Thursday, 16 February 2012


Transportation Problems
Assignment II  (Part – B)
Q1.      A cement factory manager is considering the least way transport cement from his three manufacturing centers P,Q & R to depots A,B,C,D & E. The weekly production and demands along with transportation costs are given below. Apply VAM and MODI
A
B
C
D
E
Supply
P
4
1
3
4
4
60
Q
2
3
2
2
3
35
R
3
5
2
4
4
40
Demand
22
45
20
18
30
135
What should be the distribution programme ?
Answer: PB=45, PE=15, QA=17, QD=18, RA=5, RC=20, RE=15, Total Cost =290
Q2.      Solve the following problem with NWCM apply MODI method to test its optimality
A
B
C
Supply
W
4
8
8
56
X
16
24
16
82
Y
8
16
24
77
Demand
72
102
41
215
Answer: WB=56, XA=41, XC=41, YA=31, YB=46  Total Cost =2,744
Q3.      National Oil Company has three refineries and 4 depots. Transportation Costs per ton & Requirement are given below

D1
D2
D3
D4
Supply
P1
5
7
13
10
700
P2
8
6
14
13
400
P3
12
10
9
11
800
Demand
300
600
700
400

Determine optimal allocation of output.
Answer: Total Optimal Cost for transportation =14,700
Q4.      Obtain an optimal solution by MODI Method 

D1
D2
D3
D4
Supply
P1
19
30
50
10
7
P2
70
30
40
60
9
P3
40
8
70
20
18
Demand
5
8
7
14
34
Determine optimal allocation of output.
Answer: Total Optimal Cost for transportation =743
Q5.      Given below is a table taken from the solution process of transportation problem. Test it optimality by Apply stepping stone method



Factories

 Distribution Centers
1
2
3
4
Supply
A
10
8
7
12
5000
B
12
13
6
10
6000
C
8
10
12
14
9000
Demand
7000
5500
4500
3000
     20000
20000
Answer the following questions
1)                  Is this solution feasible?
2)                  Is this solution degenerate?
3)                  Is this solution optimal? If not fine the optimal solution
4)                  Does the problem have alternate optimal solution? If yes given another optimal solution.
Answer: A2=3500, A3=1500, B3=3000, B4=3000, C1=7000 , C2=2000 Total Cost =1,62,500
Q6.      Solve the following problem with NWCM apply MODI method to test its optimality
A
B
C
Supply
W
4
8
8
56
X
16
24
16
82
Y
8
16
24
77
Demand
72
102
41
215
Answer: WB=56, XA=41, XC=41, YA=31, YB=46  Total Cost =2,744
Q7.      National Oil Company has three refineries and 4 depots. Transportation Costs per ton & Requirement are given below

D1
D2
D3
D4
Supply
P1
5
7
13
10
700
P2
8
6
14
13
400
P3
12
10
9
11
800
Demand
300
600
700
400

Determine optimal allocation of output.
Answer: Total Optimal Cost for transportation =14,700


Q8.      Obtain an optimal solution by MODI Method 

D1
D2
D3
D4
Supply
P1
19
30
50
10
7
P2
70
30
40
60
9
P3
40
8
70
20
18
Demand
5
8
7
14
34
Determine optimal allocation of output.
Answer: Total Optimal Cost for transportation =743
Q9.      The following table shows all the necessary information on the availability of supply to each warehouse, the requirement of each market and unit transportation cost from each warehouse to each market.
P
Q
R
S
Supply
A
6
3
5
4
22
B
5
9
2
7
15
C
5
7
8
6
8
Demand
7
12
17
9
45
The shipping clerk has worked out the following schedule from experience 12 units form A to Q, 1 unit form A to R, 9 units from A to S, 15 units from B to R, 7 units from C to P and 1 unit from C to R
a)      Check and see if the clerk has optimal schedule   ANS : 150       
b)      Find the optimal schedule and minimum total transportation cost ANS : 149   

Q10.    A Company has factories at F1, F2, and F3 which supply to warehouses at W1, W2, and W3 weekly factory capacities are 200, 160 and 90 units respectively. Weekly warehouses requirement are 180, 120 & 150 units respectively. Units shipping cost in (rupees) are as follow. (Apply NWCM & MODI)
  
W1
W2
W3
Supply
F1
16
20
12
200
F2
14
8
18
160
F3
26
24
16
90
Demand
180
120
150
450
            Determine the optimal distribution for this company to minimize total shipping cost.
Answer: Total Optimal Cost for transportation =5920

Q11.    ABC Limited has three production shops supplying a product to five warehouses. The cost of production varies from shop to shop and cost of transportation from one shop to a warehouse also varies. Each shop has a specific production capacity and each warehouse has certain amount of requirement. The cost of transportation is as given below:
D1
D2
D3
D4
D5
Supply
P1
6
4
4
7
5
100
P2
5
6
7
4
8
125
P3
3
4
6
3
4
175
Demand
60
80
85
105
70

The cost of manufacture of the product at different production shops is
Shops/ costs
Variable cost
Fixed cost
A
14
7000
B
16
4000
C
15
5000





Find the optimum quantity to be supplied from each shop to different warehouses at minimum total cost.
Answer: Total Optimal Cost for transportation =23605
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8 comments:

  1. Unknown17 March 2019 at 00:40

    How have you done this the last questions? ?

    ReplyDelete
  2. Unknown12 June 2019 at 08:10

    how to solve question no 11

    ReplyDelete
  3. Unknown29 June 2019 at 10:46

    can anyone post the solving of question 11 please?

    ReplyDelete
  4. Arnab Kumar Patra19 September 2020 at 23:06

    where is the detailed answer

    ReplyDelete
  5. Unknown26 April 2021 at 01:26

    Can anyone send detailed ans of Q1 please?

    ReplyDelete
  6. atnafu lakew14 May 2021 at 22:46

    can i get the full solution for the assignment II part B

    ReplyDelete
  7. atnafu lakew14 May 2021 at 22:48

    assignment II part b please i need all the solution steps please

    ReplyDelete
  8. Unknown20 July 2021 at 11:30

    Please tell how to solve the 11 th problem

    ReplyDelete

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