1
A simple, carbon friendly code-sharing
agreement between Northwest Airlines and US
Airways to maximize revenue
Prakash C. Viswanathan and Patrick T. Hester

Abstract— Competition between airlines has led to the
creation of the policy of “Code sharing”, which is an inter-airline
partnership where one carrier markets a service and places its
code on another carrier’s flights. Code share alliances not only
benefit the airlines by reducing operating costs, but also benefit
passengers by providing better connectivity and lower fares.
Currently, almost all airlines have some agreements in place,
ranging from agreements only for specific routes to full mergers.
However, with ever-changing market requirements, establishing
new code-share routes can play a vital role in maximizing airline
industry revenues, while satisfying changing customer needs.
Additionally, current code sharing agreements have failed to take
the human impact on the environment into account. The goal of
this paper is to develop a model to maximize the revenues of
Northwest and US Airways, operating between Detroit,
Charlotte, and Norfolk. The revenues are subject to the typical
constraints such as aircraft capacity, fare classes and available
seats, along with new constraints that incorporate costs incurred
to mitigate human impact on the environment. The overall goal
of the model is to design new code-share policies that could be
adopted in order to increase efficiency and profit, while satisfying
consumer demand. Our study shows that airlines can consider
the environmental impacts of their operations and still achieve
profits through successful code-sharing policies.
Index Terms—Airline code sharing, revenue optimization,
carbon footprint
I. INTRODUCTION
T
HE deregulation of the US Air Industry in the late 1970s
led to a dramatic increase in airline competition and
creation of a number of low cost airlines (LCA) to tap into the
ever-growing consumer demand [1-2]. The US has the largest
air travel system in the world, with over 750 million
passengers in the year 2006 [3] and the number of passengers
is expected to exceed one billion by the year 2015. With more
than one hundred commercial airlines in service today, air
carriers have been searching for ways to increase product
Manuscript prepared on February 15th, 2010. This work was conducted to
fulfill the requirements of MSIM 651 Analysis I course at Old Dominion
University, Norfolk, VA.
P.C. Viswanathan is a graduate student in the Modeling and Simulation
Graduate Program at Old Dominion University, Norfolk, VA (corresponding
author phone: 757-683-6602; email: pviswana@odu.edu). Patrick T. Hester is
an Assistant Professor in the Engineering Management and Systems
Engineering Department at Old Dominion University, Norfolk, Virginia
(email: pthester@odu.edu).
differentiation and market advantage. While new routes
strengthen an airline’s market power and attract customers
away from competitors, they are accompanied by higher costs
[4]. For example, airlines need to take into account new
operating costs which include both fixed (facility installation,
crew employment, use of gates, slots, terminals, and landing
rights) and variable costs (e.g. fuel, facility maintenance and
service provisions).
To address increasing competition, airlines started
forming alliances [2, 5] to reduce operating costs by sharing
overhead costs and capacity. Alliances vary from a limited
marketing arrangement, such as reciprocal frequent flyer
programs, to more complex agreements such as code-sharing.
A code sharing agreement allows an airline to sell seats on its
partner’s plane. In many cases, code-sharing effectively
expands the route network of each partner airline without the
need to add planes.
There are two main forms of code sharing:
complementary and parallel (Figure 1) [5] In complementary
code sharing, two partner airlines link their networks and
establish a new complementary network. For example, US
Airways and United Airlines are code sharing partners on the
route between Norfolk and Atlanta, but US Airways is the
only operator on this route. In parallel code sharing, allied
carriers serve the same route to pool their resources and
operations and provide more frequent flights to passengers.
For example, code share partners Lufthansa and United
Airlines serve the same route between Chicago and Frankfurt.
Some code-share alliances may benefit consumers more than
others, depending on the extent to which alliance partners’
Figure 1: Illustration of Complementary vs. Parallel Code-Sharing
2
existing route networks are complementary rather than
overlapping.
Despite the existence of over hundreds of alliances in
various forms [2], there is very limited literature on alliances.
