WARTA ARDHIA Jurnal Perhubungan Udara The Development of Yield Management Model to Optimize The Selling Income on Multi-Leg Flight by Considering Distance and Operational Cost Pengembangan Model Manajemen Untuk Optimasi Pendapatan Penjualan pada Penerbang

Historical & Currents

Demand

Estimation

Trip Range &

Operational Load Factor

Calculation of

Cost

LevelProtection

Capacity Allocation

for Optimation

Figure 2. Modified Yield Management Model

When an airplane flies to transport goods In order to optimize income by from one place to another, it needs fuel.

modified yield The number of used fuel is inversely

applying

management model, the steps taken proportioned to the distance, whereas the

are almost the same as the general number of transported cargo is equivalent

mana-gement model. to the distance [Nugraha, 2003]. The fuel

yield

However, it differs in its passengers’ and travel time variables will affect the

seats allocation in each leg for each number of required cost. In general, the

offered fare class. The total optimum cost is called airplane total operational cost

income value will be obtained by which consists of two cost categories, i.e.

the distance and direct and indirect operational cost.

considering

operational cost which is converted in costs, i.e. unit cost per passenger.

4 Warta Ardhia, Volume 39 No. 1 Maret 2013, hal. 1- 22

Based on the conceptual model as well In the probability demand, if as the problem solving model diagram, the

there is a random X variable in a objective function of the developed model

certain leg which is continuosly is to maximize the airlines profit or income

observed, the first probability of the airlines companies, which serve the

distribution calcula-tion is its route which consists of several legs (multi-

relative function (proba-bility mass leg).

function) which is a fraction The income optimizing phases of the

between the number of demands on yield management model that will be

the t observation period. Then, its conducted in this study will be probability distribution can be

categorized into two, i.e. the standard calculated/stipulated with a cumu- yield management model (YMStnd) and

lative distribution function which is the

an accumulation of relative frequen- (YMMod). The different between both

cy up to the t period. procedures that the considered additional

If demands is X = ( X 1 , X 2 ,..., X n ) variables. The conducted optimizing

and its relative frequency is procedure

is started

by

making

P ( X )   P ( X i ) , X  0 . [1]

preliminary demand model for each leg

and fare class is based on the historical P (X ) is the mass probability reservation data to determine the fare of

function on the observation period. each flight leg, the model of unit cost per

Thus, the X probability distribution passenger, make passengers’ seats is the cumulative distribution allocation model, income model, and

function, i.e.

income/ profit optimization model.

(1) Booking Estimation Model

The aim of the formulation of booking

(2) Booking Limits Model

estimation model is to find out the number Fill and discounted fare demands

of demands in each fare class in each flight on between legs are free. Thus, sales

limitation is applied to both fares to For this research, the mathematical model

determine the booking limit. The of booking estimation will be conducted

limitation for fill fare can be done by by considering the demand characteristics

calculating the protection level, which are probable and determine. The

whereas for discounted fare can be proba-bility demand is used during the

done by calculating the booking determination of the protection level on

limit.

the fill fare, whereas the determi-nation To determine the number of seats

and fixed demand will be used in allocated for the discounted fare and allocating the passengers’ seats allocation protected seats for full fare, the used

when determining the booking limit in the formula will be different for the

discount fare. single leg as well as the multi leg.

The formula for the single leg flight

The Development of Yield Management Model to Optimize The Selling Income on Multi-Leg Flight by

5 Considering Distance and Operational Cost, ( Budiarto Subroto 1) , Nelson Pardede 2) ) 5 Considering Distance and Operational Cost, ( Budiarto Subroto 1) , Nelson Pardede 2) )

unit cost per passenger. formula.

The algorithm steps that will be On the multi leg flight, each demand

conducted covers two phases which for each ODF should be immediately be

consists of protection level calcu- . decided whether to accept or refuse the

lation (simulation with Pascal tickets sales demands. If  i is the D i programming language is applied cummulatibe distribution function and X i for this study), whereas the second

is the number of seats with a fare class of i

phase

i.e.

the compartment

allocation for the economy fare, then the protection level of the I class

= 1 or 2, in which X 2 =C-X 1 and F F >F D ,

mathematical programming, i.e.

linear program is applied. should meet:

 P ( D i  X i ) [2]

F D opt

F F The conducted algorithm steps are as follow:

1. Input parameter initialization for

3) Capacity Allocation Model

the whole served leg and route; The determination of the seats allo-

including: capacity of plane (K), cation in this research is done with the no

compartment business class (K F ), control model. In the no control model,

there should not be any passengers’ seats fares (economy and fill fares), number of legs, and demands

allocation on each fare class. In addition,

pattern.

the consumer/demands will be accepterd based on the First Come First Served

2. Randomly generating demands for the fill fare for the whole leg.

principle so that the whole plane capacity

3. Whole legs protection level is filled. However, on the case study that

calculation with K F compart-ment will be conducted for the PT. Garuda

Indonesia with its Boeing737-400, the

capacity limit.

allocation by passengers seats allocation is done based

4. Fare

class

considering the shadow price of on the cabin distribution.

