BUS 660 –lecture aid
Introduction to Optimization Modeling
Introduction
The models covered thus far in this course have been descriptive, that is,they provide useful input to
decision making but do not quite provide the decision itself. This week's linear optimization modeling
technique is prescriptive in that it is normally used to determine the best decision, one that optimizes a
measurable objective under given quantitative constraints.
Linear optimization techniques are used to solve a wide array of optimization problems. This lecture
describes the general approach to setting up and solving linear optimization problems. Some common types
of problems are indicated that lend themselves to this modeling approach.
Understanding the theory and concepts behind linear programming can require one to use complex
mathematical reasoning. ExcelÂ© can be used to set up and solve linear optimization problems easily;
however, some basic math is still needed in order to set up the variables and constraints.
What is a Linear Optimization Model?
A linear optimization model essentially comprises:
1)
Variables
 whose values are to be determined
2)
Constraints
 that those variables are under
3) An
objective function
that is a linear combination of the variables and represents a measure (such as
profit, cost, resources, etc.) that is being optimized. Note that the word
optimize
is to be interpreted as
maximize or minimize
. Clearly, if the measure were profit, the desire is to maximize it. On the other hand, if
the measure were cost, the desire would typically be to minimize it.
A linear optimization model seeks to find those values of the variables that optimize (maximize or
minimize) the objective function, subject to certain constraints on the variables. It is important to note that
the constraints and the objective function need to be expressed in exact mathematical terms. Subjectivity
and intuition cannot be accommodated. This is a modeling technique that thrives on mathematical
precision.
The term
linear optimization
usually refers to
linear programming
or
integer programming
. In the latter
case, the variables can take on only integer values. For example, with a variable that represents
number of
workers assigned to machine A
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 Spring '10
 SheilaD.FournierBonilla
 Operations Research, Linear Programming, Optimization, Decision Making, $5, new owner

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