Analysis of the domestic code-sharing practice in the US has
shown that code share tickets are, on average, priced lower
than the pure online tickets [6]. Chen and Chen investigated
the effects of strategic alliances on risk pooling on the load
factors of international airline operations [7]. Load factor,
defined as the percentage of seats sold on a specific route, has
been widely accepted as the primary measure of operations
performance by an airline. At the strategic level, their results
suggests that airlines that choose parallel alliance partners
increase their load factors and reduce operating costs as a
result of risk pooling. This is not necessarily the case with
complementary code share policies, because increased demand
does not necessarily translate into a higher load factor as
airlines would have to increase their seat capacity by either
using a bigger aircraft or increasing the frequency of their
flights.
There have only been a few studies investigating the
effects of alliances on costs. Chua, Kew, and Yong
investigated the effect of code sharing alliance on the cost by
focusing on the empirical examination of code share alliances’
impact on various aspects of airline cost [8]. Their results
suggest that large alliance partners appear to reduce costs
whereas small code share partners appear to have opposite
effects on costs, although the absolute magnitude of these
results was quite negligible. Park and colleagues conducted a
number of studies investigating the effects of alliances on
partner airlines' outputs, markets and economic welfare by
comparing traffic changes on alliance routes with those on
non-alliance routes [9-11]. They also developed analytical
models of international alliances to investigate the effect of
alliances on market outcome for a fairly general demand and
cost specification [11]. In their studies they compared
complementary and parallel code sharing strategies. Their
studies showed that a complementary airline is likely to
increase total output, whereas a parallel alliance is more likely
to decrease it.
Airlines transport more than 2.2 billion passengers
annually. Nonetheless, aviation is responsible for only 2% of
global Carbon dioxide (CO2) emissions [12]. Interestingly,
even among all transportation alternatives, airlines contribute
to only 12% of emissions. However, there has been no study
incorporating emissions as a constraint while developing code
share agreements and determining operating costs of airlines.
Modern aircrafts are 70% more fuel efficient than 40 years
ago and 20% better than 10 years ago and achieve fuel
efficiencies of about 3.5 liters per 100 passenger kilometer.
Each kilogram of fuel saved reduces CO2 emissions by 3.1
Kilograms [13]. Nonetheless, the two largest manufactures of
commercial airplanes, Boeing and Airbus, have predicted
dramatic increases in the world’s airplane fleet. In 2008, there
were approximately 18,800 Boeing airplanes in service [14].
This number is expected to increase to 35,600 by 2028.
Similarly, Airbus Industries has predicted an increase in their
airplanes from 14,980 at the end of 2006 to nearly 33,000 by
2026 [15]. These staggering numbers underscore the
importance of considering the environmental impact of
airlines operation and its inclusion in the establishment of
code-sharing agreements. Thus it is possible to incorporate
constraints into the model to take into account CO2 emissions,
which can influence operating costs of an airline and thus its
revenue. Further, it is possible to show that carbon emissions
can be incorporated into code sharing policies while
maintaining profit.
In this study, a model is developed which maximizes the
revenue of Northwest and US Airways by developing optimal
code sharing agreements. Instead of developing a full scale
model incorporating multiple cities, the focus of this study is
to maximize revenue for the airline companies operating
between a very limited numbers of cities for proof of concept
purposes. In addition to the usual variables that affect cost
(such as capacity, fare classes etc), this model will also
include constraints aimed at minimizing carbon emissions.
The goal of this study is to develop suitable code-share
policies (either parallel or complementary) between the
airlines with an objective of maximizing profit and consumer
satisfaction (defined as minimizing carbon emissions?). The
results of this study will lay the groundwork for future studies
incorporating a larger city network. The hypothesis of this
study is that, given a small network of cities, constraints, and
demands, a code-sharing agreement would lead to a maximum
benefit for the two airline companies.
II. METHODOLOGY
A. Airlines and Routes
To develop a code sharing agreement, we selected
Northwest Airlines and US Airways because these companies
do not have any existing code-sharing agreement. We also
selected Detroit (D), which is a Northwest gateway (hub) city,
Charlotte (C), which is a US Airways gateway (hub) city and
Norfolk (O), a city served by both airlines. Figure 2 shows an
illustration of this small network. Northwest Airlines operates
direct flights between Detroit and Charlotte and Detroit and
Norfolk, but not between Charlotte and Norfolk (a spoke and
hub network). Similarly, US Airways operates direct flights
between Charlotte and Detroit and Charlotte and Norfolk, but
Figure 2: Network of Cities
not between Detroit and Norfolk. Therefore, the goal of this
study is to develop a code-sharing agreement such that US
3
Airways also operates between Detroit and Norfolk, while
Northwest operates between Charlotte and Norfolk, so as to
maximize the individual airlines’ net profit. The numbers next
to the arrows in Figure 2 indicate the actual flown miles
between the cities. Only one way travel is considered in this
study.