Assuming that the passengers’ seats each leg; in which when the shadow price > the fare for the

sales are determined based on the two alternative leg, then the booking

types of fare classes or com-partment demand will be accepted, and

configuration, i.e. C compartment with FF fare and Y compartment with FD fare,

when the shadow price < the fare, then the booking demands will be

then the logarithm for the compartment

declined.

allocation with the no control model

5. Checking the total capacity on the which is based on the First Come First

Served principle is described in Figure 3. allocation result; if the total capacity has not temporarily full

The algorithm in Figure 3, will be used and the demands are still coming,

for the standard yield manage-ment model, whereas the modified yield

then return to step 4; if the total of the demands allocation (the fill +

management model will be add with the economy fare demands allocation)

distance and other operational cost

6 Warta Ardhia, Volume 39 No. 1 Maret 2013, hal. 1- 22

START

Initialition

Level Protection Calculation for

Allocation Demand

Total Allocation for

Demand Comp. C

Total K F <

Comp C (K Capacity for F )

Demand for Comp. Y

Allocation for demand

of Comp. Y

Total Allocation for

Demand of Comp.C&Y

Total Allocation ≤

Total Capacity, K T

Total Revenue

STOP

> the plane capacity, then the allocation protection level is obtained when will seized.

logarithm 3 is applied. After the

6. The total income calculation, i.e. the sales protection level is obtained, the total income of the fill + economy fares.

mathematical model is made as an The fill fare income = the number of

input for the linear program demands of the fill fare times the fill

determining the fare value.

method,

i.e.

decision variables, value and objective function variable, and

By using the linear program for the YM constraint, both the functional and standard model, the steps of the capacity

the non-negative constraints. allocation data processing are conducted on the algorithm 4, after the sales

The Development of Yield Management Model to Optimize The Selling Income on Multi-Leg Flight by

7 Considering Distance and Operational Cost, ( Budiarto Subroto 1) , Nelson Pardede 2) ) 7 Considering Distance and Operational Cost, ( Budiarto Subroto 1) , Nelson Pardede 2) )

of decision variable is the combination

tion level

of a set of the point of arrival-departure Based on the said algorithm, the

(number of legs) and multiplied by the allocation is conducted based on the

number of fare classes. If the number of compartment, and then the booking

nodes is n of its pair, the number of limit will be first calculated for C n legs/ segments is C

r . Because there is f compartment class, i.e. by calculating

types of fare classes, the number of the protection level. The protection

decision variable is the number of the level will be calculated . using equation

r , leg multi-plied by f (1) and equation (2), which the

combination of n C

fare classes. In the case study of this protection level and the historical data

research the flight routes comprise four of demand will be obtained from fare

cities/nodes (n = 4), the pairs of ratio.

cities/nodes are two (r = 2), the fare

class are two classes (f = 2), and then From the equation (1), i.e. P(X) =

 the numbers of decision variable are 12.

p ( X i ) , with X > 0 and equation (2),

In other words, the decision variable is

X X

X which i = 1, 2, 3, ...., 12. i.e.

c. Determining the objective function

F D = P(D1 > X i opt ), the protection

The objective function is a compre-

F F hensive measurement of perfor-mance. level

This optimized objective function is the multiplication of the optimum number

for C compartment, i.e. X* can be of the decision variable and the increase obtained by using the following

value and every decision variable. equation:

In this research, the objective function is the maximized revenue,

F D which is the multiplication of decision P(X) <

F F variable (the number of bookings) and the decision variable value (the cost of

the fare charged for each class in each After the protection level of booking

b. Determining the decision variable

leg, i.e. the discount fare and the fill has been decided, the calculation is

fare). If R is the revenue, F f is the cost continued by allocating the passe-nger

of the fare, and X i is the decision seat

variable, the objective function that programming. In this case, the capacity

capacity by

using

linier

needs to be obtained in this research is: allocation is the selection of decision variable values in order to obtain the

if

F f . X i optimum yield.

