H.J. Greenberg - Böcker

A primer to accompany a computer-assisted analysis system for mathematical programming models and solution called ANALYZE. ANALYZE is designed to provide computer assistance for analyzing linear programs and their solutions. Although this primer is self-contained, knowledge of linear programming is assumed. The exercises throughout the book show how to use ANALYZE to retrieve information, but it does not explicitly teach what information to obtain. The book is intended for people who already use linear programming. In the latter case, ANALYZE serves to support an LP laboratory, along with lectures, and the exercises need classroom discussion to guide the students. The book is accompanied by a DOS version of ANALYZE on 3.5" diskettes and "A Laboratory Manual for Teaching Linear Programming" is available on request.

Modelling by Object-Driver 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 field 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" diskettes and "A Laboratory Manual for Teaching Linear Programming" is available on 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 current developments in the field. 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. Also examined is the special case of network models. This text could also be said to present a neglected topic in qualitative sensitivity analysis, as well as elements of mixed integer programming, and to give 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.

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 standard view of Operations Research/Management Science (OR/MS) dichotomizes the field into deterministic and probabilistic (nondeterministic, stochastic) subfields.