B. Data Collection: Operating Costs
The main source of revenue for airlines comes from the
passengers and depends on the fare class and the number of
seats that are actually sold per fare class and per flight. Other
sources of revenue not included in this study are from in-flight
sales of food and beverages, excess baggage weight, and fees
for baggage check-in. Many aircraft costs are proportional to
the hours flown, which are linear in distance. Operating costs
for individual aircraft and flights are divided into direct and
indirect (overhead costs). Direct costs in turn are subdivided
into variable and fixed costs. While the direct variable costs
can be traced to aircraft or flights that vary with the degree of
utilization, direct fixed costs do not vary according to the
degree of utilization. A breakdown of the unit operating cost
by category per available seat mile (product of the flight
capacity and distance flown) is provided in the ATA 2008
annual report available at http://www.airline.org [13]. Based
on their data, the total operating costs of an airline were
estimated to be around 14.09 cents per available seat mile. In
other words, the airline spends 14.09 cents for transporting a
single passenger by 1 mile. While their data was obtained
from multiple airline companies in order to provide the
average operating cost of an airline, the actual operating costs
of any specific airline might be quite different. This is seen in
Table 1 which shows a quarterly breakdown of the total
operating costs of US Airlines and Northwest for 2002
(Source: Air Carrier Statistics: U.S. Department of
Transportation). While these numbers are similar to that
obtained from ATA, the operating costs of US Airlines are
much higher than that of Northwest Airlines. Since these
numbers reflect a more accurate and conservative
representation of the operating costs, we will use these
numbers in our study to determine the total operating costs of
Northwest and US Airways.
Airlines 2002 Domestic Unit Costs
(Operating expenses per available seat mile in cents)
direct flights, aircraft type, and seat configuration for each pair
of cities. Only direct flights were considered. Table 2
summarizes the data for US Airlines and Northwest. Since US
Airways does not operate direct flights between Detroit and
Norfolk, the capacity for this route is 0. Similarly Northwest
does operate direct flights between Charlotte and Norfolk and
hence the capacity for this route is 0.
Capacity
CLT-ORF
DTW-ORF
DTW-CLT
F
C
F
C
F
C
US
Airways
22 (11)
664
(504)
0
0
36
(24)
580
(459)
Northwest
0
0
56
(40)
321
(237)
80
(64)
591
(459)
Table 2: Airline Flight Capacity
The fares for all the routes were also obtained from the
airline web pages. For this study we separated the fares into 3
classes: 1) First Class (denoted by “F”), 2) Premium class
(denoted by “P”), and 3) Discount Fares (denoted by “D”).
While the first class fare was obtained from the online
reservation system by selecting the first class option, the
premium and discount fares were obtained by selecting
“Unrestricted” (tickets that can be cancelled at any time with
full refund) and “Restricted” (tickets that are non-refundable)
options during reservation, respectively. Table 3 summarizes
the fare classes for the different sectors. Although US Airways
and Northwest airlines do not operate direct flights between
Detroit and Norfolk and Charlotte and Norfolk, they still
provide passengers with the option to purchase tickets for
these sectors. In this case, however, the flights are not direct,
but instead connect through another city. For example, the
Detroit-Norfolk passenger will first travel from Detroit to
Charlotte and then from Charlotte to Norfolk. These fares are
also provided in the table and indicated in bold.
