Schaum's Outline of Operations Research

, by Bronson, Richard; Naadimuthu, Govindasami

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ISBN: 9780070080201 | 0070080208
Cover: Paperback
Copyright: 7/22/1997

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Tackling the broad range of allocation problems that actually confront engineers, programmers and analysts in today's business and industrial worlds, this book takes readers step-by-step through all the mathematical programming techniques--including the trailblazing Karmarkar algorithm--needed to excel in any operations research course. It's easy to see why the first edition of this invaluable study guide sole more than 35,000 copies! It cuts down study time while it builds essential skills.

Chapter 1 MATHEMATICAL PROGRAMMING Optimization problems. Linear programs. Integer programs. Quadratic programs. Problem formulation. Solution convention.

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Chapter 2 LINEAR PROGRAMMING: BASIC CONCEPTS Nonnegativity conditions. Slack variables and surplus variables. Generating an initial feasible solution. Penalty costs. Standard form. Linear dependence and independence. Convex combinations. Convex sets. Extreme-point solutions. Basic feasible solutions.

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Chapter 3 LINEAR PROGRAMMING: THE SIMPLEX AND THE DUAL SIMPLEX METHODS The simplex tableau. A tableau simplification. The simplex method. Modifications for programs with artificial variables. The dual simplex method.

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Chapter 4 LINEAR PROGRAMMING: DUALITY AND SENSITIVITY ANALYSIS Symmetric duals. Dual solutions. Unsymmetric duals. Sensitivity analysis.

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Chapter 5 LINEAR PROGRAMMING: EXTENSIONS The revised simplex method. Karmarkar's algorithm. Summary of Karmarkar's iterative procedure. Transforming a linear programming problem into Karmarkar's special form.

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Chapter 6 INTEGER PROGRAMMING: BRANCH-AND-BOUND ALGORITHM First approximation. Branching. Bounding. Computational considerations.

124

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Chapter 7 INTEGER PROGRAMMING: CUT ALGORITHMS The Gomory algorithm. Computational considerations.

133

(7)

Chapter 8 INTEGER PROGRAMMING: THE TRANSPORTATION ALGORITHM Standard form. The transportation algorithm. An initial basic solution. Test for optimality. Improving the solution. Degeneracy.

140

(15)

Chapter 9 INTEGER PROGRAMMING: SCHEDULING MODELS Production problems. Transshipment problems. Assignment problems. The traveling salesperson problem.

155

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Chapter 10 NONLINEAR PROGRAMMING: SINGLE-VARIABLE OPTIMIZATION The problem. Local and global optima. Results from calculus. Sequential search techniques. Three-point interval search. Fibonacci search. Goldenmean search. Convex functions.

169

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Chapter 11 NONLINEAR PROGRAMMING: MULTIVARIABLE OPTIMIZATION WITHOUT CONSTRAINTS Local and global maxima. Gradient vector and Hessian matrix. Results from calculus. The method of steepest ascent. The Newton-Raphson method. The Fletcher-Powell method. Hooke-Jeeves' pattern search. A modified pattern search. Choice of an initial approximation. Concave functions.

182

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Chapter 12 NONLINEAR PROGRAMMING: MULTIVARIABLE OPTIMIZATION WITH CONSTRAINTS Standard forms. Lagrange multipliers. Newton-Raphson method. Penalty functions. Kuhn-Tucker conditions. Method of feasible directions.

198

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Chapter 13 NETWORK ANALYSIS Networks. Minimum-span problems. Shortest-route problems. Maximal-flow problems. Finding a positive-flow path.

216

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Chapter 14 PROJECT PLANNING USING PERT/CPM PERT/CPM. Construction of the network (arrow) diagram. Critical path computations for CPM. Critical path computations for PERT. Project time vs project cost.

231

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Chapter 15 INVENTORY MODELS Inventory. Fixed order quantity models. Fixed order period models. Single period models.

259

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Chapter 16 FORECASTING Forecasting. Regression methods. Simplex linear regression. Coefficients of correlation and determination. Standard error of estimate. Special case: logarithmic (exponential) models. Multiple regression. Smoothing methods. Moving averages. Weighted moving averages. Exponential smoothing. Exponential smoothing with trend (trend-adjusted exponential smoothing). Forecast accuracy. Forecasting time series with multiplicative model.

281

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Chapter 17 GAME THEORY Games. Strategies. Stable games. Unstable games. Solution by linear programming. Dominance.

312

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Chapter 18 DECISION THEORY Decision processes. Native decision criteria. A priori criterion. A posteriori criterion. Decision trees. Utility. Lotteries. Von Neumann utilities.

325

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Chapter 19 DYNAMIC PROGRAMMING Multistage decision processes. A mathematical program. Dynamic programming. Dynamic programming with discounting. Stochastic multistage decision processes. Policy tables.

342

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Chapter 20 FINITE MARKOV CHAINS Markov processes. Powers of stochastic matrices. Ergodic matrices. Regular matrices.

369

(10)

Chapter 21 MARKOVIAN BIRTH-DEATH PROCESSES Population growth processes. Generalized Markovian birth-death processes. Linear Markovian birth processes. Linear Markovian death processes. Linear Markovian birth-death processes. Poisson birth processos. Poisson death processes. Poisson birth-death processes.

379

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Chapter 22 QUEUEING SYSTEMS Introduction. Queue characteristics. Arrival patterns. Service patterns. System capacity. Queue disciplines. Kendall's notation.

391

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Chapter 23 M/M/1 SYSTEMS System characteristics. The Markovian model. Steady-state solutions. Measures of effectiveness.

398

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Chapter 24 OTHER SYSTEMS WITH POISSON-TYPE INPUT AND EXPONENTIAL-TYPE SERVICE TIMES State-dependent processes. Little's formulas. Balking and reneging. M/M/s systems. M/M/1/K systems. M/M/s/K systems.

407

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ANSWERS TO SUPPLEMENTARY PROBLEMS

422

(31)

INDEX

453

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Schaum's Outline of Operations Research

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Table of Contents

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