Introduction to Operations Research (GSDR3105)

Higher Institute of Transport and Logistics (HITL)

Semester: First Semester

Level: 300

Year: 2019

Answers (200 )
1
REPUBLIC OF CAMEROON THE UNIVERSITY OF BAMENDA
Peace-Work-Fatherland P. O Box 39 Bambili
School/Faculty: HITL Department: General Studies Lecturer(s): Prof Njimanted/G F
Level: 300 Semester: First Academic Year: 2018/2019
Course Code: TLG S3105 Course Title: Operational Research: TLG3150
Date: /03/2019 Hall: Time: 2hrs
Instructions: Answer Question one and any two Others of Your Choice
Question One 30 marks
Decision making do exist under condition of certainty, why in other cases they exist under the situation of
uncertainty with or without probability information. Consider a man who is interested in investment opportunities
in the transport sector. He could invest in taxi business (TB), inter-urban transport mini bus services (IUTMBS),
inter-urban big bus services (IUBBS), engine boat services (EBS), shipping services (SS), sand transportation (ST), Rail
way business (RB) among others. This can be presented in the table 1.1 below. All figures are in thousand fcfa
State of Nature
Boom
Depression
Recovery Recession
TB
720
110
70
79
IUTMBS
350
200
180
240
IUBBS
460
520
170
150
EBS
300
120
600
130
SS
900
250
170
80
ST
320
190
170
190
RB
520
460
290
320
The figures presented on table 1.1 are the expected gain if the resources are invested into that particular service.
Which of these investment options should the man invest in if he is out to make optimum profit given the following
theoretical conditions?
I. MAXI MAX criterion
II. MAXIMUM criterion
III. The Hurwics criterion with the coefficient of pessimism as 0.4.
IV. The principle of Rationality or insufficient reasons.
V. The MINIMAX Regret criterion.
Question Two 20marks
A manufacturing company, Njimanted limited produces three types of baby dypers called Zaki, Tobaka and Elixir. A
unit of zaki needs 1 hour of labour, 3hours of machine time and a ton of raw materials. Tobaka requires 2 hours of
labour time, 2 hours of machine time and 4 tons of raw materials. Elixir requires 1 hour of labour time and 2 hours
of machine time only. The total resources available are 430 manpower hours, 460 machine hours and 420 tons of
raw materials. The profit contribution for zaki, tobaka and Elixir are 3, 2 and 5 (000) frs per unit respectively. You
are required to:
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2
a) Define the variables for the above problem
b) Present the problem in a tabular form.
c) Formulate the above in a linear programming problem
d) Formulate the dual of the linear programming model.
e) Can the problem be solved using the graphical method? Explain your answer.
f) Solve the linear programming problem using any technique of your choice, preferably the simplex
algorithm technique.
g) Test for the optimality of your solution.
h) Derive the per unit cost of the resources in producing the dypers
i) Which resources are fully used and which are idle if any? Calculate the amount of slack or idle
resources if any.
Question Three 20marks
Table 1.2 is based on transportation programming model (TPM) demand center.
To:
From
Bamenda
Buea
Douala
Yaounde
Bafoussam
10.0
9.0
11.0
8.0
40000
Dschang
8.0
5.0
3.0
7.0
50000
Mamfe
10.0
7.0
12.0
6.0
35000
35000
20000
25000
45000
125000
You are required to:
I. Define the variables to your decision making.
II. Formulate the problem as a linear programming model.
III. Provide an initial feasible solution using any known method.
IV. Test for optimality of the feasible solution.
V. Determine the optimal allocation for the transportation problem.
Question four 20marks
A small maintenance project consists of the following twelve jobs which precedence relations are identified with
their node numbers
Job(I, j) : (1-2) (1,3) (1,4) (2,3) (2,5) (2,6) (3,7) (4,5) (5,6) (6,7) (6,8) (7,8)
Duration (in days): 10 04 06 05 12 09 12 15 06 05 07 09
i. Draw any arrow diagram representing the project
ii. Calculate earliest start, earliest finish, latest start and latest finish time for all jobs.
iii. Find the critical path and project duration.
iv. Tabulate total float, free float and independent float for the project.
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