Post on 02-Jun-2018
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Bid Price Revenue Inn
Prof. Goutam Dutta
Indian Institute Management, Ahmedabad91-79-(6)6324828
goutam@iimahd.ernet.in
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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
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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Capacity Constraint - Day 3
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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Capacity Constraint - Day 4
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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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
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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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
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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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