Interactive Operations Research with Maple: Methods and Models / Edition 1

by Mahmut Parlar

Overview

Interactive Operations Research with Maple: Methods and Models has two ob­ jectives: to provide an accelerated introduction to the computer algebra system Maple and, more importantly, to demonstrate Maple's usefulness in modeling and solving a wide range of operations research (OR) problems. This book is written in a format that makes it suitable for a one-semester course in operations research, management science, or quantitative methods. A nwnber of students in the departments of operations research, management science, oper­ ations management, industrial and systems engineering, applied mathematics and advanced MBA students who are specializing in quantitative methods or operations management will find this text useful. Experienced researchers and practitioners of operations research who wish to acquire a quick overview of how Maple can be useful in solving OR problems will find this an excellent reference. Maple's mathematical knowledge base now includes calculus, linear algebra, ordinary and partial differential equations, nwnber theory, logic, graph theory, combinatorics, statistics and transform methods. Although Maple's main strength lies in its ability to perform symbolic manipulations, it also has a substantial knowledge of a large nwnber of nwnerical methods and can plot many different types of attractive-looking two-dimensional and three-dimensional graphs. After almost two decades of continuous improvement of its mathematical capabilities, Maple can now boast a user base of more than 300,000 academics, researchers and students in different areas of mathematics, science and engineering.

Product Details

ISBN-13:	9780817641658
Publisher:	Birkh�user Boston
Publication date:	07/19/2000
Edition description:	2000
Pages:	468
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

1 Introduction to Operations Research.- 1.1 A Brief History.- 1.2 The Method of OR.- 1.3 About This Book.- 2 A Quick Tour of Maple.- 2.1 Introduction.- 2.2 Symbolics.- 2.3 Numerics.- 2.4 Graphics.- 2.5 Other Useful Commands and Packages.- 2.6 Summary.- 2.7 Exercises.- 3 Maple and Mathematical Foundations of Operations Research.- 3.1 Introduction.- 3.2 Algebra.- 3.3 Calculus.- 3.4 Linear Algebra.- 3.5 Differential Equations.- 3.6 Transform Methods.- 3.7 Probability.- 3.8 Summary.- 3.9 Exercises.- 4 Linear Programming.- 4.1 Introduction.- 4.2 Graphical Solution.- 4.3 The Simplex Method.- 4.4 Special Cases and Difficulties.- 4.5 Other Examples.- 4.6 Sensitivity Analysis and Duality.- 4.7 Integer Linear Programming.- 4.8 Summary.- 4.9 Exercises.- 5 Nonlinear Programming.- 5.1 Introduction.- 5.2 Convexity of Sets and Functions.- 5.3 Unconstrained Optimization.- 5.4 Inequality and Equality Constrained Optimization.- 5.5 Lagrangian Duality.- 5.6 Summary.- 5.7 Exercises.- 6 Dynamic Programming.- 6.1 Introduction.- 6.2 Stagecoach Problem.- 6.3 Models with a Linear System and Quadratic Cost.- 6.4 Continuous-Time Dynamic Programming.- 6.5 A Constrained Work Force Planning Model.- 6.6 A Gambling Model with Myopic Optimal Policy.- 6.7 Optimal Stopping Problems.- 6.8 Summary.- 6.9 Exercises.- 7 Shastic Processes.- 7.1 Introduction.- 7.2 Exponential Distribution and Poisson Process.- 7.3 Renewal Theory.- 7.4 Discrete-Time Markov Chains.- 7.5 Continuous-Time Markov Chains.- 7.6 Summary.- 7.7 Exercises.- 8 Inventory Models.- 8.1 Introduction.- 8.2 Classification of Inventory Models.- 8.3 Costs Associated with Inventory Models.- 8.4 Deterministic Inventory Models.- 8.5 Probabilistic Inventory Models.- 8.6 Summary.- 8.7 Exercises.- 9 Queueing Systems.- 9.1 Introduction.- 9.2 MarkovianQueueing Systems.- 9.3 Transient Solutions.- 9.4 Queueing Networks.- 9.5 Optimization of Queueing Systems.- 9.6 Summary.- 9.7 Exercises.- 10 Simulation.- 10.1 Introduction.- 10.2 Generating (Pseudo-) Random Numbers.- 10.3 Generating Random Variates from Other Distributions.- 10.4 Monte Carlo Simulation.- 10.5 Dynamic Simulation Models.- 10.6 Optimization by Random Search.- 10.7 Summary.- 10.8 Exercises.- References.

Editorial Reviews

"This book is unique in that it is the only one that uses MAPLE^®’s abilities to solve OR problems, many of which would be impossible to solve with other software. Many problems in shastic processes, queueing theory, inventory, etc., are now easy to tackle using MAPLE^®’s symbolic manipulation capabilities."

-The MAPLE^® Reporter

"Almost every MAPLE^® statement used in the solution of a problem is clearly explained. At the same time, technical background material is presented in a mathematical manner to reach the OR novice and professional. All MAPLE^® worksheets are downloadable form the author's website at www.business.mcmaster.ca/msis/profs/parlar"

-Simulation News Europe

From the Publisher