Maximize R =

The decision variable in this research

is the number of booking in each leg for every fare class (X), so that the number

8 Warta Ardhia, Volume 39 No. 1 Maret 2013, hal. 1- 22 8 Warta Ardhia, Volume 39 No. 1 Maret 2013, hal. 1- 22

d. Determining the constraints

seats for Y compartment (discount fare comprise the constraint of plane

or F D ).

capacity, constraint of C compartment In order to obtain the average value capacity, limitation of booking toward

of booking request distribution (the the plane capacity when the plane is

number of passenger) in each flying over a particular leg, and the

leg/segment the data in Picture 4 above constraint of load factor/trip range.

and the multiplying factors (% SLF) are The main constraint in this research is

used. Thus, the booking average of the constraint of the plane capacity. If K

each leg in both flight routes for the fill is the plane capacity, then the booking

fare class (C compartment) and the limit is < K – the protection level; or

discount fare class (Y compartment) can otherwise, the protection level is < K –

be set. The request (load factor) the booking limit.

distribu-tions as well as the capacity data are available for each fare class, so

Case Study

that there are 100%, 75%, 50%, and 25% The case study that will be

estimation from each conducted for the PT. Garuda

booking

compartment capacity. Indonesia with its Boeing737-400, for

multi leg route, i.e. CKG-DPS-TIM-DJJ

2. The Fare Calculation toward the

(Cengkareng-Denpasar-Timika-

Trip Range

Djayapura) and CKG-UPG-BIK-DJJ To obtain a fare cost that can be (Cengkareng-UjungPandang-Biak-

changed based on the calculation Djayapura).

estimation that will be performed, a fare calculation model using the trip

range method based on the relation To establish the optimum allocation

1. The Booking Estimation

between the trip range and fare will be of seat number for each fare class in

made. By using a regression model, the each flight leg, the booking estimation

F F (full fare) and J (trip range) of the same flight based on the fare

formulation model is as follows: classes is required. The booking

F F = 6207,989853 x J 0,801275 estimation is conducted using the

estimation method based on the Based on the above formulation historical data of booking and the

model of the fare toward the trip range, running request of booking, or based

the fare cost of each leg based on the on the estimation of the load factor.

trip range for the CKG-DPS-TIM-DJJ The future booking estimation of

flight route and CKG-UPG-BIK-DJJ each flight will be set approximately

flight route with the discount fare for as the average load factor of the passenger

many as 75%, 50%, and 25% of the full for each fare class, toward the capacity

fare are as in Table 2 and Table 2. of each compartment. The plane

capacity is 124 seats, divided according

to compartment, i.e. 22 seats for C

The Development of Yield Management Model to Optimize The Selling Income on Multi-Leg Flight by

9 Considering Distance and Operational Cost, ( Budiarto Subroto 1) , Nelson Pardede 2) )

3. The calculation of the booking

For the calculation of the booking

protection level

protection level, the data of the The

discount fare, the fill fare, and the load accept/refuse the discount fare booking

factor distribution are required. Then is performed by using the calculation of

the calculation of the fare and the load the booking protection level. The

factor data, the data that will be used as calculation of the booking protection

the input in the calculation of the level, to allocate the capacity of the fill

protection level, will be set in each leg, fare

class, is

performed

by

in each route.

accumulating the values of the arrival

The capacity allocation by using the

probability, and then the result of the

standard YM model

accumulation is compared to the ratio The capacity allocation is divided of the discount fare and the fill fare. If

into two, i.e. the capacity allocation of C the value of the accumulation is bigger

compartment seat capacity (the fill fare (>) than the ratio of the fare, the

class) and the capacity allocation of the allocation of the fill fare is provided as

discount fare class booking (the Y many as the number of the booking

compartment). In this research, the arrival accumulation.

Table 1. The fare of each leg in CKG-DPS-TIM-DJJ flight

route RUTE : CGK-DPS-TIM-DJJ

Fill Fare Skenario : Discount Fare (Rp) Leg

Trip Range

Source : PT. Garuda Indonesia & Analysis Result

Table 2. The fare of each leg in CKG-UPG-BIK-DJJ flight route.

