1
Leung/MS3053/Fall2012
MS 3053
Logistics Management 3
Distribution System Design: An Application of Integer Programming
In the previous lectures, we examined the conceptual background of logistics
management.
Then, we learned how to formulate and interpret the results (solutions) of
the transportation and the transshipment problems.
In this class, we look at how to
design a distribution system through the use of binary integer programming.
Much of the modeling flexibility provided by integer programming is due to the use of 0-
1 variables.
In many scenarios, 0-1 variables provide selections or choices with the value
of the variable equal to 1 if a corresponding activity is undertaken and equal to 0 if the
corresponding activity is not undertaken.
For example, variable y is equal to 1 if a
distribution center is constructed in the north side of San Antonio.
Variable y is equal to
0 if the center is not constructed.
Please keep in mind that not all decision variables in
the logistic model are binary.
Some of them are pure integers (0, 1, 2, 3, ….)
Example
GE operates a plant in St. Louis with an annual capacity of 30,000 units.
Product is
shipped to regional distribution centers located in Boston, Atlanta, and Houston.
Because
of an anticipated demand, GE plans to increase capacity by constructing a new plant in
one or more
of the following cities: Detroit, Toledo, Denver, or Kansas City.
The
estimated annual fixed cost and the annual capacity for the four proposed plants are as
follows:
Proposed Plant
Annual Fixed Cost
Annual Capacity (units)
Detroit
$175,000
10,000
Toledo
$300,000
20,000
Denver
$375,000
30,000
Kansas City
$500,000
40,000
The company’s sales department developed forecasts of the anticipated annual demand
at the distribution centers as follows:
Distribution Center
Annual Demand (units)
Boston
30,000
Atlanta
20,000
Houston
20,000