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SEMESTER 462
OPERATION RESEARCH (BUS 242)
Assignment II
DATE OF SUBMISSION: End of Week 13-Saturday (End of day) – Dt. May. 3, 2025
NO. OF STUDENTS IN A GROUP: 4-5
MAXIMUM MARKS: 10
Question 1 – (15 Marks) | |
Question 2 – (15 Marks) | |
Question 3 – (15 Marks) | |
Total Mark: Out of 45 marks | |
Total Mark: Out of 10 marks |
Note:
- Proper working has to be shown to achieve the conclusions.
- The assignment must be a MS Word document and uploaded to Blackboard
- The assignment must be submitted with the covering page.
- Write the ID numbers in the ascending order with names.
Using appropriate Operational Research models solve the questions given below and present a management report to the respective situations given:
Calculations: Answer all the questions
Question 1: 15 marks
The distribution system for a Arab Contracting Company consists of three plants, two warehouses and four customers. Plant capacities and shipping costs (SAR) from each plant to each warehouse are given below:
Plant | Warehouse | ||
1 | 2 | Capacity | |
1 | 7 | 4 | 600 |
2 | 8 | 5 | 380 |
3 | 6 | 7 | 700 |
Customer demand and shipping costs per unit in SAR from each warehouse to each customer are given in the table below:
Warehouse | Customer | |||
1 | 2 | 3 | 4 | |
1 | 3 | 4 | 8 | 7 |
2 | 5 | 7 | 6 | 4 |
Demand | 500 | 400 | 300 | 480 |
As a second option, the company decides to have online orders and deliver directly to the customers. The capacities and shipping cost (SAR) from the plant to the customer are given below:
Plant | Customer | ||||
1 | 2 | 3 | 4 | Capacity | |
1 | 8 | 7 | 7 | 4 | 600 |
2 | 6 | 4 | 8 | 5 | 380 |
3 | 5 | 7 | 6 | 7 | 700 |
Demand | 500 | 400 | 300 | 480 | Demand |
- Draw a network for the two options of transportation and transshipment models.
- Develop the linear program models.
- Determine the optimal solution for shipping the orders from the plant to the customers minimize total shipping and processing costs.
Using transportation and transshipment method solve the problem and present a report to the management by recommending the model that incurs optimal shipments cost.
Question 2: 15 marks
Using Critical Path Method identify the critical activities and prepare a report determining the tasks that must be crashed and the total cost incurred after crashing the project.
Given the set of activities indicated in the table below, construct a network diagram with the expected duration and the critical path:
Task | Predecessor | Normal time (Weeks) | Crash time (Weeks) | Normal cost SAR | Crash cost SAR |
A | – | 8 | 6 | 400 | 600 |
B | – | 10 | 7 | 2000 | 2900 |
C | – | 9 | 8 | 400 | 700 |
D | A | 18 | 15 | 1900 | 2500 |
E | A | 6 | 5 | 800 | 1200 |
F | B | 5 | 3 | 600 | 800 |
G | C | 7 | 5 | 900 | 1400 |
H | E, F | 15 | 12 | 1500 | 2100 |
I | G | 12 | 10 | 2500 | 3200 |
J | D | 4 | 3 | 450 | 600 |
K | G, I | 4 | 2 | 750 | 1250 |
L | H, K | 5 | 3 | 800 | 1300 |
- Construct the project network. (5 marks)
- The project is completed when activity J and L are completed. Find the critical path using normal time. What is the time taken to complete the project? (7 marks)
- Crash the project to 34 Days and determine the total cost after crashing. (3 marks)
Question 3: 15 marks:
Jubail Auto manufactures spare parts for cars, and you are asked to compute the following based on the information provided using the backorder inventory policy:
Given that the demand for wiper blades is 15000, CO = 30 SAR per, Ch= 2.5 per unit per year, the backorder cost is estimated to be 6 SAR per unit per year, and the number of working days is 350 days.
- Minimum cost order quantity (4 Marks)
- Maximum number of backorders. (3 marks)
- Maximum inventory. (2mark)
- Cycle time. (2 marks)
- Total annual cost. (4 marks)
(Round of the answer to the nearest whole number).