RUTE : CGK-UPG-BIK-DJJ

Fill Fare Skenario : Discount Fare Leg

Trip Range

(Rp) (Rp)

298,196 149,098 Source : PT. Garuda Indonesia & Analysis Result

10 Warta Ardhia, Volume 39 No. 1 Maret 2013, hal. 1- 22 10 Warta Ardhia, Volume 39 No. 1 Maret 2013, hal. 1- 22

the fill fare class that has been compartment) is performed by using

previously allocated, in order to the calculation of the booking

maximize the revenue protection level, whereas for the

To calculate the capacity allocation discount fare class (the Y compartment)

comprehensively, either for the fill fare it is performed using the no control

class or the discount fare class, the data model with the linier programming.

that have been set in the calculation of In calculating the booking protection

the booking protection level, added by level, the capacity allocation of the fill

the data of the calculation result of the fare class is performed by accumulating

obtained booking protection level are the values of the arrival probability (the

required. The setting of the data that booking of the passenger seats), and

will be completed comprises: then the result of the accumulation is

a. The setting of the discounted fare compared to the ratio of the discount

comprises the discounted fares as fare and the fill fare. For the allocation

many as 75% of the full fare, 50% of of the passenger seats of the discount

the full fare, and 25 % of the full fare. fare class, there is no exclusion (no

b. The setting of the load factor (the control) or using the ‘first come first

request) for the discounted fare serve’ (FCFS) principle.

comprises 80% of the load factor, The capacity allocation using the no

70% of the load factor, and 60% of control model is performed to

the load factor.

determine the number of request that

c. The setting of the load factor (the will be accepted or refused and the

request) for the fill fare comprises request for each discount fare class, in

100% of the capacity. each flight leg. The determination of

d. 75% of the capacity, 50% of the allocation is conducted based on the

capacity, and 25% of the capacity. load factor pattern of each fare class in each flight leg, by considering the

The allocation of the passenger seats protection level of the seat booking of

in order to obtain the optimal solution the fill fare class that has been

will use a method of the linier previously allocated, in order to

mathematical programming model. To maximize the revenue.

solve the problem of the linier The capacity allocation using the no

programming, the problem must be control model is performed to

formulated in the form of equation, determine the number of request that

comprising the decision variable that is will be accepted or refused and the

the problem whose values must be request for each discount fare class, in

determined, perfor-mance rating must each flight leg. The determination of

be stated in the mathematical function allocation is conducted based on the

known as the objective function, as well load factor pattern of each fare class in

as the restrictions known as the each flight leg, by considering the

constraints.

The Development of Yield Management Model to Optimize The Selling Income on Multi-Leg Flight by

11 Considering Distance and Operational Cost, ( Budiarto Subroto 1) , Nelson Pardede 2) )

As an illustration to solve the

Maksimasi

problem of the capacity allocation R= F F 1  2 X 1 + F D 1  2 X 2 + F F 1  3 X 3 + using the linier programming for both

F D 1  3 X 4 + F F 1  4 X 5 + F D 1  4 X 6 + F F 2  3 X 7 + routes, i.e. CKG-DPS-TIM-DJJ flight

2  3 X 8 + F F 2  4 X 9 + F D 2  4 X 10 + F F 3  4 X 11 + route, F the calculation D 3  4 X 12 (6)

route and CKG-UPG-BIK-DJJ flight

sequence/formulation for both routes

Determining the objective function

will be identical (since the calculation The objective function R that will be uses the same scenario data), the optimized is to maximize the revenue

difference occurs as the objective for flight that serves a route comprising function formulation based on the fare

four cities, which the amount of fare of is different. The sequence/formulation

one leg, from one point of departure to of the calculation of the capacity

one point of arrival, is varied, based on allocation for the scenario 1 is as

some matters especially the trip range of the plane.

follows: The formulation of the objective function to solve the problems of a.

Decision variable

From the fare calculation, the Decision variable that will be

formulation of the objective function decided is the number of booking for

for both routes that has scenario data 1, each leg in each fare class. In the

i.e. 75% discount fare, 80% load factor case study of this research the flight

of discount fare, and 100% load factor route comprises four cities/nodes, so

of fill fare, is as follows: Route : CKG-DPS-TIM-DJJ

that there are six legs/segments in that flight route (Figure 4), whereas there

Maximize

are two fare classes for each leg, so that

there are 12 decision variables (Figure

4), i.e.: X 1 , X 2 , X 3 , X 4 , X 5 , X 6 , X 7 , X 8 , X 9 ,

X X 3 3 &X &X 4 4

X X 5 5 &X &X 6 6

X X 7 7 &X &X 8 8

X X 9 9 &X &X 10 10

11 11 &X &X 12 12

Figure 4 : Decision Variable in CKG-UPG-BIK-DJJ flight route.

