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OPSM 405 Service Management
Class 16:
Yield management: overbooking
Koç University
Zeynep [email protected]
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Yield Management System
Reservation System
Forecasting
Overbooking Levels
Discount Allocation
current demandcancellations
cancellation rate estimates
overbooking levels
futuredemandestimates
fare class allocations
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Dealing with cancellationsOverbooking control
Basic Problem:
opportunity cost of unsold seats
total cost
E[Rev] $
capacityoverbooking limit (BL)
0#seats sold
overbooking costs
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Overbooking
Two basic costs:1)Stock outs
customers have a reservation and there are no rooms left
2)Overagecustomers denied advance reservation
and rooms are unoccupied
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Example: Hotel California
Stock outs: 0.8 x $150 = $120
Overage: $50
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Table 9.1: Hotel California No-Show ExperienceNo-Shows % of Experiences Cumulative % of
Experiences 0 5 5 1 10 15 2 20 35 3 15 50 4 15 65 5 10 75 6 5 80 7 5 85 8 5 90 9 5 9510 5 100
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Overbooking Approach 1: Using Averages
In Table 9.1 the average number of no-shows is calculated by 0x0.05 + 1x0.10 + 2x0.20 + 3x0.15 +…+ 10x0.05 = 4.05.
Take up to four overbookings.
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Overbooking Approach 2: Spreadsheet Analysis
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Book more guests until:
E(cost of dissatisfied customer) = E(cost of empty room)
• Cost of dissatisfied customer *Probability that there are fewer no-shows than overbooked rooms =
• Cost of empty room *Probability that there are more no-shows than overbooked rooms
Overbooking Approach 3: Marginal Cost Approach
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Hotel California Co/(Cs + Co) = P(Overbook No
Shows) Hotel Data
• Cs = $120, Co = $50.00
• Co/(Cs + Co) = 29.%– Overbook 2 rooms
Table 9.1: Hotel California No-Show ExperienceNo-Shows % of Experiences Cumulative % of
Experiences 0 5 5 1 10 15 2 20 35
29%
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Dynamic Overbooking
Overbooking
Time to EventEvent Occurs Reservations Start
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Overbooking over time
100%
%Capacity
o90 days to departure
booking limit
reservations with overbooking
reservations without overbooking
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Bulvar Palas
The contribution of each room is 40YTL per night.
If a guest holding a reservation is turned away owing to overbooking, then other costs are incurred:– Arrangements with a nearby hotel– Penalties associated with lost good will
Management estimates this cost as 100YTL per guest “walked”
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Example: Bulvar Palas
Bulvar Palas No-Show Experience: (Daily)No-shows Probability P[no show] Cum. Prob. P[no show<x]
0 0.07 0.001 0.19 0.072 0.22 0.263 0.16 0.484 0.12 0.645 0.10 0.766 0.07 0.867 0.04 0.93 8 0.02 0.979 0.01 0.99
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Marginal analysis
How much can I overbook?
Overbook too few 40YTL, P(no show>x)Overbook too many 100YTL, P(no show<x)
Keep overbooking as long as40*P(no show>x) > 100*P(no show<x)
orP(no show<x) < 40/(40+100)=0.286
Overbook 2 rooms based on no-show distribution
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Example
The Ozhas bus company is currently assessing its Istanbul-Adana run. The number of customers that do not show up after making a reservation are uniformly distributed from 1 to 10. Tickets costs are 45YTL, and if a particular bus run is full, a passenger with a reservation is given passage on a rival company’s bus at a cost of 75YTL. Using the averages method, what should Ozhas’s overbooking policy be?
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Averages method
Using the averages method, the average number of no shows is calculated by:
0(0.0)+1(0.1)+2(0.1)+3(0.1)+4(0.1)+5(0.1)+6(0.1)+7(0.1)+8(0.1)+9(0.1)+10(0.1)
= 5.5
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Spreadsheet approachC0 = $45
Cs = $75
Number of Reservations Overbooked
No shows Probability 0 1 2 3 4 5 6 7
0 0 $0 ($75) ($150) ($225) ($300) ($375) ($450) ($525)
1 0.1 ($45) $0 ($75) ($150) ($225) ($300) ($375) ($450)
2 0.1 ($90) ($45) $0 ($75) ($150) ($225) ($300) ($375)
3 0.1 ($135) ($90) ($45) $0 ($75) ($150) ($225) ($300)
4 0.1 ($180) ($135) ($90) ($45) $0 ($75) ($150) ($225)
5 0.1 ($225) ($180) ($135) ($90) ($45) $0 ($75) ($150)
6 0.1 ($270) ($225) ($180) ($135) ($90) ($45) $0 ($75)
7 0.1 ($315) ($270) ($225) ($180) ($135) ($90) ($45) $0
8 0.1 ($360) ($315) ($270) ($225) ($180) ($135) ($90) ($45)
9 0.1 ($405) ($360) ($315) ($270) ($225) ($180) ($135) ($90)
10 0.1 ($450) ($405) ($360) ($315) ($270) ($225) ($180) ($135)
Total cost ($248) ($203) ($170) ($149) ($140) ($143) ($158) ($185)
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Likya World
Number of customers who book a night and fail to show up is Normally distributed with mean 20 and standard deviation 10
Bumping a customer costs 300 YTL If room is not sold, hotel loses revenue of
105 YTL
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Likya World
105/(300+105)=0.2592 Look up in a standard normal table to
obtain z=-0.645 So number of seats to overbook=
20-0.645*10=13.5 Alternatively use NORMINV(0.2592,20,10)
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mz = 0
s Z = 1
Z2.0
Z .00 .01
0.0 .50000 .50399
: : : :
2.0 .97725 .97784 .97831
2.1 .98214 .98257 .98300
Standardized Normal Probability Standardized Normal Probability Table (Portion)Table (Portion)
Probabilities in bodyProbabilities in body
Obtaining the Probability
.02
.50798
.97725