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The Transportation Models

The Transportation Models

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Page 1: The Transportation Models

The Transportation Models

Page 2: The Transportation Models

Transportation model is one of the class of linear programming models, so named because of the linear relationships among variables in transportation model, transportation cost are treated as a direct linear function of the number of units shipped.

Page 3: The Transportation Models

Transportation models can be used to determine how to allocate the supplies available from various factories to the warehouses that stock or demand those goods, in such a way that total shipping cost (time, distance) is minimized.

The shipping (supply) points can be factories, warehouses, department or any other place from which goods are sent.

The destination (demand) can be factories, warehouses, departments or other place that receive goods.

Page 4: The Transportation Models

Major assumptions for the transportation model

1. The items to be shipped are homogeneous.2. Shipping cost per unit is the same regardless of the number of units shipped.3. There is only one route or mode of transportation being used between each source and each destination.

Page 5: The Transportation Models

The information needed to use the model

1. A list of the origins and each one’s capacity or supply quantity per period2. A list of the destinations and each one’s demand per period3. The unit cost of shipping items from each origin to each destination.

Page 6: The Transportation Models

The transportation model starts with the development of a feasible solution, which is then sequentially tested and improved until an optimal solution is obtained.

Page 7: The Transportation Models

Major Steps

1.Obtaining an initial solution2.Testing the solution for optimality3.Improving sub optimal solution

Page 8: The Transportation Models

Approaches

1. Intuitive Lowest cost approach2. North West Corner stepping stone method3. Modified Transportation Approach

Page 9: The Transportation Models

With the intuitive approach, cell allocations are made according to cell cost, beginning with the lowest cost. The procedure involves these steps:

Intuitive Lowest-Cost Method

Page 10: The Transportation Models

Intuitive Lowest-Cost Method

1. Identify the cell with the lowest cost2. Allocate as many units as possible to that cell

without exceeding supply or demand; then cross out the row or column (or both) that is exhausted by this assignment

3. Find the cell with the lowest cost from the remaining cells

4. Repeat steps 2 and 3 until all units have been allocated

Page 11: The Transportation Models

Intuitive Lowest-Cost Method

To

From Albuquerque Boston Cleveland

Des Moines $5 $4 $3

Evansville $8 $4 $3

Fort Lauderdale $9 $7 $5

Page 12: The Transportation Models

Intuitive Lowest-Cost Method

Albuquerque(300 unitsrequired)

Des Moines(100 unitscapacity)

Evansville(300 unitscapacity)

Fort Lauderdale(300 unitscapacity)

Cleveland(200 unitsrequired)

Boston(200 unitsrequired)

Figure C.1

Page 13: The Transportation Models

Transportation Matrix

From

ToAlbuquerque Boston Cleveland

Des Moines

Evansville

Fort Lauderdale

Factory capacity

Warehouse requirement

300

300

300 200 200

100

700

$5

$5

$4

$4

$3

$3

$9

$8

$7

Cost of shipping 1 unit from FortLauderdale factory to Boston warehouse

Des Moinescapacityconstraint

Cell representing a possible source-to-destination shipping assignment (Evansville to Cleveland)

Total demandand total supply

Clevelandwarehouse demand

Figure C.2

Page 14: The Transportation Models

Intuitive Lowest-Cost MethodTo (A)

Albuquerque(B)

Boston(C)

Cleveland

(D) Des Moines

(E) Evansville

(F) Fort Lauderdale

Warehouse requirement 300 200 200

Factory capacity

300

300

100

700

$5

$5

$4

$4

$3

$3

$9

$8

$7

From

100

First, $3 is the lowest cost cell so ship 100 units from Des Moines to Cleveland and cross off the first row as Des Moines is satisfied

Figure C.4

Page 15: The Transportation Models

Intuitive Lowest-Cost MethodTo (A)

Albuquerque(B)

Boston(C)

Cleveland

(D) Des Moines

(E) Evansville

(F) Fort Lauderdale

Warehouse requirement 300 200 200

Factory capacity

300

300

100

700

$5

$5

$4

$4

$3

$3

$9

$8

$7

From

100

100

Second, $3 is again the lowest cost cell so ship 100 units from Evansville to Cleveland and cross off column C as Cleveland is satisfied

Figure C.4

Page 16: The Transportation Models

Intuitive Lowest-Cost MethodTo (A)

Albuquerque(B)

Boston(C)

Cleveland

(D) Des Moines

(E) Evansville

(F) Fort Lauderdale

Warehouse requirement 300 200 200

Factory capacity

300

300

100

700

$5

$5

$4

$4

$3

$3

$9

$8

$7

From

100

100

200

Third, $4 is the lowest cost cell so ship 200 units from Evansville to Boston and cross off column B and row E as Evansville and Boston are satisfied

Figure C.4

Page 17: The Transportation Models

Intuitive Lowest-Cost MethodTo (A)

Albuquerque(B)

Boston(C)

Cleveland

(D) Des Moines

(E) Evansville

(F) Fort Lauderdale

Warehouse requirement 300 200 200

Factory capacity

300

300

100

700

$5

$5

$4

$4

$3

$3

$9

$8

$7

From

100

100

200

300

Finally, ship 300 units from Albuquerque to Fort Lauderdale as this is the only remaining cell to complete the allocations

Figure C.4

Page 18: The Transportation Models

Intuitive Lowest-Cost MethodTo (A)

Albuquerque(B)

Boston(C)

Cleveland

(D) Des Moines

(E) Evansville

(F) Fort Lauderdale

Warehouse requirement 300 200 200

Factory capacity

300

300

100

700

$5

$5

$4

$4

$3

$3

$9

$8

$7

From

100

100

200

300

Total Cost = $3(100) + $3(100) + $4(200) + $9(300)= $4,100

Figure C.4

Page 19: The Transportation Models

Intuitive Lowest-Cost MethodTo (A)

Albuquerque(B)

Boston(C)

Cleveland

(D) Des Moines

(E) Evansville

(F) Fort Lauderdale

Warehouse requirement 300 200 200

Factory capacity

300

300

100

700

$5

$5

$4

$4

$3

$3

$9

$8

$7

From

100

100

200

300

Total Cost = $3(100) + $3(100) + $4(200) + $9(300)= $4,100

Figure C.4

This is a feasible solution, and an improvement over the previous solution,

but not necessarily the lowest cost alternative