Overbooking policy for airline is one of the main channels that enhance revenue and improve profit; it should be carefully implemented to avoid any negative effects of denied boarding impact especially on the brand name for the airline. It should be address the best strategy that minimize cost between no-show cost and denied boarding cost, by implement cost based overbooking model (U curve technique)

1. Defining
An Optimum
Overbooking Policy
Defining
An Optimum
Overbooking Policy
Cost Based Overbooking Model
By : Mohammed S. Awad
Research Scholar

2. Defining An Optimum Overbooking Policy
Three factors lead to the best earning of revenue in
aviation, they are, right flight scheduling, optimum fare
maxing and proper inventory control. While the main
principle of airline revenue management is to sell the
right service to the right customer at the right time for
the right fare, and can be achieved by developing by
optimum overbooking policy that minimize the cost of
two main cost elements. i.e No Show Cost and Denied
Boarding Cost, the problem is solved by implementing
U curve technique which define the right overbooking
policy, so by analysis the historical data of specified
route, defining the existing overbooking policy that
also may reflect a denied boarding cases and the
corresponding no-shows distribution. A good
overbooking strategy will be the one that minimize the expected of denied boarding and
opportunity cost of spoilage, this clearly leading to define Overbooking and No-show curves.
Introduction:
Revenue Management (RM) is the process of understanding, anticipating and influencing
passenger behavior in order to maximize revenue or profits from a fixed, perishable resource as
availability of airline seats. The problem is to sell the available seats to the passengers at the right
time for the right fare. So revenue management is a set of revenue maximization strategies and
tactics meant to improve the profitability of certain businesses.
Airline Revenue Management:
Based on the revenue management theory, the cross
functional of managing revenue is impact three main factors:
1- Flight Scheduling
2- Pricing
3- Inventory Control
The product of an airline offers to a great extent defined by
Scheduling, Pricing and Capacity. Scheduling defines the
routing, the frequency, the departure time, whether it is a
non-stop or a connection. The role of Revenue Management
is to match the demand with the capacities given by
scheduling. This is done by determining the availability of
the capacity aircraft . In order to optimize the availability,
Revenue Management has to know how much money the
Pricing
Flight
Schedule
Inventory
Control
REVENUE

3. company will get when this product is sold.
Yield Management (YM) involves the tactical control
of an airline’s seat inventory for each future flight
departure. YM is the airline’s last chance to maximize
revenue.
Yield Management (YM)
It is a process determines the number of seats to be
made and available for each fare class by setting
booking limits on low fare seat. Usually YM systems
take a set of differential prices/products, schedules and
assigned flight capacities. Figure ( 1 ). Shows Normal Booking Curve.
Yield Management System:
Four Steps describe typical Yield Management System.
Data Collection-
- The Basic collected data of revenue management are: Revenue Data , Historical Booking,
No-Show Data, Actual Booking
Forecasting –
- It is for No-Show Data keeping in mind the capacity constrains
Optimization –
- Cost based Overbooking model
Reservation:
- The reservation procedure is related to the
airline patterned, it is legacy or low cost
carriers, and with the advanced, so feeding by
the outcomes of the optimization models to
define the overbooking level, terms as AU
(Authorized Capacity), CAP (Physical
Capacity), BKD (conformed booking) and NSR
( No-Show Rate), are interfere in overbooking issue.
Overbooking Problem:
The goal of overbooking is to minimize the risk of spilled revenue due to passenger cancellations
and no-shows, to accomplish this, airlines routinely overbook flights to balance the need of
generating additional revenue while minimizing the risk of over sales.

4. Cost-based Overbooking Model:
The objective of Cost-based overbooking model is to find
the optimum overbooking policy that minimize the total
combined cost of denied boarding and spoilage ( no-show )
cost.
Optimum Overbooking Policy =
MIN Cost of DB + Cost of SP ………1
Where
DB : Denied Boarding
SP : Spoilage
A simple overbooking algorithm takes the no-show forecast and overbooking to compensate for
those no-shows.
A more sophisticated overbooking takes the different costs of no-shows and denied boarding into
account as well as the uncertainty of the no-show forecasts. It calculates the expected costs of
spoiled seats and denied boarding for each possible overbooking level and selects that with
minimum expected costs.
Figure shows the two cost elements.
The risk of spoilage, that is empty seats despite high demand is the greater, the smaller the
overbooking limit is. On the other hand the risk of denied boarding increases with increasing
overbooking limits.
The sum of both costs has a minimum and the corresponding booking limit minimizes the
expected total costs.
Case Study :
Based on actual data of Yemenia for sector SAH-DXB, the no-show data for the period Oct.
2010. It is a complex issue to forecast the number of no-
show per flight, as mentioned above, demand can be
forecast, likely wise No-Show passengers can be
forecasted in the same manner, to get No-show
passengers per month, assuming the process is follows
Poisson Sampling, so by considering a historical data of
No-show of one month, and fitted to a Poisson by
minimum least square analysis and chi square test or
Kologorov test based on the number of sampling.
The collection data represented by histogram, Figure no.

