Name: Caraig, Jeuen Miko L. Reyes, Jean Jaucian B.

Score: ________________
_______________________________________________________________
Dadula,
Course/Year: BSMA
Darlyn
1-9S. Yebra, Nicole M.Room: _____________________
______________________________ Date: ___________________

Prof. Jeffrey A. Costales

Day: _____________________ Time: _____________________ Professor: _____________________________________

Exercise No. 1
Balanced Transportation Problem

I. Solve the following transportation problems:

1. Enriquez manufacturing company must ship its products from three plants to three warehouse. The weekly
production of the plants are 120, 75 and 55. The weekly requirements of the warehouses are 100, 90 and 60.
The shipping cost from each plant to the warehouse is given below:

Warehouses

Plants From/ To W1 W2 W3
P1 P9 P13 P7
P2 4 6 8
P3 6 5 10

Find the following:

a) The minimum cost transportation schedule using an initial basic feasible solution obtained
by each following methods:

(i). Northwest Corner Rule

To
From W1 W2 W3 Supply
9 13
P1 7 120
100 20

6 8
P2 4 75
70 5

10
P3 6 5 55
55

Demand
100 90 60 250

Cost = 100 (9) + 20 (13) + 70 (6) + 5 (8) + 55 (10)

= 900 + 260 + 420 + 40 + 550
= ₱ 2,170.00
(ii). Minimum Entry Method

To W1 W2 W3
From Supply
9 13 7
P1 120
25 35 60

4
P2 6 8 75
75

5 55
P3 6 10
55

Demand
100 90 60 250

Cost = 25 (9) + 35 (13) + 60 (7) + 75 (4) + 55 (5)

= 225 + 455 + 420 + 300 + 275
= ₱1,675.00

(iii). Vogel’s Approximation Method

To Row
From W1 W2 W3 Supply Difference
9 13 7
P1 25 35 60 120 2 4

P2 4 8
75 6 75 2

P3 6 5
55 10 55 1

Demand
100 90 60 250
Column
2 3 1 8 1 3
Difference

Cost = 25 (9) + 35 (13) + 60 (7) + 75 (4) + 55 (5)

= 225 + 455 + 420 + 300 + 275
= ₱1,675.00
 b. the optimal solution using Stepping Stone Method
Iteration 1
To
From W1 W2 W3 Supply
9 13
P1 7 120
100 20

6 8
P2 4 75
70 5

10
P3 6 5 55
55

Demand
100 90 60 250

Cost = 100 (9) + 20 (13) + 70 (6) + 5 (8) + 55 (10)

= 900 + 260 + 420 + 40 + 550
= ₱ 2,170.00
Cell Evaluation: P1W3 : 7 - 13 + 6 - 8 = -8
P2 W1 : 4 - 9 + 13 - 6 = 2
P3 W1 : 6 - 9 + 13 - 6 + 8 - 10 = 2
P3 W2: : 5 - 6 + 8 - 10 = -3

Iteration 2
To
From W1 W2 W3 Supply
9 13 7
P1 120
100 15 5

6
P2 4 8 75
75

P3 6 5 10 55
 55

Demand
100 90 60 250

Cost = 100 (9) + 15 (13) + 5 (7) + 75 (6) + 55 (10)

= 900 + 195 + 35 + 450 + 550
= ₱2,130.00

Cell Evaluation: P2 W1 : 4 - 6 + 13 - 9 = 2
P 2W3 : 8 – 7 + 13 – 6 = 8
P3 W1 : 6 – 10 + 7 – 9 = -6
P3 W2: : 5 – 10 + 7 – 13= -11

Iteration 3
To
From W1 W2 W3 Supply
9 7
P1 13 120
100 20

6
P2 4 8 75
75

5 10
P3 6 55
15 40

Demand
100 90 60 250

Cost = 100 (9) + 20 (7) + 75 (6) + 15 (5) + 40 (10)

= 900 + 140 + 450 + 75 + 400
= ₱1,965.00

Cell Evaluation: P1 W2 : 13 – 5 + 10 – 7 = 11
P 2 W1 : 4 – 6 + 5 – 10 + 7 – 9 = 9
P2 W3 : 8 – 10 + 5 – 6 = -3
P3 W1: : 6 – 10 + 7 – 9 = -6

Final Tableau
To
From W1 W2 W3 Supply
9 7
P1 13 120
60 60
 4 6
P2 8 75
40 35

5
P3 6 10 55
55

Demand
100 90 60 250

Cost = 60 (9) + 60 (7) + 40 (4) + 35 (6) + 55 (5)

= 540 + 420 + 160 + 210 + 275
= ₱1,605.00

Cell Evaluation: P1 W2 : 13 – 9 + 4 – 6 = 2
P 2 W3 : 8 – 4 + 9 – 7 = 6
P3 W1 : 6 – 5 + 6 – 4 = 3
P3 W3: : 10 – 5 + 6 – 4 + 9 – 7 = 9

Decision:

From To No. of Units for Shipment Cost/ Unit Shipment Cost

P1 W1 60 9 540

P1 W3 60 7 420

P2 W1 40 4 160

P2 W2 35 6 210

P3 W2 55 5 275

Total Cost ₱1,605.00

Name: Caraig, Jeuen Miko L. Reyes, Jean Jaucian B. Score: ________________
_______________________________________________________________
Dadula,
Course/Year: BSMA
Darlyn
1-9S. Yebra, Nicole M.Room: _____________________
______________________________ Date: ___________________

Prof. Jeffrey A. Costales

Day: _____________________ Time: _____________________ Professor: _____________________________________

Exercise No. 2
Unbalanced Transportation Problem
l. Solve the following transportation problems using Stepping Stone Method:
1.
To
From
W1 W2 W3 W4 Supply

P1 11 17 12 10 240

13
P2 12 14 16 280

P3 20 11 10 17 230

Demand
250 200 340 110 900 / 750
 To
From
W1 W2 W3 W4 Supply

P1 11 17 12 10 240

13
P2 12 14 16 280

P3 20 11 10 17 230

dummy

Demand
250 200 340 110 900 / 750