12 Warta Ardhia, Volume 39 No. 1 Maret 2013, hal. 1- 22

R = 1062853X 1 + 791140X 2 +

X 1 < 13; X 3 < 14; X 5 < 14; X 7 < 12;

2763413X 3 + 2072563X 4 + 2880102X 5 +

X 9 < 15; X 11 < 14

2160077X 6 + 436688X 7 + 327516X 8 +

2654357X 9 + 1990768X 10 + 578615X 11 Constraint of demands for discount + 433961X 12 (7)

fare (based on load factor): Route : CKG-UPG-B1K-DJJ

1. X i < 82, untuk load factor = 80%, Maximize :

dimana i = 2, 4, 6, 8, 10, dan 12

R = 1352371X 1 + 1014278X 2 +

2. X i < 72, untuk load factor = 70%,

2804994X 3 +

dimana i = 2, 4, 6, 8, 10, dan 12

2103346X 4 + 2880102X 5 + 2160077X 6

3. X i < 62, untuk load factor = 60%, 1599588X 7 + 2199691X 8 + 1975848X 9 dimana i = 2, 4, 6, 8, 10, dan 12 +

Constraints for non negative :

1481886X 10 + 596391X 11 + 447293X 12

X i > 0, dimana i = 1, 2, 3, 4, 5, 6, 7, 8, 9, (8)

10, 11, dan 12

Determining the constraints

Based on the route in which there is

The capacity allocation using the

a probability that the plane will load or

modified YM model

unload passengers, the constraints that In the capacity allocation of the should be estimated in this research

modified YM model, the algorithm of comprise the constraint of plane

the capacity allocation is similarly capacity, constraint of C compartment

conducted as the calculation of the capacity, constraint of load factor of fill

capacity allocation of the standard YM fare, and constraint of load factor of

model.

discount fare. The capacity allocation of the modified YM model will calculate the Constraints of seat factor :

variables of trip range and operational

1. X 1 +X 2 +X 3 +X 4 +X 5 +X 6 < 124

cost represented to the unit cost per passenger/flight.

The difference

2. X 3 +X 4 +X 5 +X 6 +X 7 +X 8 +X 9 +

X 10 –X between these two models is on the 1 –X 2 < 124 value of the objective function that not

3. X 5 +X 6 +X 9 +X 10 +X 11 +X 12 –X 1 –

X 2 –X 3 –X 4 –X 7 –X 8 < 124

only calculates the fares, but also

calculates the operational costs per unit

Constraints of C Compartement : of passenger for each leg and considers

1. X 1 +X 3 +X 5 < 22

the

comprising the additional capacity as well as fuel.

constraints

2. X 3 +X 5 +X 7 +X 9 –X 1 < 22

In order to obtain the unit cost per

3. X 5 +X 9 +X 11 –X 1 –X 3 –X 7 < 22

passenger required in the capacity allocation of the modified YM model,

Constraints of demands for fare class the calculation and the formation of the (level protection) : model comprising the model of

passenger fare regarding the trip range,

The Development of Yield Management Model to Optimize The Selling Income on Multi-Leg Flight by

13 Considering Distance and Operational Cost, ( Budiarto Subroto 1) , Nelson Pardede 2) )

14 Warta Ardhia, Volume 39 No. 1 Maret 2013, hal. 1- 22

J Max =

W Max =

Tabel 3. Variable Cost and Multiplying Load Factor

Component of Variable

Cost

Total (Rp/trip)

Multiplying Load

Factor

Pax Comisión

On Borrad Service

Muatan (kg)

Source : PT. Garuda Indonesia & Analysis Result

the model of load factor regarding the trip range, the model of trip time and trip fuel regarding the trip range, as well as the estimation of plane operational cost based on the components of variable cost and fixed cost are conducted.

In transporting the load from one point of departure to one point of arrival, the plane needs trip fuel during the flight period. In other words, the trip fuel affects the cost spent to transport that load.

If the amount of the load is smaller than the maximum capacity of the plane, the amount of trip fuel needed by the plane to cover the same trip range will be smaller than when the plane is fully loaded. By assuming that the weight of a passenger and his/her baggage is 90 kg, and by the fact that the maximum payload W p0 = 15.772 kg,

and the seat capacity = 124 seats, the maximum weight of cargo that can be

carried by the plane can be calculated by using the equation, so that the correction factor of the trip fuel can be stated as: W p0 =K.W pb +W pF , so

W pF =W p0 –K.W pb W pF = 15.772 – 124 * 90 = 4.612 kg

a nd for the model formation and selection,

the equation

of the relationship between the load and the trip range is:

k f = 9,24009 . 10 -9 x (35.488 + 11.160LF p + 4612 . LF b ) 1,70941

W p = 22.346,33634 - 5,33965 . J Max

Since W p0 = 15.772 kg, the relation-ship between the load and the maximum trip range and vice versa is as follows (12) and (13).