5. ( ) these no-show data are related to the environmental / operational pattern, that mean we have
to restricted to capacity of aircraft, time of departure,
route connectivity and other factors.
The data analysis first based on average value of
LAMDA i.e 2.143 then adjusted to reached optimum
value 3.055 to us it in Overbooking Lose Table. The
followings figures shows the collection of LAMDA.
ANALYSIS:
The analysis is based on Cost Based Overbooking Model based on the following inputs:
1- No-show Passenger Cost:
This is an opportunity lose revenue cost due to
the no-show of passenger it is the revenue
almost in hand, as empty flown seat never get
back. So it can be calculated as the fare of
SAH-DXB = 270 USD per no-show
passenger.
2- Denied Boarding Cost:
This is a critical cost, caused by oversells
polices of airlines, and its includes a variety of
elements, some of them are not quantifiable in monetary terms.
o Cash compensation paid to involuntary denied boarding.
o Free travel vouchers as incentive for involuntary denied boarding
o Meals and hotel costs for displaced passengers.
o Space on other airlines to accommodate displaced passengers.
o Cost of lost passengers goodwill.
Based on Yemenia compensation program, it cost =150 USD for SAH-DXB sector.
So by developing Overbooking lose table, Table ( 4 ) probability of no-show is calculated based
on Poisson distribution and accordingly cost.
So – first we have to represent the data by Poisson distribution, and accordingly to utilize the
probability function of Poisson distribution in Overbooking Lose Table.

6. Two cost are evaluated
1- No-Show Cost:
The loss of opportunity may calculate as the following
Fare SAH-DXB = 270 USD
So the expected cost of lose opportunity
0 × 0.47 + 1 × 0.134 + 2 × 0.219 … … . . +7 × 0.024 × 270 = 2.958 × 270
= 798 USD per flight
So No Show Cost = ( No. of No-show -- No. of Overbooking ) * Probability of No Show *
Cost of no show cost per seat.
Provided that No Show is greater than Overbooking
2- Denied Boarding Cost
Airline Estimate the cost incurred per overbooking procedure per reservation is 150 USD
per passenger.
So Denied Boarding Cost = ( No. of Overbooking – No. of Noshow) * Probability of
Noshow* Cost of denied boarding per passenger.
Provided that Overbooking is greater than No show.
3- No Show passengers equal Overbooking reservation:
Net cost result is Zero
That’s lead us to develop an overbooking lose table. This shows clearly the Zero
Diagonal Values across the table.

7. Results:
Based on Yemenia No-show data of Oct. 2010 for sector SAH-DXB, and a initial costs of
no-shows and denied boarding as inputs, two main curves are plotted, no-show cost curve
and denied boarding cost, resulting a U shape curve that define the optimum
overbooking policy i.e Three overbooking reservation. The analysis based on monthly
data and should be repeated on monthly bases taking in consideration the seasonality’s,
shocks and trends keeping in mind the other environmental operation and other constrains
factors are not change.

8. Summary:
The study shows the importance of no-show rates and its sampling / art of fit with
Poisson distribution. The historical data is collected and demonstrated by frequency
distribution, which analysis by minimum least square analysis using cdf data ( cumulative
density function), the data examine by the tentative average value of the sample then
fitted by kolomogorovo test to get the optimum value of LAMDA ( parameter of Poisson
distribution, which is used in the cost-based overbooking model) .
Finally the ratio of Denied Boarding Cost to No-show Cost, play a major rules in shaping
the U curve approach, which give a clear picture for the top management of airlines to
select the right policy, and the real impacts on the performance of airline especially in the
commercial side.