 
would
 go
 down
 by
 €350.
 That
 tells
 us
 is
 we’re
 going
 to
 close
 the
 15th
 to
 €250
 reservations,
 
specific
 to
 €250

 one-­‐night
 stays.
 The
 marginal
 value
 on
 the
 15th
 is
 €350,
 whereas
 a
 one-­‐night
 
request
 for
 a
 €250
 only
 brings
 in
 €250.
 
If
 we
 go
 back
 to
 the
 14th,

 if
 a
 guest
 was
 going
 to
 stay
 two
 nights
 on
 the
 14th,
 so
 he
 is
 going
 to
 
consume
 one
 room
 on
 the
 14th
 and
 one
 room
 on
 the
 15th,

 so
 logically
 he
 has
 to
 bring
 in
 
revenue
 in
 access
 of
 those
 two
 marginal
 values—that
 is,
 the
 €150
 plus
 the
 €350,
 which
 is
 a
 total
 
of
 €500.
 That

 means
 while
 everything
 is
 open
 on
 the
 14th
 and
 I
 have
 closed
 the
 €250
 one-­‐night
 
stays
 on
 the
 15th,
 I’m
 actually
 going
 to
 sell
 some
 multi-­‐night
 €250s
 on
 the

 14th,
 i.e.
 I
 would
 
allow
 reservations
 to
 be
 made
 to
 the
 €250
 rate
 for
 a
 two-­‐night
 stay
 on
 the
 14th
 because
 that
 
would
 bring
 in
 €500
 worth
 of

 revenue.
 Keep
 in
 mind
 the
 marginal
 value
 here
 is
 the
 €150
 plus
 
the
 €350
 for
 a
 total
 of
 €500.
 

 

Transcript: Using Rate And Availability Controls
In
 this
 lesson
 we
 examine

 rate
 and
 availability
 controls
 at
 the
 Hotel
 Ithaca.
 You
 will
 have
 an
 
opportunity
 to
 practice
 in
 the
 following
 lesson.
 We’ll
 use
 the
 Hotel
 Ithaca
 spreadsheet
 and
 
Solver
 to

 do
 allocations,
 generate
 shadow
 prices,
 and
 use
 the
 shadow
 prices
 to
 determine
 
availability.
 
The
 information
 on
 this
 tab
 is
 divided
 into
 five
 parts.
 
Part
 1
 stores
 the

 decision
 variables.
 
Part
 2
 stores
 the
 total
 number
 of
 rooms
 sold
 on
 each
 day.
 This
 includes
 both
 arrivals
 on
 that
 
stay
 date
 as
 well
 as
 stay-­‐overs—that
 is,
 guests

 who
 checked
 in
 yesterday
 or
 the
 day
 before
 and
 
stayed
 two
 or
 three
 nights.
 
Part
 3
 contains
 the
 rooms
 available—that
 is,
 hotel
 capacity
 minus
 any
 reservations
 (and
 stay-­‐

overs)
 already
 accepted
 for
 those
 dates.
 
Part
 4
 stores
 the
 total
 revenue
 for
 all
 rooms
 and
 days
 listed.
 
Part
 5
 displays
 the
 forecasted
 demand
 for
 the
 stay
 dates

 in
 question.
 
We
 have
 already
 built
 the
 model.
 Now
 we
 need
 to
 run
 Solver.
 

24
 
© 2015 eCornell. All rights reserved. All other copyrights, trademarks, trade names, and logos are the sole property of their respective owners.
 


 



  SHA541:
 Price
 and

 Inventory
 Controls
 
School
 of
 Hotel
 Administration,
 Cornell
 University
 
Our
 objective
 is
 to
 maximize
 revenue
 by
 determining
 the
 number
 of
 reservations
 we
 will
 accept
 
for
 each
 day,
 rate

 class,
 and
 length
 of
 stay.
 We
 have
 two
 constraints.
 The
 first
 constraint
 is
 that
 
the
 number
 of
 reservations
 we
 are
 able
 to
 accept
 must
 be
 less
 than
 or
 equal

 to
 our
 forecasted
 
demand.
 The
 second
 constraint
 is
 that
 the
 number
 of
 reservations
 we
 accept
 must
 be
 less
 than
 
or
 equal
 to
 the
 rooms
 available.
 
We
 also

 need
 to
 require
 that
 the
 result
 be
 non-­‐negative
 and
 use
 “Simplex
 LP”
 for
 a
 solution
 
method.
 Click
 Solve.
 Once
 the
 solution
 comes
 back,
 click
 Sensitivity.
 Click
 OK.
 
In

 Excel,
 we
 navigate
 to
 the
 Sensitivity
 report
 tab
 and
 copy
 the
 shadow
 prices.
 
Navigate
 to
 the
 Restrictions
 tab.
 We
 have
 already
 created
 a
 table
 to
 use
 in
 calculating
 our

 
demand.
 
Paste
 the
 copied
 shadow
 prices
 into
 the
 shadow
 price
 column.
 Now
 we
 can
 determine
 our
 
minimum
 available
 rates
 by
 using
 the
 shadow
 prices.
 The
 bid
 prices,

 the
 average
 of
 the
 
appropriate
 shadow
 prices,
 become
 our
 minimum
 daily
 rates.
 

 For
 a
 one-­‐night
 stay,
 the
 bid
 price
 is
 equal
 to
 the
 minimum
 daily
 rate.
 

The
 bid
 price
 for
 a
 two-­‐night
 stay
 is
 the
 average
 of
 the
 first
 two
 nights’
 shadow
 prices.
 
The
 bid
 price
 for
 a
 three-­‐night
 stay
 is
 the
 average
 of
 the

 shadow
 prices
 for
 all
 three
 nights
 of
 the
 
stay.
 Copy
 these
 three
 formulas
 down
 to
 fill
 columns
 C,
 D,
 and
 E.
 Now
 we
 want
 to
 check
 to
 see
 

if
 our
 rate
 (€195,
 €250,
 or
 €350)
 is
 greater
 than
 these
 bid
 prices.
 If
 our
 rate
 is
 greater
 than
 the
 
bid
 price,
 then
 the
 rate
 is
 available.
 If
 the

 rate
 is
 less
 than
 the
 bid
 price
 our
 rate
 is
 not
 available.
 
In
 F3,
 G3,
 and
 H3
 we
 enter
 these
 formulas.
 The
 formula
 will
 place
 an
 X
 in
 the

 cell
 if
 the
 rate
 is
 
closed
 and
 leave
 the
 cell
 blank
 if
 the
 rate
 is
 open.
 Copy
 the
 columns
 and
 paste
 into
 the
 
remaining
 cells
 for
 the
 €250

 and
 €350
 rates.
 We
 can
 take
 this
 one
 step
 further
 and
 use
 Excel’s
 
conditional
 formatting
 to
 color-­‐code
 the
 cells
 and
 make
 it
 easier
 to
 read.
 The
 green
 cells
 

indicate
 the
 rate
 is
 available.
 The
 red
 cells
 indicate
 the
 rate
 is
 closed.
 For
 example,
 on
 Oct.
 20th
 
we
 will
 accept
 a
 one-­‐
 or
 two-­‐night
 reservation
 at
 €195,
 but

 a
 three-­‐night
 reservation
 is
 closed
 at
 
the
 €195
 rate.
 The
 lowest
 rate
 we
 can
 offer
 for
 a
 three-­‐night
 reservation
 is
 €250
 as
 the
 bid
 price
 
is
 €233.
 

 

 

 
25
 
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