Formulation Techniques Involving Transformations of Variables

Katta G. Murty ()
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Katta G. Murty: University of Michigan

Chapter Chapter 2 in Optimization for Decision Making, 2010, pp 39-125 from Springer

Abstract: Abstract Operations Research (OR) is the branch of science dealing with tools or techniques for decision making to optimize the performance of systems, that is, to make those systems better. Measures of performance, of which there may be several, are numerical criteria that gauge the quality of some aspect of system’s performance, for example, annual profit or market share of a company, etc. They are of two types: (1) profit measures: (for these, the higher the value the better), (2) cost measures: (for these the lower the value the better). OR deals with techniques for designing ways to operate the system to maximize profit measures or minimize cost measures as desired. Hence OR is the science to make systems better. Linear Programming (LP) is an important branch of OR dealing with decision problems modeled as those of optimizing a linear function of decision variables subject to linear constraints that may include equality constraints, inequality constraints, and bounds in decision variables. In an LP, all decision variables are required to be continuous variables that can assume all possible values within their bounds subject to the constraints. LPs are special instances of mathematical programming. Besides LP, the subject mathematical programming includes network, integer, combinatorial, discrete, quadratic, and nonlinear programming. The focus of this book is to study important aspects of LP and QP (quadratic programming) and their intelligent applications for decision making.

Date: 2010
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DOI: 10.1007/978-1-4419-1291-6_2

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