Chapter 6
Transportation and Assignment
Problems
The Transportation Problem
• Given:
– Capacity of each source;
– Demand of each destination;
– Transportation cost to ship one unit from a
source to a destination.
• To find the most economical way of
satisfying the demands of the
destinations by using the resources.
A Transportation Example,
p.227-228 (234-235)
Suppliers
(Sources)
Demanders (Destinations)
Chicago
St. Louis Cincinnati
Capacities
of Suppliers
Kansas City
$6 /ton
$8 /ton
$10 /ton
150 tons
Omaha
$7 /ton
$11 /ton
$11 /ton
175 tons
Des Moines
$4 /ton
$5 /ton
$12 /ton
275 tons
200 tons
100 tons
300 tons
Demands of Demanders
How to satisfy the demands by using the sources with lowest total cost?
(That is: How many tons should be shipped from each source
to each destination?)
Solving Transportation Problem
• The solution method (algorithm) is
elegant. But, as business people, we
do not need to know the details since
computers can help us solve it.
• Use the ‘transportation module’ in
QM.
Total Supply and Total Demand
• Total supply is not necessary equal to
total demand.
• A dummy source or a dummy
destination appears in the QM result if
total supply is not equal to total
demand.
Dummy Source or Destination
• A dummy source in the result of QM
indicates an overall shortage, and at which
destinations shortages will occur.
• A dummy destination in the result of QM
indicates an overall surplus, and which
sources will have surpluses.
Prohibited Route
• If a route is prohibited to use, just set
the unit transportation cost of that route
to a very large number.
The Assignment Problem
• Given
– The cost (or efficiency index) for a
person to a job.
• To assign Y persons to Y jobs so that
the total cost is minimized or total
efficiency is maximized.
An Assignment example, p.240 (247)
Distances to drive for each official.
Official
(persons)
Raleigh
Game Sites (jobs)
Atlanta Durham Clemson
A
210
90
180
160
B
100
70
130
200
C
175
105
140
170
D
80
65
105
120
Solving Assignment Problem
• It is a special transportation problem
(why?), so it can be solved by using
‘Transportation Module’ in QM.
• More conveniently, we use the
‘Assignment Module’ in QM.
Assignment Problem vs.
Transportation Problem
• The assignment problem is a special case of
the transportation problem in which
demands of all destinations are 1, and
capacities of all sources are 1.