Introduction to transportation model and steps in solving a transportation problem

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Transportation model deals with the distribution of goods from several sources (supply) to several destinations (demand).

Objective: To minimize total transportation cost (or maximize profit) Types of Transportation Problem Balanced transportation problem

Unbalanced transportation problem

Supply = Demand

Supply ≠ Demand

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Set up a transportation table

Find the initial solution

Find the optimal solution

R‐Women Company produces their products at three factories namely K, L, and M. Factory K produces 300 units of products per month while factory L and M each produces 200 units of products per month. The company distributes their products to three warehouses namely P, Q, and R. Every month, warehouse P, Q, and R make a request for 200, 400 and 100 units of products respectively. The table below shows the transportation costs rom each factory to each warehouse. Set up a transportation table for this problem.

From

To P

Q

R

K

2

5

9

L

7

3

6

M

4

8

3

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To

Q

P

From

K L M

Supply

2

5

9

7

3

6

4

8

3

400

200

Demand

R

300 200 200

100

Tinker Bell Company produces their products at three factories namely X, Y, and Z. Factory X and Y produce 300 units of products each in a month while factory Z produces 100 units of products. The company distributes their products to three warehouses K, L, and M. Every month, each warehouse makes a request for 200 units of products. The table below shows the transportation costs rom each factory to each warehouse. Set up a transportation table for this problem.

From

To K

L

M

X

4

2

8

Y

7

3

5

Z

2

6

9

3

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To From

K

L

M

Dummy

Supply

X

4

2

8

0

300

Y

7

3

5

0

300

Z

2

6

9

0

100

Demand

200

200

200

100

Add a dummy column with zero transportation cost and the insufficient demand amount.

Maleficent Company produces their products at three factories namely A, B, and C. Factory A and B produce 200 units of products each in a month while factory C produces 700 units of products. The company distributes their products to three warehouses namely D, E, and F. Every month, warehouse D, E, and F make a request for 400, 500 and 400 units of products respectively. The table below shows the transportation costs rom each factory to each warehouse. Set up a transportation table for this problem.

From

To D

E

F

A

4

9

5

B

4

2

4

C

8

7

3

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To From

D

E

F

Supply

A

4

9

5

200

B

4

2

4

200

C

8

7

3

700

Dummy

0

0

0

200

Demand

400

500

400

Add a dummy row with zero transportation cost and the insufficient supply amount.

Steps in Northwest corner method: 1. Begin at the first square in the table. Look at the corresponding supply and demand value and choose the smallest value. Assign the smallest value to the square. Cross the supply and demand values and write the remaining amount.

2. Move to the next square (either to the right or down depending on which one has the remaining amount from the previous step) and repeat the same thing as in the first square.

3. Repeat the process until the last square is reached and all supply and demand values are satisfied.

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Steps in MODI method: 1. Set R1 = 0.

2. Calculate all R and K values by using formula R+K=C, where C is the transportation cost. This formula is only applied to used squares.

3. Calculate improvement index, I, for all unused squares by using formula I=C – R – K. 4. For minimization problem, the optimal solution is reached when all I ≥ 0. For maximization problem, the optimal solution is reached when all I ≤ 0.

5. If an optimal solution has not yet been reached, draw a loop for the square with the most negative improvement index value (for minimization problem) or the square with the most positive improvement index value (for maximization problem). To draw the loop, bear in mind that: * you can only move horizontally or vertically. * you can only make a stop at a used square. * if you make a stop, when you want to move again, you must change the direction of your movement. * you must put plus and minus sign alternately at the squares that you make a stop.

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6. Get ready with a new table. Look at the loop, look at the squares with minus sign and look at the values assigned to the squares. Choose the smallest value. At the new table, add this smallest value to the assigned values at the squares with plus sign and subtract this smallest value from the assigned values at the squares with minus sign.

7. Repeat step 1.

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