Turban, Aronson, and Liang
Decision Support Systems and Intelligent Systems,
Seventh Edition
Chapter 4
Modeling and Analysis
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
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MSS Mathematical Models
• Link decision variables, uncontrollable
variables, and result variables together
• decision variables, uncontrollable variables
are the parameters while result variables
are the outcomes which considered as
dependent variables.
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
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MSS Mathematical Models
– Decision variables describe alternative choices
they could be people, time and schedules.
– Uncontrollable variables are outside decisionmaker’s control these factors con be fixed, in
which case they are called parameters and they
can vary.
– Fixed factors are parameters.
– Intermediate outcomes produce intermediate
result variables.
– Result variables are dependent on chosen
solution and uncontrollable variables.
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
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MSS Mathematical Models
Non-quantitative models // like employee
satisfaction (intermediate outcome), which
in turn determines the productivity level
(final result)
– Symbolic relationship
– Qualitative relationship
– Results based upon
• Decision selected
• Factors beyond control of decision maker
• Relationships amongst variables
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Turban, Aronson, and Liang
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© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
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© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
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The structure of MSS Mathematical Models
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Mathematical Programming optimization
• Tools for solving managerial problems
• Decision-maker must allocate resources
amongst competing activities
• Optimization of specific goals
• Linear programming is the best known
technique in a family of optimization tools called
mathematical programming.
– Consists of decision variables, objective function and
coefficients, uncontrollable variables (constraints),
capacities, input and output coefficients
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
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Mathematical Programming optimization
linear programming
Mathematical programming is a family of tools designed
to help solve the managerial problems in which the
decision-maker must allocate scarce resources among
competitive activities to optimize a measurable goal.
Ex. The distribution of machine time (the resource)
among various products (the activities) is a typical
allocation problem. Linear programming (LP) allocation
problems usually the following characteristics.
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
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Mathematical Programming optimization
linear programming
LP Characteristics:
• A limited quantity of economic resources is available
for allocation.
• The resources are used in the production of products
or services.
• There are two or more ways in which the resources
can be used. Each is called a solution or a program.
• Each activity (product or service) in which the
resources are used yields a return in terms of the
stated goal.
• The allocation is usually restricted by several
limitations & requirements called constraints.
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
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Mathematical Programming optimization
linear programming
LP allocation model is based on the following rational
economic assumptions:
• Return from different allocation can be measured &
compared.
• The return from any allocation is independent of other
allocations.
• The total return is the sum of the returns yielded by the
different activities.
• All data are known with certainty.
• The resources are to be used in the most economical
manner.
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
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Mathematical Programming optimization
linear programming
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
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Mathematical Programming optimization
The most common optimization models can be solved by
a variety of mathematical programming methods, they are:
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
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End of Chapter 4
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
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