Assignment2
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School
University of Windsor *
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Course
8290
Subject
Industrial Engineering
Date
Jan 9, 2024
Type
Pages
2
Uploaded by DeaconPowerDolphin31
Optimization (MECH8290-38)
1
Assignment # 2, Due Date: December 6, 2023, 10 PM
Q1. (15 marks)
Three industrial sites are considered for locating manufacturing plants. The plants send their supplies to three
customers. The supply at the plants, the demand at the customers, and the unit transportation costs from the
plants to the customers are given in the following table. In addition to the transportation costs, fixed costs are
incurred at the rate of $8,000, $7,500, and $9,000 for plants A, B, and C, respectively.
Formulate the problem as an ILP.
Customer
Plant
Unit transportation cost
Supply
1
2
3
A
$12
$16
$14
400
B
$15
$13
$18
750
C
$10
$11
$12
850
Demand*
700
800
500
*
Demand is the number of requested supplies by each customer.
Q2. (10 marks)
Consider the given table in Q1 for supply, demand, and unit transportation costs, and find a basic feasible
solution for the problem
using both
NorthWest Corner and Least-Cost Rules.
Q3. (25 marks)
Solve this problem by
Dynamic Programming
.
A college student has
7 days
remaining before final examinations begin in her four courses, and she wants to
allocate this study time as effectively as possible
. She needs
at least 1 day on each course
, and she likes to
concentrate on
just one course each day
, so she wants to allocate 1, 2, 3, or 4 days to each course. Having
recently taken an OR course, she decided to use dynamic programming to make these allocations to
maximize
the total grade points to be obtained from the four courses
. She estimates that the alternative allocations for
each course would yield the number of grade points shown in the following table:
Study Days
Estimated Grade Points
Course 1
Course 2
Course 3
Course 4
1
4
2
3
4
2
4
3
4
6
3
5
5
4
8
4
5
7
6
9
Optimization (MECH8290-38)
2
Q4. (25 marks)
An engineering plant can produce five types of products: P
1
, P
2
, . . . P
5
by using two production processes:
grinding and drilling. Each product requires the following number of hours of each process and contributes the
following amount (in hundreds of dollars) to the net total profit.
Formulate the problem
considering the following facts:
•
Each unit of each product takes
20 manhours
for final assembly.
•
The factory has
three
grinding machines and
two
drilling machines.
•
The factory works a
six-day
week with
two shifts of 8 hours/day
.
Eight workers
are employed in assembly,
each working
one shift per day
.
•
If we manufacture P
1
or P
2
(or both), then
at least one
of P
3
, P
4
, and P
5
must
also be manufactured.
Hours of Process
P
1
P
2
P
3
P
4
P
5
Grinding
15
25
0
30
20
Drilling
12
10
20
0
0
Profit (× $100)
50
70
40
45
30
Q5. (25 marks)
Suppose a genetic algorithm uses chromosomes of the form
x = abcdef
with a fixed length of 6 genes. Each gene
can be
any digit between 0 and 6
. Let the fitness of individual x be calculated as
f(x) = (a + b) + (c - d) + (e - f)
,
and let the initial population consist of four individuals with the following chromosomes:
x
1
= 3 4 6 1 5 1
x
2
= 2 1 5 3 1 4
x
3
= 5 3 5 4 3 2
x
4
= 6 1 4 2 6 3
a)
Evaluate the
fitness
of each individual.
b)
Crossover
the fittest two individuals
using two-point cross-validation in the middle.
c)
Cross the
second
and
third
fittest individual using the single-point crossover.
d)
Evaluate
the fitness of the new generation
. Has the overall fitness improved?
e)
Considering the initial population of the algorithm, is it possible to reach the optimum solution without
mutation? Explain.
•
Please carefully read the questions and provide detailed and clear answers.
•
You can do this assignment in a group of a minimum of 3 and a maximum of 4 people.
•
Typed reports earn bonus credits.
Good Luck!
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