CLT-ORF
DTW-ORF
DTW-CLT
Fare
Classes
F
P
D
F
P
D
F
P
D
US Airways
979
684
213
894
234
175
812
699
158
Northwest
1467
681
542
905
705
403
834
710
222
Table 3: Fares and Fare Classes
Carrier
1st
Q
2nd Q
3rd Q
4th Q
Average
Std
Dev
US
Airways
16.1
15.7
14.4
15.8
15.5
4
Northwest
11.2
11.1
11.2
13.3
11.7
3.5
Table 1: Quarterly Operating Costs of Northwest and US Airways
C. Data Collection: Capacity and Fares
The seats available in each flight sector were obtained
from the airline web pages by determining the number of
D. Data Collection: Demand
Demand is defined as the number of passengers who
travel on a specific route. To get an estimate of the demand,
we used the load factor, which provides the percentage of
seats that are filled on any airline. These numbers are available
from the aviation database (http://www.aviationdb.com) and
are listed on a month-month basis [16]. However, the load
factor represents the entire US Airways, and Northwest
operations network and not for any specific flight routes.
Thus, the load factor is used as an estimate to calculate the
demand for this study. From the aviation database, the average
4
load factor from July 2007-July 2008 was 77±4% and
81±3.5% for US Airways and Northwest, respectively. Using
these numbers the demand for the specified routes was
determined and these data are shown in Table 4. It was also
assumed that only 15% of the coach passengers pay premium
fare, while remaining pay the discount fare. It should be noted
that the choice of these numbers could have a significant
impact on the overall revenue.
Demand
CLT-ORF
DTW-ORF
DTW-CLT
F
P
D
F
P
D
F
P
D
US
Airways
17
77
437
0
0
0
28
67
382
Northwest
0
0
0
45
39
220
64
71
404
Table 4: Demand for select routes
E. Data Collection: Carbon Emissions and Footprint Offset
The contribution of aircraft emissions to total carbon
dioxide (CO2) emissions was considered to be about 2% in
1990. However, air traffic in the world is growing at an
exponential rate and aircraft emissions could become a major
player in future debates over emissions. Emissions for a flight
depend on the type of aircraft, type of engines, the altitude,
and the distance flown. There is much debate on how best to
calculate the CO2 emissions and equate it to a per passenger
contribution [17]. Nonetheless, there are currently several
online calculators that allow travelers to get an estimate of the
amount of CO2 that would be emitted on a specific route and
airline company. An online calculator from terrapass.com was
used to get an estimate of CO2 emissions for the specified
routes and an estimate of an individual’s carbon footprint
offset [18]. Table 5 shows the CO2 emitted for the specific
flights and for the first class and coach class.
Sector
Airline
Fare Class
Lbs of CO2
DTW-CLT
US
Coach
242
First
349
NW
DTW-ORF
CLT-ORF
NW
US
Coach
208
First
283
Coach
227
First
313
Coach
168
First
236
Table 5: Carbon dioxide emissions
Most airlines companies have started offering what is
known as a carbon footprint offset during the purchase of an
airline ticket. By purchasing the offset, airlines invest money
in nature conservancy programs, such as planting trees, or the
donation of money to nature organizations for the purchase
and replenishment of rainforest, etc. The amount for the offset
is automatically calculated based on the distance flown and the
type of aircraft used. While the purchase of a carbon footprint
offset is not mandatory, this study includes these costs as part
of the operating costs of the airline regardless of whether the
passenger pays for it or not. Nature conservancy
(Natureconservancy.org) charges $20 to offset every ton of
CO2 emitted [19] and we use this value in our study.
F. Optimization: Linear Programming
The objective in this paper is to develop a code share
policy between Northwest and US Airlines in order to
maximize revenue and profit for each airline. This is
accomplished through the use of linear programming to obtain
feasible solutions to the maximization problem. The goal is to
determine how many seats need to be allocated to each fare
class in order to maximize revenue. In the route network, the
Detroit-Charlotte sector is the only route in which both
companies provide service. Therefore it is assumed that the
companies do not share their seat inventory for this route. On
the other hand, since only one of the companies offers service
on the other routes, it is assumed that only those routes will
require some form of code sharing agreement. For the given
problem, a total of 24 decision variables are used.
The objective function for the LP problem is given by the
relation:
MAX ∑∑ farei,c * Xi,c
(1)
Subject to the capacity and demand constraints given by the
following two relations
∑∑ Xi,c ≤ CAPf for each fare class in the flights
(1a)
Xi,c ≤ DMDi,c
(1b)
for each itinerary i and fare class c
The demand and capacity constraint values are obtained from
the tables.
