Interactive Operations Research with Maple: Methods and Models - Brossura

Parlar, Mahmut

Brossura

ISBN 10: 146127110X ISBN 13: 9781461271109

Casa editrice: Birkhäuser, 2012

Riassunto

This work fills an important gap in the literature by providing an important link between MAPLE and its successful use in solving problems in Operations Research (OR). The symbolic, numerical, and graphical aspects of MAPLE make this software package an ideal tool for treating certain OR problems and providing descriptive and optimization-based analyses of deterministic and stochastic models. Detailed is MAPLE's treatment of some of the mathematical techniques used in OR modeling: e.g., algebra and calculus, ordinary and partial differential equations, linear algebra, transform methods, and probability theory. A number of examples of OR techniques and applications are presented, such as linear and nonlinear programming, dynamic programming, stochastic processes, inventory models, queueing systems, and simulation. Throughout the text MAPLE statements used in the solutions of problems are clearly explained. At the same time, technical background material is presented in a rigorous mathematical manner to reach the OR novice and professional. Numerous end-of- chapter exercises, a good bibliography and overall index at the end of the book are also included, as well as MAPLE worksheets that are easily downloadable from the author's website at www.business.mcmaster.ca/msis/profs/parlar, or from the Birkhauser website at www.birkhauser.com/cgi-win/ISBN/0-8176-4165-3. The book is intended for advanced undergraduate and graduate students in operations research, management science departments of business schools, industrial and systems engineering, economics, and mathematics. As a self-study resource, the text can be used by researchers and practitioners who want a quick overview of MAPLE's usefulness in solving realistic OR problems that would be difficult or impossible to solve with other software packages.

Su questo libro

Recensione

"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

Contenuti

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 the Erlang―An Equivalent Derivation.- 7.2.7 Nonhomogeneous Poisson Process.- 7.2.8 Compound Poisson Process.- 7.3 Renewal Theory.- 7.3.1 Preliminaries.- 7.3.2 Distribution of N(t).- 7.3.3 Renewal Function and Renewal Density.- 7.3.4 Renewal Equation and the Key Renewal Theorem.- 7.3.5 Renewal Reward Process.- 7.4 Discrete-Time Markov Chains.- 7.4.1 Chapman-Kolmogorov Equations.- 7.4.2 Limiting Probabilities and the Stationary Distribution.- 7.4.3 Classification of States.- 7.4.4 Imbedded Markov Chain Technique.- 7.4.5 Transient Behavior of Markov Chains.- 7.5 Continuous-Time Markov Chains.- 7.5.1 Kolmogorov Differential Equations.- 7.5.2 Limiting Probabilities.- 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.- 8.3.1 Procurement Cost.- 8.3.2 Holding (or Carrying) Cost.- 8.3.3 Penalty Cost.- 8.4 Deterministic Inventory Models.- 8.4.1 The Basic EOQ Model.- 8.4.2 The EOQ Model with Planned Backorders.- 8.4.3 Analysis of Implied Backorder Costs.- 8.4.4 Quantity Discounts.- 8.5 Probabilistic Inventory Models.- 8.5.1 The Continuous-Review Model: Approximate Formulation.- 8.5.2 The Continuous-Review Model: Exact Formulation.- 8.5.3 One-Period (Newsvendor) Model with Random Demand.- 8.5.4 Dynamic Inventory Models.- 8.5.5 Diversification Under Yield Randomness.- 8.6 Summary.- 8.7 Exercises.- 9 Queueing Systems.- 9.1 Introduction.- 9.2 Markovian Queueing Systems.- 9.2.1 Birth and Death Processes.- 9.2.2 M/M/1 Queueing System.- 9.2.3 Finite Capacity Markovian Queue: M/M/1/K.- 9.2.4 Multiserver Queue M/M/c.- 9.2.5 Markovian Bulk Arrival System: MX/M/1.- 9.3 Transient Solutions.- 9.3.1 Finite Capacity M/M/1/K Queue with K= 1.- 9.3.2 Ample Server System M/M/?.- 9.4 Queueing Networks.- 9.4.1 Serial Queue with Blocking.- 9.4.2 Jackson Networks.- 9.5 Optimization of Queueing Systems.- 9.5.1 A Transportation Queueing Process.- 9.5.2 An M/M/1 System with Controlled Arrivals.- 9.5.3 Optimal Dynamic Service Rate Control.- 9.6 Summary.- 9.7 Exercises.- 10 Simulation.- 10.1 Introduction.- 10.2 Generating (Pseudo-) Random Numbers.- 10.2.1 Mixed-Congruential Method.- 10.2.2 Maple’s Uniform Random Number Generator.- 10.2.3 Kolmogorov-Smirnov Test for Uniformity.- 10.3 Generating Random Variates from Other Distributions.- 10.3.1 Exponential Random Variates.- 10.3.2 Maple’s Random Variate Generators.- 10.4 Monte Carlo Simulation.- 10.4.1 Numerical Evaluation of Definite Integrals.- 10.4.2 Simulation of a Static (Single-Period) Problem.- 10.5 Dynamic Simulation Models.- 10.5.1 Simulation of an Inventory System with Random Yield.- 10.5.2 Simulation of a Non-Markovian Queue.- 10.6 Optimization by Random Search.- 10.7 Summary.- 10.8 Exercises.- References.

Dettagli dell'edizione

• Editore: Birkhäuser
• Data di pubblicazione: 2012
• Lingua: Inglese
• ISBN 10: 146127110X
• ISBN 13: 9781461271109
• Rilegatura: Copertina flessibile
• Numero di pagine: 488
• Contatto del produttore: non disponibile
• Persona responsabile: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Germania