Session 1 Revenue Inn

8/11/2019 Session 1 Revenue Inn

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1

Bid Price Revenue Inn

Prof. Goutam Dutta

Indian Institute Management, Ahmedabad91-79-(6)6324828

[email protected]


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Demand Forecast for Leisure

X[i,j,2] 2 3 4 5 6 7

1 1 2 3

2 1 1 1

3 1 1 1

4 1 4 55 4 6

6 5

Arrival

Date, i

Departure Date, j


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Objective Function

Maximize Revenue =

Demand constraint

Xi,j,k di,j,k for i = 1, 2, 6; j = i+1..min {i + 3,7}; k = 1,2

Non-negativity constraint

Xi,j,k 0 for i = 1, 2, 6; j = i+1..min {i + 3,7}; k = 1,2

99}]i)-(j{129}i)-(j[{ 2,,1,,

}3,7min{

1

6

1

jiji

i

iji

XX


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Decision Variables-By changing Cells

Departure Date, j

X[i,j,1] 2 3 4 5 6 7

1

2

3

4

5

6

ArrivalDate,

i

Decision variables for corporate

Departure Date, j

X[i,j,2] 2 3 4 5 6 7

1

2

3

4

5

6

Decision variables for leisure

ArrivalDate,i


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Unit Revenue for Leisure

Departure Date, j

X[i,j,2] 2 3 4 5 6 7

1 = 1*99 = 2*99 = 3*99

2 = 1*99 = 2*99 = 3*99

3 = 1*99 = 2*99 = 3*99

4 = 1*99 = 2*99 = 3*99

5 = 1*99 = 2*99

6 = 1*99

ArrivalDate,

i


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Capacity Constraint

Day # of guests Capacity

1 10

2 10

3 10

410

5 10

6 10


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Capacity Constraint

10)( 2,,11,,14

2

jj

j

XXDay 1:

10)( 2,,1,,

3

3

2

1

jiji

i

ji

XX

10)( 2,,1,,

3

4

3

1

jiji

i

ji

XX

Day 2:

Day 3:


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Capacity Constraint

Day 4:

Day 5

Day 6:

10)( 2,,1,,3

5

4

2

jiji

i

ji

XX

10)( 2,,1,,}7,3min{

6

5

3

jiji

i

ji

XX

10)( 2,7,1,7,

6

4

ii

i

XX


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Capacity Constraint - Day 1

Departure Date, j

X[i,j,1] 2 3 4 5 6 7

1

2

3

4

5

6

ArrivalDate,

i


Departure Date, j

X[i,j,2] 2 3 4 5 6 7

1

2

3

4

5

6


ArrivalDate,i


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Departure Date, j

X[i,j,1] 2 3 4 5 6 7

1

2

3

4

5

6

ArrivalDate,

i


Departure Date, j

X[i,j,2] 2 3 4 5 6 7

1

2

3

4

5

6


ArrivalDate,i


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14


Departure Date, j

X[i,j,1] 2 3 4 5 6 7

1

2

3

4

5

6

ArrivalDate,

i


Departure Date, j

X[i,j,2] 2 3 4 5 6 7

1

2

3

4

5

6


ArrivalDate,i


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Capacity Constraint -Day 5

Departure Date, j

X[i,j,1] 2 3 4 5 6 7

1

2

3

4

5

6

A

rrivalDate,

i


Departure Date, j

X[i,j,2] 2 3 4 5 6 7

1

2

3

4

5

6


ArrivalDate,i


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Capacity Constraint -Day 6

Departure Date, j

X[i,j,1] 2 3 4 5 6 7

1

2

3

4

5

6

A

rrivalDate,

i


Departure Date, j

X[i,j,2] 2 3 4 5 6 7

1

2

3

4

5

6


ArrivalDate,i


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Optimal Decision Variables - Corporate

Departure Date, jX[i,j,1] 2 3 4 5 6 7

1 1 2 32 0 1 1

3 0 3 1

4 1 1 1

5 1 1

6 1

A

rrivalDate,

i


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Optimal Decision Variables - Leisure

Departure Date, jX[i,j,2] 2 3 4 5 6 7

1 1 2 12 0 0 0

3 0 0 0

4 0 0 2

5 0 3

6 2

A

rrivalDate,

i


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Shadow Price / Bid Price

Shadow price tell us how much it would be

worth to weaken each of the capacity

constraints by one unit. OR how much wouldan additional room be worth?