III. RESULTS
A. Monte Carlo Simulation
The overall objective of this study was to develop a codesharing agreement between Northwest and US Airlines to
maximize revenue for a small network of cities. Given the
capacity, fares and load factor, the first step was to determine
the maximum and minimum revenue for US Airways and
Northwest Airlines operating between the three cities in the
absence of any code-sharing agreement. To accomplish this, a
Monte Carlo simulation approach was used to determine
revenue for 500 trials where the demand was varied for the
different classes. The net profit was given by the relation:
Profit = Revenue – (Total Op Cost + Carbon Footprintt Offset)
(2)
Where
Revenue = ∑ (Fare class * Demand)
(2a)
Here Demand was estimated from the load factor for each
airline in isolation.
5
Total Op cost = Available seat miles * Operating cost per
ASM (11.7 or 15.5 cents for Northwest and US Airways,
respectively)
(2b)
However, for convenience sake and to remain within the scope
of this study, it is assumed that this is true and the total
percentage of seats sold would equal 100.
Carbon Footprint Offset = $20 * Capacity * CO2 emitted (in
tons)
(2c)
Table 6 provides the summary statistics and provides the
lowest and highest profit that each airline can expect to make
for the given conditions. For both airlines, the difference
between maximum and minimum revenues was about
$40,000, suggesting that the demand plays a significant role in
determining the revenue for the airlines.
Summary Statistics
US Airways
Northwest
Mean Profit
211751.29
286010.47
Standard Deviation
7020.75
6981.4
Minimum Profit
191595.47
266616.92
Maximum Profit
231572.47
304578.92
Table 6: Summary Statistics from Monte Carlo Simulations
B. Linear Programming Formulation
As mentioned earlier, all domestic code-sharing
agreements in the US use the free-sale model in which the
operating carrier maintains and controls the seat inventory, but
allows its code-share partners to market and sell seats on
designated code-share flights under their own marketing code
[6]. Hence, both the operating and code-share carriers sell
seats out of the same general inventory, and the operating
carrier receives all of the ticket revenue. However, in this
study, it is assumed that the carrier that sells the seats retains
all of the ticket revenue. In addition, it is also assumed that the
operating costs and carbon footprint offset are also shared
between the airlines, in a manner proportional to the number
of seats sold by each airline. Since the goal is to maximize
profit, the best combination of tickets to be sold by each
airline in the Charlotte-Norfolk and Detroit-Norfolk sectors
must be determined.
This can be illustrated using the following example. If the
code sharing agreement allows each airline to sell 40% of the
seats in its partner airline, the objective function would reflect
this by changing the seat capacity and modifying the
constraints accordingly. And unlike the simulations conducted
in the previous section using the Monte-Carlo approach, the
demand for a given sector takes into account the combined
load factor for both airlines. By using Excel’s premium solver,
the decision variable values that maximize revenue for that
particular code-sharing agreement can be determined. This
procedure would then be repeated for a different code-sharing
arrangement in which each airline is allowed to sell only 30%
of the seats in its partner airline and so on. This procedure
would be repeated for different combinations and the revenue
from each case would then be compared to determine the mix
that would allow for maximum revenues for the two airlines. It
is important to note that if US Airways sells 60% of their seats
in the Charlotte Norfolk sector, it does not imply that they will
sell 40% of the Northwest seats in the Detroit Norfolk sector.
Figure 3: Net Profit for different code-sharing scenarios (original
capacity)
Preliminary analysis of the data shown in tables 2 and 4
suggests that the demand will always be lower than the
capacity. It also implies that on any given day the airlines are
operating more planes than are actually necessary. Therefore
in this study, in addition to using the original capacity (Table
2), we also examined the effect of a reduced capacity
(numbers within parenthesis in table 2). Microsoft Excel’s
Premium Solver was used to determine the optimal solution
for the revenue. Figure 3 summarizes the data for US Airways
(panel A) and Northwest Airlines (panel B) for original
capacity; while Figure 4 summarizes the data for reduced
capacity. The figures show the net profit for different
scenarios. The scenario “100/0” in Figures 3A, 3B, 4A, and
4B were obtained by assuming that no code sharing was
involved. All other conditions were obtained assuming
different levels of a code-sharing agreement. For example, for
US Airways in Figure 3A, the net profit for 90/10 condition
was the sum of the profit from the Charlotte-Detroit route
(operated exclusively by US Airways), profit from selling
90% of the seats between Charlotte and Norfolk (on US
Airways), and profit from selling 10% of seats between
Detroit and Norfolk (on Northwest Airlines). Similarly, for
Northwest Airlines in Figure 3B, the net profit for 80/20
condition was the sum of the profit from the Detroit-Charlotte
route (operated exclusively by Northwest Airlines), profit
from selling 80% of the seats on the Detroit-Norfolk route (on
Northwest), and profit from selling 20% of the seats between
Charlotte and Norfolk (on US Airways).
