Interactive Operations Research with Maple

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.