In order to be able to calculate the plane operational cost, the operational cost component based on variable cost

The Development of Yield Management Model to Optimize The Selling Income on Multi-Leg Flight by

Considering Distance and Operational Cost, ( Budiarto Subroto 1) , Nelson Pardede 2) )

15

Component

Operational Cost

CGK-DPS-TIM-DJJ Route

Business Fare

Economic Fare

CGK-UPG-BIK-DJJ Route

Business Fare

Economic Fare

Operational Cost Component

Catering Cost

21,018 10,509 Other Variabel Cost

Fuel Cost 3,166

289,940 284,940 Source : PT. Garuda Indonesia & Analysis Result

and fixed cost should be recognized. Since the cost component will be calculated mainly on the variable cost in the further calculation, the variable costs either affected by the carried load (the number of passengers), or variable cost and trip time estimation are as follow:

By using the above calculation model, the extents that will be used as the new constraints or objective function values are obtained for CKG- DPS-TIM-DJJ route and CKG-UPG- BIK-DJJ route. After putting the parameter of both routes into the above calculation model, the algorithm calculation of the capacity allocation is done

by the

calculation

sequence/formulation as follows:

Decision variable

Decision variable that will be decided is the number of booking for each leg in each fare class. The number of decision variables for both YM

model is 12 for each model, i.e.: X 1 ,X 2 ,

X 3 ,X 4 ,X 5 ,X 6 ,X 7 ,X 8 ,X 9 ,X 10 ,X 11 , and X 12 .

Determining the objective function

The objective function R that will be optimized is to maximize the revenue. The objective function R that will be optimized is to maximize the revenue for flight that serves a route comprising four cities, which the amount of fare of one leg, from one point of departure to one point of arrival, is varied, based on some matters especially the trip range of the plane.

Tabel 4. Fare and Operational Cost Component

Maximize R =  (Fare – OperationaI_Cost). X i (14)

or Maximize

+ F D 2  3 X 8 + F F 2  4 X 9 + F D 2  4 X 10 + F F 3  4 X 11 + F D 3  4 X 12 (15)

When the trip range variable, objective function value for CKG- especially the operational cost variable,

UPG-BIK-DJJ route can be obtained. By increases, the

objective function putting that objective function value formulation will also change. A change

into the formula, the objective function from only considering the fare factor

formulation for both routes by using for each leg in each class to considering

the data scenario can result in 75% the operational cost per passenger unit,

discounted fare.

comprising the cost of pax commission, catering, reservation, on

Determining the Constraints

board services, and fuel trip usage, is The constraints will change with the occurred.

increase in the trip range and payload Those costs will be grouped based

variables, so that the constraints for the on the frequency of those costs charged

modified YM model having a data to each passenger, i.e. the costs charged

scenario in which there is 75% only on the ticket purchasing such as

discounted fare, will be the same as the

standard YM model comprising, the reservation, on board services and the

costs of pax

commission,

constraints of the plane capacity (seat costs charged for several times

factor), the constraints of the C according to the number of legs passed

compartment, the obstacles/limita- through by the passenger to get to

tions of booking for fill fare class his/her destination such as the

(protection level), and the obstacles/ catering cost. The cost for trip fuel will

limitations of booking for discount fare depend on the number of payload (the

class (based on load factor). The passenger and his/her baggage). From

difference between these constraint is the above formula the objective

only on the constraint of the payload function value can be formulated, by

toward the trip range that is calculated, decreasing every variable cost on the

by assuming that the capacity of cargo applied fare, as follows.

is 20% and the payload weight of the From the calculation result using the

passenger and his/her baggage is 90 data of fare and operational cost for

kg, the payload per passenger = 108 kg each leg, the objective function value

so that the contraintsof the payload for CKG-DPS-TIM-DJJ route or the

comprises:

16 Warta Ardhia, Volume 39 No. 1 Maret 2013, hal. 1- 22

(i) 108X1 + 108X2 + 108X3 + 108X4 + The results of the above optimized 108X5 + 108X6 < 15572

solution comprise:

(ii) 108X3 + 108X4 + 108X5 + 108X6 +

a) The number of all passengers carried 108X7 + 108X8 < 15572

in one flight,

(iii) 108X5 + 108X6 + 108X9 + 108X10 +

b) The number of the passengers in 108X11 + 108X12 < 12807*

each segment comprising three Note: *) is a requirement (15)

segments (determined based on the obstacle of plane and compart-ment

The Optimization

c) The revenue obtained and the The

allocation result in one flight, and conducted in a linier program model by

d) The average of the revenue per using a computer program, i.e. QS

passenger (yield). (Quantitative System) Version 3.0. The result (solution) obtained for the

