Chapter 9
Transportation, Assignment,
Network Models
A Transportation Example, p.325
Suppliers
(Sources)
Demanders (Destinations)
Albuquerque
Boston Cleveland
Capacities
of Suppliers
Des Moines
$5/unit
$4/unit
$3/unit
100 units
Evansville
$8/unit
$4/unit
$3/unit
300 units
Fort Lauderdale
$9/unit
$7/unit
$5/unit
300 units
300 units
200 units
200 units
Demands of Demanders
How to satisfy demands by using the sources with minimized total cost?
(That is: How many units should be shipped from each source
to each destination?)
The Transportation Problem
• To find the most economical way of
allocating m sources to n destinations.
• Given:
– Capacity of each source;
– Demand of each destination;
– Transportation cost to ship one unit from a source
to a destination.
Solving Transportation Problem
• The methods in textbook 9.5, and 9.6 are
for doing by hand.
– Do not worry about them.
• Management users use computer software
‘QM for Windows’. (p.360-362)
– We use this method!
Unbalanced Transp. Problem
• Where total supply ≠ total demand
• Solve the problem same way as for the
balanced transportation problem
• Dummy source / dummy destination
Prohibited Route
• If a route is prohibited to use, just set the
unit transportation cost of that route to a
large number.
Facility Location Analysis by
Using Transportation Model
• If a new facility (a plant or a warehouse for
example) is to be added to an existing
transportation system, then the
transportation model can be used in
decision making on the location of the new
facility by evaluating the alternatives of the
new facility location.
Example p.327-328
• A new plant is to be added to an existing
system (Table 9.1).
• Two alternatives for the new plant: Seattle
and Birmingham.
• Unit shipping cost from plants to
warehouses are in Table 9.2.
Example (continued)
• We need to run the transportation model
twice to evaluate:
– The total production/shipment cost if the new
facility were placed in Seattle;
– The total production/shipment cost if the new
facility were placed in Birmingham.
• Then, select the alternative with the lower
total cost.
The Assignment Problem
• To assign m persons to m jobs.
• Given
– The cost (or efficiency index) for a person
to do a job.
An Example of Assignment Problem, p.330
Costs of doing projects
Projects
2
Persons
1
3
Adams
$
11
$
14
$
6
Brown
$
8
$
10
$
11
Cooper
$
9
$
12
$
7
Solving Assignment Problem
• It can be solved conveniently by using
the ‘Assignment module’ in computer
software “QM for Windows”.
• It is a special transportation problem.
An Example of Assignment Problem
Driving distances (miles) for the officials
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
What Is a Network
• A network is composed of nodes and arcs.
Maximum Flow Problem
• Given flow-capacities between nodes,
find the maximum amount of flows from
the origin node to the destination node.
• Applications: Capacity of traffic flows
between two points of a city.
• Example: p.335
Shortest Route Problem
• Given distances (costs) between nodes,
find the shortest route between any pair
of nodes.
• Applications: Find the shortest route from
one place to another.
• Example: p.337
Minimum Spanning Tree
Problem
• Given costs (distances) between nodes,
find a network (actually a “tree”) that
covers all the nodes with minimum total
cost.
• Applications: Planning water pipe, power
cable, or phone line to the residents in a
community.
• Example: p.338
What You Need to Know
• For each of the five models:
– What is the model? (what are given and what is to
calculate)
– What is the model for? (Applications)
– Solve it by QM
• You do not need to know the solution
technique since QM does it for us.
• But given an application, you should tell which
model fit the application and solve it by QM.