Download operations research 16 marks question bank

OPERATIONS RESEARCH 16 MARKS QUESTION BANK
1.Find the initial basic feasible solution for the following problem using north west corner rule,
least cost method and vogel’s approximation method and comment which of the following
gives better solution
I
II
III
SUPPLY
A
2
7
4
5
B
3
3
1
8
C
5
4
7
7
D
1
6
2
14
DEMAND
7
9
18
2. A commodity has to be supplied to 3 warehouses A,B &C whose requirements are 70,100 &
40 tons respectively. It is available at 3 places X,Y& Z in quantities of 55,80&75 tons
respectively. Transportation costs between different places are shown below. .
A
X 5
B
C
10 10
Y 20 30 20
Z 10 20 30
Find least cost transportation schedule.
3. A company has built a new office building in order to centralise administration functions. Six
managers will be moved to the new office building. All the offices of the manager are on the
same floor. Other than exposure and view, all the offices are a like in room area facilities. As the
company was interested in pleasing as many managers as possible, the managers were asked to
rank their preferences for offices with 6 being the most desirable and 1 being the least
desirable. The following rankings were submitted by the managers. Determine the assignment
that will provide optimal satisfaction.
Offices
Managers
01
02
03
04
05
06
M1
4
2
5
1
3
6
M2
2
3
5
1
4
6
M3
3
5
6
2
1
4
M4
2
4
6
1
3
5
M5
5
2
6
4
1
3
M6
2
6
3
5
1
4
4. A salesman wants to visit cities A,B,C,D&E. He does not want to visit any city twice before
completing the tour of all cities and wishes to return to his home city. The starting station Cost
of going from one city to another in Rs. Is given below. Find the least cost route.
A
0
6
8
12
1
A
B
C
D
E
B
2
0
7
4
3
C
5
3
0
6
2
D
7
8
4
0
8
E
1
2
7
5
0
5.Draw the network for the given project. also find the total elapsed time and critical path
predecessor
10
Event
20
20
20
30
40
40
60
60
80
70
successor
event
20
40
30
70
90
60
70
70
80
90
90
duration
days
10
20
30
20
8
0
10
20
25
15
10
6. Draw a network for the following project.
A is the start event and K is the end event.
A precedes event B,
J is the successor event to F,
C and D are the successor event to B,
D is the preceding event to G,
E and F occur after event C,
E precedes F ,
C restraints the occurrence of G and G precedes H,
H precedes J and K succeeds J,
7.Two products are manufactured by passing sequentially through three machines. Time per
machine allocated to the two products is limited to 10 hours per day. The production time and
profit per unit of each product is given below
Minutes per unit
Product
Profit (Rs)
Machine 1
Machine 2
Machine 3
10
6
8
2
II
5
F restraints the occurrence of H.
20
15
3
I
Find the optimal mix of the product.
8. Solve the equation using simplex method
Maximise Z = X1-X2+3X3
Subject to
X1+X2+X3≤ 10
2X1-X3≤ 2
2X1-2X2+3X3≤ 0
X1,X2,X3≥0
9.Solve by Two Phase Method
Minimize Z = 5X1 - 6X2 - 7X3
Subjected to
X1 + 5X2 - 3X3 > 15
5X1 - 6X2 + 10X3 < 20
X1 + X2 + X3 = 5
X1, X2, X3 > 0
10. Solve by Big M method
Minimize Z = -3X1+X2+3X3
Subject to
X1-2X2+X3≤ 11
-4X1+X2+2X3≤ 3
2X1-X3= -1
X1,X2,X3≥0
11. Solve the problem using graphical method.
Minimize Z= 40X1+36X2
Subject to
X1≤ 8
X2 ≤ 10
5X1+3X2+X3 ≥45
X1,X2 ≥0
12. A canning company operates two canning plants. Three growers are willing to supply fresh
fruits in the following amounts:
Smith
200tons @ Rs.10/ton
Jones
300tons@ Rs.9/ton
Richard 400 [email protected]/ton
Shipping costs in dollar per ton are
From
To
Plant a
Plant b
Smith
2
2.5
Jones
1
1.5
Richard
5
3
13.Solve the following sequencing problem when passing is not allowed. Find the sequence of
job that minimizes the total elapsed time to complete job.
Machine
Item
A
B C D
E
1
9
7 4 5 11
2
8
8 6 7 12
3
7
6 7 8 10
4
10 5 5 4
8
14. A Fleet owner finds from his past records that the costs per year of running a vehicle whose
purchase price is Rs 50,000 are as under:
Year:
1
2
3
4
Running cost(Rs):
5,000
6,000
Resale value(Rs):
30,000 15,000 7,500 3,750
5
6
7
7,000 8,000 11,500 16,000 18,000
2,000
2,000
2,000
16.There after running cost increases by Rs 2,000 but resale value remains constant at Rs 2,000. At what age is
the replacement due?
17. The demand for a particular item is 12000 units per year. The holding cost per unit is Rs. 1.50 per year, and
the cost of one procurement is Rs.300. The replacement rate is instantaneous .Determine :
(14)
a) Optimum order quantity
c) Time between orders
b) Number of orders per year
d) Total cost per year when the cost of one is Rs.1.50
18. Customers arrive at box office window, being manned by single individual according to serve a customer
has an exponential distribution with a mean of 90 sec. Find the average waiting time of customer. Also
determine the average number of customer in the system and average queue length.
19. Solve the following game
B
1 2 3 4
A 1 1 7 3 4
2 5 6 4 5
3 7 2 1 3
20. Find the optimum strategy for each player and find the value of the game.
Player A
Player B
1
2
3
4
5
1
4
0
1
7
-1
2
0
-3 -5 -7
5
3
3
2
3
4
3
4 -6
1
-1
0
5
5
0
0
0
0
0
21. we have 5 jobs each of which must go through machines A ,B and C in order A B C
processing time (hrs) are given in following table. Find the sequence of job that minimizes the
total elapsed time to complete job.