The ratio of the result of the standard YM method and the modified

optimized solution using Standard YM YM method for CGK-DPS-TIM-DJJ

and Modified YM according to CGK- route and CGK-UPG-BIK-DJJ route is

DPS-TIM-DJJ Scenario. The ratio of the presented in the following table. In the

result of the optimized solution using solution table, the fare scenario column

Standard YM and Modified YM contains the discounted fares being set,

i.e. 75%, 50%, and 25% of the normal

Scenario.

fare. The LF TEkom column designed in 80%, 70%, and 60% is the scenario of

b. The analysis and discussion of

the load factor for the passenger of the

the influence of additional

discount fare class. The LF TBsn column

variable

designed in 100%, 75%, 50%, and 25% is In the formulation of the the scenario of the load factor for the

function, there are passenger of the fill fare class.

objective

differences in the value of the objective function in which the

Analysis and Discussion

modified YM method has calculated

a. The result and the ratio of the

the component variable of the

optimized solution

charged to each The results of the optimized solution

operational

passenger (such as the costs of whether using the standard YM model

catering, pax commission, on board (YMStandard) or the modified YM

services, and reservation) as well as model (YMModified), which are

the operational cost of the trip fuel presented in the tables below, are the

charged on each kg of the payload solution ratios obtained by using the

standard YM model and the modified

YM model, for each route by using 36 scenario data.

The Development of Yield Management Model to Optimize The Selling Income on Multi-Leg Flight by

17 Considering Distance and Operational Cost, ( Budiarto Subroto 1) , Nelson Pardede 2) )

100% Load Factor 75% Load Factor

180 No. 210

0 Business Fare Economic Fare 0

Business Fare Economic Fare Standard YM Modifed YM Standard YM Modified YM

50% Load Factor 25% Load Factor

No.

Pax. 180

0 Business Fare 30 Economic Fare 0 Business Fare Economic Fare

Standard YM Modified YM Standard YM Modified YM

Figure 5. Comparison of optimized solution using Yield Management (Standard vs Modified Model) according to CGK-DPS-TIM-DJJ scenario.

100% Load Factor 75% Load Factor

0 Business Fare 30 Economic Fare 0

Business Fare Economic Fare Standard YM Modified YM Standard YM Modified YM

50% Load Factor 25% Load Factor

of

Pax.

0 Business Fare Economic Fare 0 Business Fare Economic Fare Standard YM Modified YM Standard YM Modifikasi YM

Figure 6 : Comparison of optimized solution using YM Standar Model Vs YM

Modofication according to CGK-UPG-BIK-DJJ scenario.

18 Warta Ardhia, Volume 39 No. 1 Maret 2013, hal. 1- 22

The influence of these operational From the result of this testing, it is costs to the objective function will

shown that the constraint of the result in the reduction of the objective

payload, either for the CKG-DPS-TIM- function value of the modified YM

DJJ route or CKG-UPG-BIK-DJJ route, method, so that the alternative of the

in the segment 1, segment 2, or segment decision of the passenger selection

3, this technical requirement can still be based on fare classes that will be served

met or, in other words, it does not in each leg will change.

affect the revenue In the formulation of the constraints,

significantly

optimization (there are 36 types of data there is a difference between the

scenario).

standard YM method and the modified YM method due to the increase of the

d. Validating the developed method

constraint of the payload toward the One way to have model validity is trip range. The constraint of the

by testing the data consistency. This payload toward the trip range is

data consistency testing is done after determined based on the actual trip

completing the rechecking on the range of each leg (point of departure).

problem formulation and there is no To analyze the impact of the new

failure found in it.

additional variable in the standard YM The validating/testing of the data method, the analysis and discussion are

consistency-based model is done by conducted by testing the optimized

performing the revenue calculation result of the standard YM method

manually (conventionally), using the toward the limitation of modified YM

optimized solution (decision variable) method.

that has been obtained using linier program. Manually, the decision

c. The analysis of the solution result

variables, which are the optimal

testing

solution and linier program-ming The solution testing of the standard

method, are multiplied by each fare in YM method toward the constraint of

the same scenario to obtain the sum of the modified YM is performed by

the revenue.