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Bid PricesRevenue Inn

Arrival Date1 2 3 4 5 6

Bid price 39 129 129 99 99 99

Open rate classes,1-night stay

99129

129 129 99129

99129

99129

Open rate classes,

2-night stay

99

129

129 129 99

129

99

129

Open rate classes,

3-night stay

99

129

129 129 99

129

Rooms filled 10 10 10 10 10 10


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Overbooking


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How to Take Overbooking Decision?

Step 1 : Determine the maximum allowable number of

rooms to overbook the property for a given night.

2 different approach

Economic approach: In this approach the revenue manager

balances the cost of walking customers with the cost of

an empty room.

Service-level approach: In this approach the revenue managerspecify a risk factor for example manager wants to walk a guest

no more than once every five night.


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Economic Approach

N = number of no-shows

P[N x]= number of no-shows is greater than or equal

to some value of x

In order to overbook the room we must have and it

should remain true for each room that we overbook:

Expected revenue from the room Expected loss from theroom

(average room rate) XP[N 1] (cost of walking a

customer) XP[N < 1]


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Economic Approach

Suppose we overbook property by one room we will overbook ifthe expected revenue from the room is greater than the expectedloss

So we will overbook by the largest value of x such that for the

last room overbooked:

Expected revenue form the room Expected loss from the room

(average room rate)X P[N > x] (cost of walking a customer) XP[N x]

(average room rate) XP[N > x] (cost of walking a customer) X (1-P[N >x])

(cost of walking a customer)P[N > x] -----------------------------------

(average room rate) + (cost of walking a customer)


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Critical Fractile Method

Use the binomial distribution to computeP[N x]

given that we have overbooked the hotel by x:

ixcix

ip

ixcixcxNP p

)1(

)!(!)!(1}[

0

p = 0.15the probability that any given reservation willbe a no-show

c=capacity of the hotel (here it is 10)

c+x= capacity plus overbooking


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From formula we get various values ofx

Overbooking limit x Probability of not walking a guestP[N x]

1 0.83

2 0.56

3 0.31

4 0.155 0.06

6 0.02

Critical Fractile Method


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Optimal Overbooking Level for Day 1

Calculate average room rate for day 1 = $117

We have 6 guests at the corporate rate and 4 guests at the leisure rate foran average rate of $117 = average cost of underbooking

Cost of walking a customer = $200 (assumed) = Average cost

of overbooking

Critical Fractile= 200/(200+117) = 0.63

Choose the largest overbooking limitxsuch thatP[N >x]

0.63 orx = 1 You can also rewrite it is P[N x] = 117/(200+117) = 0.37

P[N x] can be found out from binomial distribution


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Service-level Approach

If the property is overbooked byxrooms, a

guest will be walked if the number of no-

shows is less thanxi.e. IfN , x.

we choose the largest value ofxsuch that the

probability we will not have to walk a gust,

P[N > x], is at least 4/5 = 0.8

From above table correct overbooking limit is

againx= 1 room.


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Overbooking Capacity Constraint

11)( 2,,11,,1

7

2

jj

j

XXDay 1:

11)( 2,,1,,

7

3

2

1

jiji

ji

XXDay 2:

Update Capacity constraint by increasing right hand side by

level of overbooking.

Suppose the manager of Revenue Inn has decided to allow

overbooking by 1 room every night except day 3, when hewill allow the hotel to be overbooked by 5 rooms


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Overbooking Capacity Constraint

Day 4:

Day 5:

Day 6:

11)( 2,,1,,

7

5

4

2 jiji

ji XX

11)( 2,,1,,

7

6

5

1

jiji

ji

XX

11)( 2,7,1,7,

6

1

ii

i

XX

15)( 2,,1,,

7

4

3

1

jiji

ji

XXDay 3:


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Bid Prices with Overbooking

Arrival Date1 2 3 4 5 6

Bid price 39 159 99 99 99 99

Open rate classes,

1-night stay

99

129

99

129

99

129

99

129

99

129

Open rate classes,2-night stay

99129

129 99129

99129

99129

Open rate classes,

3-night stay

99

129

129 99

129

99

129

By resolving the updated model, we find following bid prices

Session 1 Revenue Inn

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