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Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
MCA SEMESTER- IV EXAMINATION SUMMER 2017
Subject Code:2640003 Date:03/06/2017
Subject Name: Operations Research
Time: 10.30 AM TO 01.00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1

What is Operations Research? Briefly explain the Applications of OR in various fields.
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A plastic products manufacturer has 1,200 boxes of transparent wrap in stock at one factory and another 1,000 boxes at its second factory. The manufacturer has orders for this product from three different retailers, in quantities of 1,000, 700 and 500 boxes respectively. The unit shipping costs (in rupees per box) from the factories to retailers are as follows:
From To:
Retailer I
Retailer II
Retailer III
Factory A
14
13
11
Factory B
13
13
12
The manufacturer needs to determine a minimum cost shipping schedule for satisfying all demands from current inventory. Formulate this problem as an LP Model. Do not solve it.
07
Q.2

Solve the following LPP through Graphic Method:
Minimize Z 200x1 400x2
Subject to x1 x2 200
x1 3x2 400
x1 2x2 350
x1 x2 0
07

Solve the following LPPs through Simplex Method.
Maximize: Z 5x1 2x2
Subject to 4x1 2x2 16
3x1 x2 9
3x1 x2 9
x1, x2 0
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OR

Solve the following LPPs through Big-M Method.
Maximize: Z 2x1 4x2
Subject to 2x1 x2 18
3x1 2x2 30
x1 2x2 26
x1 x2 0
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Q.3

The transportation costs (in rupees) per unit from factories S1, S2, S3 to warehouses D1, D2, D3 and D4 are given in the following table.
D1
D2
D3
D4
Capacity
(in units)
S1
19
30
50
10
7
S2
70
30
40
60
9
S3
40
8
70
20
18
Demand (units)
5
8
7
14
34
Find out the initial solution using LCM and VAM.
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Obtain the Dual of the following Primal LP problem:
Minimize Z x1 3x2 2x3
Subject to the following constraints:
3x1 x2 2x3 7
2x1 4x2 12
4x1 3x2 8x3 10
and x1, x2, x3 unrestricted
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OR
Q.3

Consider the problem of assigning 5 jobs to 5 persons. The costs are given as below:
JOBS
1
2
3
4
5
A
10
5
13
15
16
B
3
9
18
13
6
C
10
7
2
2
2
D
7
11
9
7
12
E
7
9
10
4
12
Determine the optimum assignment schedule and minimum cost by HAM.
07

What is simulation? Explain the Monte Carlo Method in brief.
07
Q.4

Consider the game with the following payoff matrix:
Player A
Player B
B1
B2
B3
B4
B5
A1
A2
A3
A4

3

5
0
2

3
0
1
0
4
5
2

2
3
2
6
6
Determine the saddle point
Determine the value of game
Determine the optimal strategies for players A and B
Is the game fair? Why?
Is the game strictly determinable? Why?
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3

The precedence relationships of the activities, and activity time estimates (in Days) of a project is as follows:
Activity
Predecessors
Duration (days)
A
B
C
D
E
F
G
H
I
J
K
L
M

A
B
A
D
E

G
H

A
K
L
6
4
7
2
4
10
2
10
6
13
9
3
5
Draw a network diagram for this project
Find out 'Earliest Start Time' and 'Latest Finish Time' for each activity.
Indicate the critical path
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OR
Q.4

Explain the following:
Alternative (or Multiple) Optimal Solution
Unbounded Solution
Maximin Value and Minimax Value
Value of Game
Saddle Point
Event
Activity
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Each unit of an item costs a company Rs. 40. Annual holding costs are 18% of unit cost for interest charges, for insurance, allowance for obsolescence, Rs. 2 building overheads, Rs. 1.50 for damages and loss and Rs. 4 miscellaneous costs. The annual demand for the item is constant at 1,000 units. Placing each order costs the company Rs. 100. Find out
The optimal/economic order quantity
The optimal order cycle time
Optimal number of orders in one year
The optimal minimal total variable inventory cost
The optimal total inventory cost
If the supplier of the item will only deliver batches of 250 units, how are the stock holding costs affected?
If the supplier relaxes his order size requirement, but the company has limited warehouse space and can stock a maximum of 100 units at any time, what would be the optimal ordering policy and associated costs?
07
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Q.5

A road transport company has one reservation clerk on duty at a time. He handles information of bus schedules and makes reservations. Customers arrive at a rate of 8 per hour and the clerk can, on an average, service 12 customer per hour. Answer the following:
What is the average number of customers waiting for the service of the clerk?
What is the average time a customer has to wait before being served?
What is the probability of 3 customers waiting in the queue?
What is the expected number of customers in the queue?
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The data collected in running a machine-A, the cost of which is Rs. 60,000, is given below:
Year
1
2
3
4
5
Resale Value
42,000
30000
20,400
14,400
9,650
Cost of spares
4,000
4,270
4,880
5,700
6,800
Cost of labour
14,000
16,000
18,000
21,000
25,000
Determine the optimum period for replacement of the machine.
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OR
Q.5

Find an optimal sequence for the following sequencing problem of four jobs and five machines, when passing is not allowed. Its processing time (in hours) is given below:
Job
Machine
M1
M2
M3
M4
M5
A
B
C
D
7
6
5
8
5
6
4
3
2
4
5
3
3
5
6
2
9
10
8
6
Also find the total elapsed time and idle time.
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Machine A costs Rs. 45,000 and its operating costs are estimated to be Rs. 1,000 for the first year increasing by Rs. 10,000 per year in the second and subsequent years. Determine the optimal period for replacement of the machine.
Another Machine B has the lowest average annual running cost of Rs. 20,000 in the 5th year of life. If at present we have a machine of type should we replace it with If so, when? Assume that both the machines have no resale value and their future costs are not discounted.
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