Transportation models

1. TRANSPORTATION
MODELS

2. LEARNING OBJECTIVES
Identify or define:
 Transportation modeling
 Facility location analysis
Explain or be able to use:
 Northwest-corner rule
 Stepping-stone method

3. TRANSPORTATION MODELING
Transportation 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.

4. 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.

5. TRANSPORTATION PROBLEM OF ABC, INC.
Transportation Costs per bathtub for ABC Inc.
Albuquerque Boston Cleveland
Chicago $5 $4 $5
Evansville $8 $4 $8
Fort Lauderadale $9 $7 $9
From
To
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)

6. TRANSPORTATION MATRIX FOR ABC, INC.
Albuquerque Boston Cleveland
Factory
Capacity
Chicago 100
Evansville 300
Fort Lauderadale 300
Warehouse
requirement 300 200 200 700
From
To
$5 $4 $3
$8 $4 $3
$9 $7 $5
Chicago
capacity
constraint
Cell
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

7. NORTHWEST-CORNER RULE
The 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 100 200 300
Warehouse
requirement 300 200 200 700
From
To
$5 $4 $3
$8 $4 $3
$9 $7 $5
$5

8. NORTHWEST-CORNER RULE
From To
Chicago Albuquerque 100 $5 $500
Evansville Albuquerque 200 8 1600
Evansville Boston 100 4 400
Fort Lauderadale Boston 100 7 700
Fort Lauderadale Cleveland 200 5 1000
$4,200
Route Tubs
shipped
Cost per
Unit
Total
Cost
Computed Shipping Cost

9. INTUITIVE LOWEST COST-METHOD
The 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 300 300
Warehouse
requirement 300 200 200 700
From
To
$5 $4 $3
$8 $4 $3
$9 $7 $5
$5

10. INTUITIVE LOWEST COST-METHOD
Computed Shipping Cost
From To
Chicago Cleveland 100 $3 $300
Evansville Boston 200 4 800
Evansville Cleveland 100 3 300
Fort Lauderadale Albuqueque 300 9 2700
$4,100
Cost per
Unit
Total
Cost
Route Tubs
shipped

11. STEPPING-STONE METHOD
An 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.