Using backorder for EOQ model, present a report to the management of the company by determining the EOQ size to be ordered.
***END OF ASSIGNMENT***
Department of Business Administration
Semester 462
Assignment No: II
Section No:
Course Code: BUS 242
Course Name: Operation
Research
Student ID
Student Name
1.
2.
3.
4.
5.
Page 1 of 4
SEMESTER 462
OPERATION RESEARCH (BUS 242)
Assignment II
DATE OF SUBMISSION: End of Week 13-Saturday (End of day) – Dt. May. 3, 2025
NO. OF STUDENTS IN A GROUP: 4-5
MAXIMUM MARKS: 10
Question 1 – (15 Marks)
Question 2 – (15 Marks)
Question 3 – (15 Marks)
Total Mark: Out of 45 marks
Total Mark: Out of 10 marks
Note:
a.
b.
c.
d.
Proper working has to be shown to achieve the conclusions.
The assignment must be a MS Word document and uploaded to Blackboard
The assignment must be submitted with the covering page.
Write the ID numbers in the ascending order with names.
Page 2 of 4
Using appropriate Operational Research models solve the questions given below and present a
management report to the respective situations given:
Calculations: Answer all the questions
Question 1: 15 marks
The distribution system for a Arab Contracting Company consists of three plants, two warehouses
and four customers. Plant capacities and shipping costs (SAR) from each plant to each warehouse
are given below:
Plant
Warehouse
1
2
Capacity
1
7
4
600
2
8
5
380
3
6
7
700
Customer demand and shipping costs per unit in SAR from each warehouse to each customer are
given in the table below:
Warehouse
1
2
Demand
1
3
5
500
Customer
3
8
6
300
2
4
7
400
4
7
4
480
As a second option, the company decides to have online orders and deliver directly to the
customers. The capacities and shipping cost (SAR) from the plant to the customer are given below:
Plant
1
2
3
Demand
Customer
1
8
6
5
500
2
7
4
7
400
3
7
8
6
300
4
4
5
7
480
Capacity
600
380
700
Demand
a. Draw a network for the two options of transportation and transshipment models.
b. Develop the linear program models.
c. Determine the optimal solution for shipping the orders from the plant to the customers
minimize total shipping and processing costs.
Using transportation and transshipment method solve the problem and present a report
to the management by recommending the model that incurs optimal shipments cost.
Page 3 of 4
Question 2: 15 marks
Using Critical Path Method identify the critical activities and prepare a report determining
the tasks that must be crashed and the total cost incurred after crashing the project.
Given the set of activities indicated in the table below, construct a network diagram with the
expected duration and the critical path:
Task
Predecessor
A
B
C
D
E
F
G
H
I
J
K
L
A
A
B
C
E, F
G
D
G, I
H, K
Normal
time
(Weeks)
8
10
9
18
6
5
7
15
12
4
4
5
Crash
time
(Weeks)
6
7
8
15
5
3
5
12
10
3
2
3
Normal
cost SAR
Crash
cost SAR
400
2000
400
1900
800
600
900
1500
2500
450
750
800
600
2900
700
2500
1200
800
1400
2100
3200
600
1250
1300
a. Construct the project network. (5 marks)
b. The project is completed when activity J and L are completed. Find the critical path using
normal time. What is the time taken to complete the project? (7 marks)
c. Crash the project to 34 Days and determine the total cost after crashing. (3 marks)
Question 3: 15 marks:
Jubail Auto manufactures spare parts for cars, and you are asked to compute the following based
on the information provided using the backorder inventory policy:
Given that the demand for wiper blades is 15000, CO = 30 SAR per, Ch= 2.5 per unit per year, the
backorder cost is estimated to be 6 SAR per unit per year, and the number of working days is 350
days.
a. Minimum cost order quantity (4 Marks)
b. Maximum number of backorders. (3 marks)
c. Maximum inventory. (2mark)
d. Cycle time. (2 marks)
e. Total annual cost. (4 marks)
(Round of the answer to the nearest whole number).
Using backorder for EOQ model, present a report to the management of the company by
determining the EOQ size to be ordered.
***END OF ASSIGNMENT***
Page 4 of 4
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