GUJARAT TECHNOLOGICAL UNIVERSITY
SEMESTER-VI(NEW) — EXAMINATION - SUMMER 2019
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Subject Code:2163201 Date:10/05/2019
Subject Name:Operation Research
Time:10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
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MARKS
Q.1 (a) Discuss the advantages of Model Building in Operations research. 03
(b) Use simplex method to maximize z = 4x; + 3x,
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Subject to constraints
2xq + x5, <1000, x; +x, <800, x; <400, x, £700,x4,x, =0 04
(¢) What are the features of Operations research approach? Discuss in brief. 07
Q.2 (a) Solve the following LPP graphically 03
Minimize Z = 600x + 400y
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Subject to 3x + 3y > 40,3x +y = 40,2x + 5y = 44,x,y = 0
(b) Explain the primal — dual relationship. 04
(¢) Maximize Z = 2x, + 3x, + 4x3 07
Subject to constraints
3x; +x, + 4x5 < 600, 2x; + 4x, + 2x5 > 480,
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2x1 + 3x, + 3x3 = 540,%1,%x,,x3 =0
OR
(¢) Use Two phase method to solve the following LPP 07
Minimize z = x1 + x5
Subject to the constraints
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ZX1+XZ24, X1+7XZ27, xl,xZZO
Q.3 (a) Give an algorithm for solving a transportation problem. 03
(b) Solve the following Assignment problem 04
| I | 1I | 111 | v | Vv | |
|---|---|---|---|---|---|
| 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 |
(¢) Solve the transportation problem (find initial basic solution with VAM and 07
Optimal Solution using MODI method)
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To D1 D2 D3 D4 Supply
From
S1 19 30 50 10 7
S2 70 30 40 60
S3 40 8 70 20 18
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Demand 5 8 7 14
OR
Q.3 (a) How would you solve the assignment problem where the objective 03
function is of maximization type?
(b) Explain Degeneracy in Transportation problem and its resolution. 04
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(¢) A manufacturer wants to ship 22 loads of his product as shown below. 07
D1 D
S1 5 6 3
S2 4 6 5 5
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S3 8 9 6 4
Demand | 4 4 8
The shipping cost is Rs. 10 per load per km. What shipping schedule
should be used in order to minimize the total transportation cost?
[Use VAM to find the initial basic feasible solution and MODI method
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for Optimal solution]
Q4 (a) Draw the network diagram for following 03
Activity | A B C D E F G
Pre. - A A B B,C |E D,F
(b) What is critical activity in network diagram? What is the importance of 04
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critical path in any project?
(c) Information on the activities required for a project is as follows: 07
Activity | A B (¢ D E F G H 1 J K
Name
Activity | 1-2 | 1-3 | 14 |2-5 [3-5 [3-6 | 3-7 |4-6 | 5-7 | 6-8 | 7-8
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Node
Duration | 2 7 8 3 6 10 |4 6 2 5 6
(Days)
Find total float, free float and independent float for each activity.
OR
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Q.5 (a) Define Reneging, Balking and Jockeying in Queuing System. 03
(b) A TV repairman finds that the time spent on his job has an exponential 04
distribution with a mean of 30 minutes. If he repairs the sets in order in
which they came in, and if the arrival rate of sets follows a poisson
distribution with an average rate of 10 per/8-hour a day, what is the
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repairman’s expected idle time each day? Find the expected number of
TV sets in the system.
(c) The data on the running costs per year.and resale price of equipment A, 07
whose price is Rs. 2,00,000 are as follows.
| Year | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| Running cost | 30000 | 38000 | 46000 | 58000 | 72000 | 90000 | 110000 |
| Resale value | 100000 | 50000 | 25000 | 12000 | 8000 | 8000 | 8000 |
What is the optimum period of replacement?
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OR
Q.5 (a) Define Simulation. Enlist the types of simulation. 03
(b) Explain the Group replacement policy versus Individual replacement 04
policy.
(c) A company trading in motor vehicle spare parts wishes to determine the 07
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levels of stock it should carry for the items in its range. The demand is not
certain and there is a lead time for stock replenishment. For an item A,
the following information is obtained;
| Demand (units/day | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|
| Probability | 0.1 | 0.2 | 0.3 | 0.3 | 0.1 |
Carrying cost: Rs. 2 /unit/ day
Ordering cost: Rs. 50/ oder
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Lead time for replenishment: 3 days
Stock on hand at the beginning of simulation process was 20 units
Carry out the simulation over a period of 10 days with the objective of
evaluating the inventory rule: Oder 15 units when present inventory plus
any outstanding oder falls below 15 units.
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Random number: 0,9,1,1,5,1,8,6,3,5
Your calculation should include the total cost of operating inventory rule
for 10 days.
Q4 (a) What is Random number? 03
(b) What are the advantages of Simulation? 04
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(c) The following mortality rates have been observed for certain type of fuse: 07
| Week | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| % failing by the end of week | 5 | 15 | 35 | 57 | 100 |
There are 1000 fuses in use and it costs Rs. 5 to replace an individual
fuse. If all fuses were replaced simultaneously it would cost Rs. 1.25 per
fuse. What is the optimal replacement plan?
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