1 OPSM 405 Service Management Class 16: Yield management: overbooking Koç University Zeynep Aksin [email protected].

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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