TRANSPORTATIONMODELS

LEARNINGOBJECTIVES

Identify or define: Transportation modeling Facility location analysis

Explain or be able to use: Northwest-corner rule Stepping-stone method

TRANSPORTATION MODELINGTransportation modeling finds the least-cost means of shipping supplies from several origins to several destinations.Key notes in using transportation modeling: The origin points and the capacity

or supply per period at each. The destination points and the

demand per period at each. The cost of shipping one unit from

each origin to each destination.

CASE STUDY ABC Inc. is a manufacturer of quality bathtubs. With these product growing in popularity in the home improvement industry, the Company wanted to penetrate the U.S. market and quickly expand its presence in the market place.

The Company opened three (3) production facilities and three (3) warehouses in selected areas in the country and wants to know the least-cost means of shipping finished products from production facilities to warehouses.

TRANSPORTATION PROBLEM OF ABC, INC.

Transportation Costs per bathtub for ABC Inc.

Albuquerque Boston Cleveland

Chicago $5 $4 $5Evansville $8 $4 $8Fort Lauderadale $9 $7 $9

FromTo

Albuquerque

(300 units required)

Chicago(100 units capacity)

Fort Lauderdale(300 units capacity)

Evansville(300 units capacity)

Cleveland(200 units required)

Boston(200 units required)

TRANSPORTATION MATRIX FOR ABC, INC.

Albuquerque Boston Cleveland Factory Capacity

Chicago 100

Evansville 300

Fort Lauderadale 300Warehouse requirement 300 200 200 700

FromTo

$5 $4 $3

$8 $4 $3

$9 $7 $5

Chicago capacity constraintCell representing a possible source-to-destination shipping assignment (Evansville to Cleveland)Total demand and total supply.Cleveland

warehouse supply.

Cost of shipping 1 unit from Fort Lauderadale to Boston warehouse

NORTHWEST-CORNER RULEThe Northwest-Corner rule requires that we start in the upper left-handed cell (or northwest corner) of the table and allocate units to shipping routes. 1. Exhaust the supply (factory

capacity) of each row before moving down to the next row.

Allocation Procedures:

2. Exhaust the (warehouse) requirements of each column before moving to the next column to the right.3. Check to ensure all supplies and demands are met.

Albuquerque Boston Cleveland Factory Capacity

Chicago 100 100

Evansville 200 100 300

Fort Lauderadale 100 200 300Warehouse requirement 300 200 200 700

FromTo

$5 $4 $3

$8 $4 $3

$9 $7 $5

$5

NORTHWEST-CORNER RULE

From ToChicago Albuquerque 100 $5 $500Evansville Albuquerque 200 8 1600Evansville Boston 100 4 400Fort Lauderadale Boston 100 7 700Fort Lauderadale Cleveland 200 5 1000

$4,200

Route Tubs shipped

Cost per Unit

Total Cost

Computed Shipping Cost

INTUITIVE LOWEST COST-METHODThe intuitive method makes initial allocations based on the lowest cost.

1. Identify the cell with the lowest cost. Break any ties for the lowest cost arbitrarily.

Allocation Procedures:

2. Allocate as many units as possible to that cell without exceeding the supply and demand. Then cross out that row or column (or both that is exhausted by this assignment.3. Find the cell with the lowest cost from the remaining (not crossed out) cells.4. Repeat steps 2 and 3 until all units have been allocated.

Albuquerque Boston Cleveland Factory Capacity

Chicago 100 100

Evansville 200 100 300

Fort Lauderadale 300 300Warehouse requirement 300 200 200 700

FromTo

$5 $4 $3

$8 $4 $3

$9 $7 $5

$5

INTUITIVE LOWEST COST-METHOD

Computed Shipping CostFrom ToChicago Cleveland 100 $3 $300Evansville Boston 200 4 800Evansville Cleveland 100 3 300Fort Lauderadale Albuqueque 300 9 2700

$4,100

Cost per Unit

Total Cost

Route Tubs shipped

STEPPING-STONE METHODAn iterative technique for moving from an initial feasible solution to an optimal solution in the transportation method.

The stepping-stone method is used to evaluate the cost effectiveness of shipping goods via transportation routes not currently in the solution.