Interactive Operations Research with Maple: Methods and Models (Hardcover, 2000)

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.- 2.2.1 Expanding, Factoring and Simplifications.- 2.2.2 Function Definitions Using "-" and unapply ().- 2.2.3 Lists, Sets and Arrays.- 2.2.4 Additional Commands to Manipulate Expressions.- 2.2.5 Solving Equations Analytically.- 2.3 Numerics.- 2.3.1 Solving Equations Numerically.- 2.3.2 Statistical Computations Using the stats Package.- 2.3.3 The simplex Package.- 2.4 Graphics.- 2.4.1 Two-dimensional Plots.- 2.4.2 Three-Dimensional Plots.- 2.5 Other Useful Commands and Packages.- 2.5.1 The piecewise () Command.- 2.5.2 The interface () Command.- 2.5.3 The infolevel[] Command.- 2.5.4 Exporting to C, FORTRAN and LaTeX.- 2.5.5 Programming in Maple.- 2.5.6 The finance Package.- 2.6 Summary.- 2.7 Exercises.- 3 Maple and Mathematical Foundations of Operations Research.- 3.1 Introduction.- 3.2 Algebra.- 3.2.1 Solution of a Single Equation or Inequality.- 3.2.2 Solution of a System of Nonlinear Equations.- 3.3 Calculus.- 3.3.1 Limits.- 3.3.2 Derivatives.- 3.3.3 Integrals.- 3.3.4 Finite Sums and Infinite Series.- 3.4 Linear Algebra.- 3.4.1 Matrix Operations.- 3.4.2 Solution of Simultaneous Linear Equations.- 3.4.3 Eigenvalues, Eigenvectors and Diagonalization.- 3.4.4 Least Squares Fitting to Data.- 3.4.5 Special Matrices.- 3.4.6 Positive Definiteness.- 3.5 Differential Equations.- 3.5.1 Ordinary Differential Equations.- 3.5.2 Partial Differential Equations.- 3.5.3 Difference (Recurrence) Equations.- 3.6 Transform Methods.- 3.6.1 Laplace Transforms.- 3.6.2 Generating Functions.- 3.7 Probability.- 3.7.1 Continuous and Discrete Random Variables.- 3.7.2 Expectation.- 3.7.3 Jointly Distributed Random Variables.- 3.8 Summary.- 3.9 Exercises.- 4 Linear Programming.- 4.1 Introduction.- 4.2 Graphical Solution.- 4.3 The Simplex Method.- 4.3.1 Manual Solution of the Production Problem.- 4.3.2 Solution Using Maple's simplex Package.- 4.3.3 A Problem with Mixed Constraints.- 4.4 Special Cases and Difficulties.- 4.4.1 Infeasibility.- 4.4.2 Unbounded Solutions.- 4.4.3 Degeneracy.- 4.5 Other Examples.- 4.5.1 The Transportation Problem.- 4.5.2 Two-Person Zero-Stun Games.- 4.5.3 A Linear Program with Randomly Generated Data.- 4.6 Sensitivity Analysis and Duality.- 4.6.1 Changes in the RHS Values and Dual Prices.- 4.6.2 Changes in the Objective Function Coefficients.- 4.6.3 Addition of a New Decision Variable.- 4.6.4 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.- 5.2.1 Positive and Negative Definite Matrices.- 5.2.2 Convexity of a Function and Definiteness of its Hessian.- 5.2.3 Examples of Definiteness/Convexity.- 5.2.4 Cholesky Factorization.- 5.3 Unconstrained Optimization.- 5.4 Inequality and Equality Constrained Optimization.- 5.4.1 Geometric Interpretation of Kuhn-Tucker Conditions.- 5.4.2 Constraint Qualification.- 5.4.3 An Equivalent Formulation Using the Lagrangian.- 5.4.4 Economic Interpretation of the Lagrange Multipliers.- 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.- 6.3.1 The Infinite-Stage Problem.- 6.4 Continuous-Time Dynamic Programming.- 6.4.1 A Problem with Linear System and Quadratic Cost.- 6.4.2 A Problem with Quadratic and Linear Costs.- 6.5 A Constrained Work Force Planning Model.- 6.6 A Gambling Model with Myopic Optimal Policy.- 6.7 Optimal Stopping Problems.- 6.7.1 The Infinite-Stage Problem.- 6.8 Summary.- 6.9 Exercises.- 7 Stochastic Processes.- 7.1 Introduction.- 7.2 Exponential Distribution and Poisson Process.- 7.2.1 Memoryless Property of the Exponential Distribution.- 7.2.2 Hazard Rate Function.- 7.2.3 The Erlang Random Variable.- 7.2.4 Poisson Process.- 7.2.5 Interarrival Times of the Poisson Process.- 7.2.6 Density of t