The validation testing using this way putting the value of the optimal

is conducted to observe the data decision variable into each payload

consistency being used. If there is no limitation, toward the trip range

difference in the revenue calculation grouped in three segments. The

result between calculation and linier optimized solution of the decision

programming or manual calculation, variable either for the standard YM

the data being used in the modeling method or the modified YM method is

process are valid (consistent), otherwise multiplied by the payload weight of

if there is the difference, the data or the each passenger in accordance with the

model is invalid (inconsistent). If the segment when the plane flies.

data/model is invalid, it is necessary to

The Development of Yield Management Model to Optimize The Selling Income on Multi-Leg Flight by

19 Considering Distance and Operational Cost, ( Budiarto Subroto 1) , Nelson Pardede 2) ) 19 Considering Distance and Operational Cost, ( Budiarto Subroto 1) , Nelson Pardede 2) )

the modified yield management model, And from this data testing result to

contravene several examine the model validity, a obstacles/limitations so that the result significant difference on the sum of the

it

will

of the optimized solution is invalid. revenue done manually or by linier

The objective function, i.e. the sum programming is not found. The existing

of the revenue obtained from one flight difference is not too significant because

to serve a certain route (the it is too small, caused by the rounding

accumulation and revenue of each leg) off of the decision variable.

using the standard yield management model is bigger than the total revenue

Conclusion and Suggestion

obtained by using the modified yield

Conclusion

management model, yet the yield (the From the result of the development

average revenue from each passenger) of the yield management model for

is bigger if using the modified yield multi leg flight by adding the variables

management model. of trip range and operational cost, it can

be concluded that:

Sugestion

In the case of the flight of the single The development of the yield leg route, the yield management that

management model in this research still only considers the variables of booking,

shortcomings to be fare, and plane capacity will not create

has many

improved. Therefore, the research can any problem if it is applied; whereas in

be developed further to: the case of the flight of the multi leg

1. In this research the variables added route, it will create a problem if the

to the yield management model are number of booking in each leg is even

the variables of trip range (related to or bigger than the plane capacity.

payload and trip fuel) as well as The settlement formulation of the

operational cost, especially catering optimized solution of the yield

cost, so that there is a possibility to management using linier programming

add other variables. method after the adding of the

2. The improvement of the booking cost will experience changes in the

variables of trip range and operational

estimation for both fill fare class and objective function and limitation, in this

discount fare class or for the matter the limitation relates to the

problems with more than two fare payload.

classes (in this research, it is assumed The result of the optimized solution

that there are only two fare classes is the decision variable, i.e. the number

which it is in accordance with the of passenger of a certain fare class

types of the compartment of Boeing obtained using the standard yield

737-400 operated by PT. Garuda management model (without the

Indonesia to serve the route studied addition/ consideration of the trip

as the case in this research). range and operational cost variables),

20 Warta Ardhia, Volume 39 No. 1 Maret 2013, hal. 1- 22 20 Warta Ardhia, Volume 39 No. 1 Maret 2013, hal. 1- 22

3. is completed by using a computer

revenue

www.stern.nyu.edu/~billcop/scrm. the problem solution procedure, the

Pdf

calculation/processing is separately Brumelle, S.L., J. I. McGill (1993), completed. It will be better if the

Airline seat allocation with multiple calculation/processing

the

nested fare classes, Operation Research ,41, 127-137.

prediction of the booking estimation, the calculation of the protection

Chang, Yih Long (1995), Quanti-tative level, and the allocation of the

system version 3.0 , Engle-wood Cliffs, NJ.: Prentice Hall.

passenger seat entirely. The most probable

Chen, Victoria C.P., Dirk P. Günther, development that will give many

and

important

Ellis L. Johnson (1999), Airline yield management : optimal bid prices for

benefits to the airlines is to prepare a

problems without yield

(information) that integra-tes all

William L., Diwakar aspects of marketing, ticket booking Gupta(2003),Stochastic compari-son in

Cooper,

service, and

yield management planning/determination.

www/me.umn.edu/divisions/ie/sc orlab/techrep/scpym.Pdf

4. In the matter of model testing, this research uses a testing process based

Coulter, Keith S. (1999), The application on the optimized solution ratio (the

of

yield management techniques to a holiday retail

airline

revenue) between the standard YM shopping setting; Journal of Product model and the modified YM model, & Brand Management , 8, 61 – 72.

as well as performs the testing to the Daudel, Sylvian., Georges Vialle, Versi

data consistency. It will be better if bahasa Inggris oleh Barry K. the actual (historical) data, for

(1994), Yield example, and the data of several

Humphreys

Management : Application to air flights are used. However, it is not

transport and other service industries , completed in this research since there

Institut du Transport Aĕrien, Paris. is no actual data; so that the scenario

V. (1999), data suitable based on the load factor

de Boer,

Sanne

Stochastic programming for multi leg data are used.

network

revenue management ,

www.eur.nl/ WebDOC/doc/econometrie/feweco

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