Job
1
2
3 4
5
Machine A (Ai) 8 10 6 7 11
Machine B (Bi) 5
6
2 3
4
Machine C (Ci) 4
9
8 6
5
22. Fleet cars have increased their cost as they continue in service due to increased direct
operating cost (gas & oil) and increased maintenance .The initial cost is Rs .3500 and trade in
value drops as time passes until it reach constant value of Rs.500. Given the cost of operating,
maintaining and trade in values as, determine proper length of service before cars should be
replaced
Years of service:
1
2
3
4
5
600
500
500
Yearend trade in value:
1900 1050
Annual operating cost:
1500 1800 2100 2400 2700
Annual maintaining cost:
300
400
600
800
1000
23. The demand for a particular item is 18000 units per year. The holding cost per unit is Rs.
1.20 per year, and the cost of one procurement is Rs.400 .No shortages are allowed , and the
replacement rate is instantaneous. Determine : a) Optimum order quantity b) No. of
orders/year c) Time between orders d) Total cost/year when the cost of one is Rs.1
24. A TV repairman finds that the time spent on his job has an exponential distribution with
mean 30 minutes. If he repairs sets in the order in which they come in and if the arrival of sets
is approximately Poisson with an average rate of 10 per 8 hours day. What is the repairman’s
expected idle time each day? How jobs are ahead of the average set just brought in
25. Consider the game having the following pay-off matrix. Determine whether it has a saddle
point. If it does, determine the optimum strategy for each player and find the value of the
game.
Player A
Player B
1
2
3
4
5
1
3
-1
4
6
7
2
-1
8
2
4
12
3 16
8
6
14 12
4
11 -4
1
2
26. Solve the following game
Player B
Player A
1
2
3
1 -2 15 -2
2 -5
-6
-4
3 -5 20 -8
1
27.There are 3 factories located at places p,q,r. these factories supply products to wholesale
agents located at places s,t,w. the weekly capacities of factories p,q and r are 76,82,77 units
respectively. The weekly requirements of the agents s,t,w are 72,102, 41 units respectively.
The unit transportation cost in Rs. From p to s,t,w are 5,8,8 respectively from q to s,t,w are
16,25,15 respectively
, from r to s,t,w are 9,16,25 respectively. Determine optimal
transportation schedule, minimum cost of transportation and also predict whether the solution
is unique or not. Use least cost method to check optimality.
28.Solve by Two Phase Method (14)
Minimize Z = 5X1 - 6X2 - 7X3
Subject to
X1 + 5X2 - 3X3 > 15 ; 5X1 - 6X2 + 10X3 < 20 ; X1 + X2 + X3 = 5 ; X1, X2, X3 > 0
29. A salesman wants to visit cities 1,2,3 and 4. He does not want to visit any city twice before
completing the tour of all cities and wishes to return to his home city. The starting station. Cost
of going from one city to another in Rs. Is given below. Find the least cost route.
1
2
3
4
1
0
30
80
50
2
40
0
140
30
3
40
50
0
20
4
70
80
130
0
30. Solve the problem using graphical method.
Minimize Z= 40X1+36X2 Subject toX1≤ 8 ; X2 ≤ 10 ; 5X1+3X2+X3 ≥45 ;
X1,X2 ≥0
31.A canning company operates two canning plants. Three growers are willing to supply fresh
fruits in the following amount .Smith - 200tons @ Rs.10/ton; Jones - 300tons@ Rs.9/ton ;
Richard - 400 [email protected]/ton
Shipping costs in dollar per ton are
From
To
Plant a
Plant b
Smith
2
2.5
Jones
1
1.5
Richard
5
3
32.A company has built a new office building in order to centralise administration functions. Six
managers will be moved to the new office building. All the offices of the manager are on the
same floor. Other than exposure and view, all the offices are a like in room area facilities. As the
company was interested in pleasing as many managers as possible, the managers were asked to
rank their preferences for offices with 6 being the most desirable and 1 being the least
desirable. The following rankings were submitted by the managers.
Offices
Managers
01
02
03
04
05
06
M1
4
2
5
1
3
6
M2
2
3
5
1
4
6
M3
3
5
6
2
1
4
M4
2
4
6
1
3
5
M5
5
2
6
4
1
3
M6
2
6
3
5
1
4
Determine the assignment that will provide optimal satisfaction.
33. It is required to schedule five lectures on weekdays. It is required to make sure that the
schedule does not overlap conflicting with one another. It has been observed that because of
other close schedules, some participants (student) will be forced to drop out of these lectures.
The number of absentees has been shown in table, lecture wise and days wise.
Lectures
L1
L2
L3
L4
L5
Mon
3
2
3
10
11
Tue
12
5
10
11
3
Wed
1
3
9
2
4
Thu
9
12
11
6
2
Fri
9
7
6
7
10
Days
Use Hungarian method and schedule the lectures to reduce the number of participants forced
to remain absent.
34.There are three factories located at places P, Q, R. These factories supply products to
wholesale agents located at places S, T, W. The weekly capacities of the factories P, Q and R are
76, 82, 77 units respectively. The weekly requirements of the agents S, T, W are 72, 102, 41
units respectively. The unit transportation cost in rupees from P to S, T, W are 9, 16, 25
respectively.
Determine the following:
 Optimal transportation schedule,
 Minimum Cost of transportation,
 Is the solution Unique? Justify your answer.
Use the solution obtained by the least cost method to check for optimality.