Figure 4: Net Profit for different code-sharing scenarios (reduced
capacity)
6
Our results clearly demonstrate that US Airways and
Northwest Airlines increase their net profits by implementing
some form of code-sharing agreement (Figures 3 and 4).
Specifically, it is seen that agreements that allow the other
airline to sell 20-30% of the seats maximize the profits. For a
greater percentage of code-sharing, the profits start decreasing
for both airlines. In this study we also incorporated additional
costs for offsetting carbon emissions for both airlines. The
costs were estimated based on the amount of CO2 emissions
for each route and number of seats sold by each airline. Figure
5 shows the costs incurred by each airline for different levels
of code-sharing (figure shows costs for both original and
reduced capacity). It is observed that US Airlines spend less
money to offset emissions with increasing levels of
agreements. In contrast, Northwest Airlines spend more
money with increasing code-sharing agreements. This effect
was mainly due to the greater flight capacity for the CharlotteNorfolk route, leading to reduced costs for US Airways with
increasing percentage of code-sharing.
Figure 5: Carbon footprint offset costs for different code-sharing
conditions
The results of our simulations therefore suggest the best
code sharing agreement that would maximize profits for both
airlines, which is illustrated in Figure 6. Both airlines make
the most profit when they develop a code-sharing agreement
in which each airline markets 80% of their available seats in
the Charlotte-Norfolk and Detroit-Norfolk sectors, while
allowing the partner airline to market the remaining 20% of
the available seats. It is interesting to note that reducing the
capacity reduced the net profit; however, the trend was similar
to the results obtained with original capacity. In both cases,
the net profit was significantly higher when code-sharing was
implemented.
IV. CONCLUSIONS AND FUTURE RESEARCH
Results of this study provide evidence to suggest that
code-sharing agreements, and in particular a complementary
agreement, can increase the profit of airline companies. While
this study focused on a select group of cities, large scale
cooperation between airlines can lead to correspondingly
larger profits for all participating airline companies. In
addition, by performing appropriate sensitivity analysis, the
range of optimality and also the dual prices for additional
flight capacity in the event of additional demand due to
seasonal changes in travel can be determined.
For the purpose of this study several assumptions were
made. For example, it was assumed that each airline could tap
into the demand pool first. Therefore, to compute the revenue
of a US Airways for a particular code-share configuration, it
was assumed that all seats on US Airways would be filled
first, followed by Northwest Airlines. Similarly to compute
the revenue for Northwest Airlines, passengers would first
select Northwest and once all seats were filled, would then
choose US Airways. While this method may increase the
revenue for the airline that got the first pick, it could reduce
the revenue for the second (partner) airline. This assumption
was made mainly because of the difficulty in estimating the
percentage of passengers who might prefer one airline over
another operating between the same routes. Passenger choice
for a particular airline is influenced by several factors such as
loyalty to a particular airline, frequent flier mile availability,
availability of lower fares, convenience and or available flight
schedule.
A second assumption that was made was that if US
Airways allowed Northwest airlines to sell 20% of US
Airways seats between the Charlotte to Norfolk sector,
Northwest would allow US Airways to sell 20% of Northwest
seats between the Detroit to Norfolk sector. This type of
agreement may or may not necessarily lead to the best
possible solution especially in terms of maximizing revenue.
However, due to scope of this paper, the study was limited to
such an agreement.
The above two assumptions clearly suggest that additional
studies need to be conducted to establish a more realistic code
sharing agreement between Northwest Airlines and US
Airways. Nonetheless, the results presented in this paper
suggest the usefulness of using simple linear programming
techniques to establish a simple agreement, especially if the
number of participating airlines and cities is large, is likely to
be limited.
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Figure 6: Best code-sharing agreement to maximize profits
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