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Modeling by Object-Driven Linear Elemental Relations (MODLER) is a
computer language for representing linear programming models,
completely separate from instances defined by data realizations. It
also includes representations of binary variables and logical
constraints, which arise naturally in large-scale planning and
operational decision support. The basic input to MODLER is a model
file, and its basic output is a matrix file that is in a standard
(MPS) format for most optimizers and for ANALYZE and RANDMOD.
MODLER can also generate a syntax file for ANALYZE to enable
automatic translation of activities and constraints into English
for intelligent analysis support. The book is accompanied by a DOS
version of MODLER on 3.5 inch diskettes and A Laboratory Manual for
Teaching Linear Programming is available upon request.
Welcome to ANALYZE, designed to provide computer assistance for
analyzing linear programs and their solutions. Chapter 1 gives an
overview of ANALYZE and how to install it. It also describes how to
get started and how to obtain further documentation and help
on-line. Chapter 2 reviews the forms of linear programming models
and describes the syntax of a model. One of the routine, but
important, functions of ANALYZE is to enable convenient access to
rows and columns in the matrix by conditional delineation. Chapter
3 illustrates simple queries, like DISPLAY, LIST, and PICTURE. This
chapter also introduces the SUBMAT command level to define any
submatrix by an arbitrary sequence of additions, deletions and
reversals. Syntactic explanations and a schema view are also
illustrated. Chapter 4 goes through some elementary exercises to
demonstrate computer assisted analysis and introduce additional
conventions of the ANALYZE language. Besides simple queries, it
demonstrates the INTERPRT command, which automates the analysis
process and gives English explanations of results. The last 2
exercises are diagnoses of elementary infeasible instances of a
particular model. Chapter 5 progresses to some advanced uses of
ANALYZE. The first is blocking to obtain macro views of the model
and for finding embedded substructures, like a netform. The second
is showing rates of substitution described by the basic equations.
Then, the use of the REDUCE and BASIS commands are illustrated for
a variety of applications, including solution analysis,
infeasibility diagnosis, and redundancy detection."
The numerous advances in mathematical programming have opened up
new insights about sensitivity analysis. The paradigm What if...?'
question is no longer the only question of interest. Often, we want
to know Why...?' and Why not...?' Such questions were not analyzed
in the early years of mathematical programming to the same extent
that they are now, and we have not only expanded our thinking about
post-optimal analysis', but also about solution analysis', even if
the solution obtained is not optimal. Therefore, it is now time to
examine all the recent advances on sensitivity analysis and
parametric programming. This book combines the origins of
sensitivity analysis with the state of the art. It covers much of
the traditional approaches with a modern perspective, and shows
recent results using the optimal partition approach, stemming from
interior methods, for both linear and quadratic programming. It
examines the special case of network models. It presents a
neglected topic, qualitative sensitivity analysis, as well as
elements of mixed integer programming and gives a modern
perspective of nonlinear programming. It provides recent advances
in multi-criteria mathematical programming and also describes the
state-of-the-art in stochastic programming. It covers recent
advances in understanding redundancy in quadratic programs,
considers an approach to diagnosing infeasibility in linear and
nonlinear programs, and gives an overview of sensitivity analysis
for fuzzy mathematical programming.
Welcome to ANALYZE, designed to provide computer assistance for
analyzing linear programs and their solutions. Chapter 1 gives an
overview of ANALYZE and how to install it. It also describes how to
get started and how to obtain further documentation and help
on-line. Chapter 2 reviews the forms of linear programming models
and describes the syntax of a model. One of the routine, but
important, functions of ANALYZE is to enable convenient access to
rows and columns in the matrix by conditional delineation. Chapter
3 illustrates simple queries, like DISPLAY, LIST, and PICTURE. This
chapter also introduces the SUBMAT command level to define any
submatrix by an arbitrary sequence of additions, deletions and
reversals. Syntactic explanations and a schema view are also
illustrated. Chapter 4 goes through some elementary exercises to
demonstrate computer assisted analysis and introduce additional
conventions of the ANALYZE language. Besides simple queries, it
demonstrates the INTERPRT command, which automates the analysis
process and gives English explanations of results. The last 2
exercises are diagnoses of elementary infeasible instances of a
particular model. Chapter 5 progresses to some advanced uses of
ANALYZE. The first is blocking to obtain macro views of the model
and for finding embedded substructures, like a netform. The second
is showing rates of substitution described by the basic equations.
Then, the use of the REDUCE and BASIS commands are illustrated for
a variety of applications, including solution analysis,
infeasibility diagnosis, and redundancy detection.
Modeling by Object-Driven Linear Elemental Relations (MODLER) is a
computer language for representing linear programming models,
completely separate from instances defined by data realizations. It
also includes representations of binary variables and logical
constraints, which arise naturally in large-scale planning and
operational decision support. The basic input to MODLER is a model
file, and its basic output is a matrix file that is in a standard
(MPS) format for most optimizers and for ANALYZE and RANDMOD.
MODLER can also generate a syntax file for ANALYZE to enable
automatic translation of activities and constraints into English
for intelligent analysis support. The book is accompanied by a DOS
version of MODLER on 3.5 inch diskettes and A Laboratory Manual for
Teaching Linear Programming is available upon request.
The numerous advances in mathematical programming have opened up
new insights about sensitivity analysis. The paradigm 'What if...?'
question is no longer the only question of interest. Often, we want
to know 'Why...?' and 'Why not...?' Such questions were not
analyzed in the early years of mathematical programming to the same
extent that they are now, and we have not only expanded our
thinking about 'post-optimal analysis', but also about 'solution
analysis', even if the solution obtained is not optimal. Therefore,
it is now time to examine all the recent advances on sensitivity
analysis and parametric programming. This book combines the origins
of sensitivity analysis with the state of the art. It covers much
of the traditional approaches with a modern perspective, and shows
recent results using the optimal partition approach, stemming from
interior methods, for both linear and quadratic programming. It
examines the special case of network models. It presents a
neglected topic, qualitative sensitivity analysis, as well as
elements of mixed integer programming and gives a modern
perspective of nonlinear programming.It provides recent advances in
multi-criteria mathematical programming and also describes the
state-of-the-art in stochastic programming. It covers recent
advances in understanding redundancy in quadratic programs,
considers an approach to diagnosing infeasibility in linear and
nonlinear programs, and gives an overview of sensitivity analysis
for fuzzy mathematical programming.
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