Presented to the Industrial & Systems Engineering Department
De La Salle University - Manila
Term 2, A.Y. 2024-2025
In partial fulfillment
of the course
In LBYIE3D-ER1
Case study no. 1 - Progress Report
Submitted by:
Salim, Jacob Vincent M.
Portes, Aldon Roland Sumayo
Submitted to:
Bongo, Miriam
May 19, 2025
Summary of the Case
Each flight of All-Universe Airlines must have a flight attendant assigned to it. The
operations manager of the airlines insist on focusing on a portion of this constraint which is to
consider the flight sequences of three flight attendants based in Manila.These three flight
attendants must be assigned to any of 12 feasible flight sequences offered by the airlines which
both start and end in Manila. The respective origin and destination of each leg of the flight
sequence is labeled in Table 1. Along with the respective costs of each feasible flight sequence.
Table 1. Data for the All-Universe Airlines Problem
Flight
Feasible Flight sequence
1
1
Manila - Cebu
2
Manila - Siargao
3
Manila - Coron
4
Cebu - Davao
5
Cebu - Manila
6
Davao - Siargao
7
Davao - Coron
8
Siargao - Manila
9
Siargao - Davao
10
Coron - Manila
11
Coron - Cebu
Cost (in thousand dollars)
2
3
1
4
5
6
1
1
7 8
9
1
1
1
1
2
1
2
3
3
4
4
2
3
4
7
3
5
5
3
3
2
2
6
2
4
5
2
2
1
4
3 3
2
12
1
3
3
11
1
1
2
10
5
2
4 4
7 8
5
2
4
4
2
9
9
8
9
Each number in the table denotes the order of the flight in its flight sequence. Three
different sequences at most can be chosen. More than one flight attendant can be in the same
flight with only one working and the rest as passengers but union contracts mandate that the
additional flight attendants be paid for their time as if they are working.
Goal of the study
The goal of the study is to minimize the total cost of flight attendant assignments that cover all
the flights
Discussion questions
● Formulate and use an optimization model to provide a recommendation for the company
which includes flight attendant assignments and its respective costs.
● Describe in mathematical form and in words the constraint that every flight has to be
staffed by a flight attendant.
● How does cancelling all flights to and from Coron affect the recommendation provided?
● What additional insights can be given to airline management using sensitivity analysis?
Draft of the Expanded Model formulation
Model components
Decision Variables
Xij = Flight i to be taken in feasible flight sequence j
Objective Function
Min cost = Summation of cost of feasible flight sequences chosen
To correctly reflect the goal of minimizing the total cost of flight attendant assignments,
the objective function is to minimize the value of cost which is equated to the summation of all
feasible flight sequences chosen.
Constraints
1. Flight Coverage Constraint
Each of the 11 flights must be covered by at least one selected sequence
12
∑ aij xj ≥ 1 ; i = 1, 2 …, 11
𝑗=1
i= represents each flight (from flight 1-11)
j= represents each feasible flight sequence (from sequence 1-12)
aij = 1 if sequence j includes flight i; otherwise = 0
xj =1 if sequence j is selected; otherwise = 0
2. Crew Limit Constraint
The operations manager can only assign a maximum of three different feasible flight
sequences due to the number of available flight attendants.
12
∑ xj ≤ 3
𝑗=1
3. Origin constraint
Each flight attendant must be allocated to a sequence of flights that starts and ends in
Manila
4. Sequence constraint
The flights chosen by the airlines for each flight attendant to be assigned to must be from
one of the available feasible flight sequences. This means that flights cannot be taken out
of sequence.
5. Binary Constraint
xj ∈ {0,1}, ∀j = 1, 2 …, 11
0
