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 Stochastic 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.
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"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 stochastic 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
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