## Operations Research: An IntroductionWith an emphasis placed on the formulation and applications aspects, this text provides coverage of the theory, applications and computations of operations research techniques. Numerical examples are the main vehicle for explaining new ideas, with each numeric example followed by a set of problems. This edition contains much new material, including: Floyd's shortest route algorithm, goal programming, analytic hierarchy approach, review of propability, probabilistic DP, and simulation modelling, as well as updated versions of TORA software and the simulation language SIMNET II. More than 1,000 problems are examined in the text. |

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### Contents

OVERVIEW OF OPERATIONS RESEARCH | 1 |

INTRODUCTION TO LINEAR PROGRAMMING | 11 |

THE SIMPLEX METHOD | 67 |

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activity artificial variable associated assuming basic solution basic variables capacity changes column computations constraint convex combination convex set current solution daily defined demand Determine the optimal dual prices dual problem dynamic programming entering variable equations Example exterior paint extreme points flow following LP following table Formulate the problem given goal programming holding cost increase infeasible integer inventory Karmarkar's algorithm leaving variable linear program LP model machine matrix Maximize maximum Minimize minimum network flow node nonbasic variables nonnegative objective coefficients objective function objective value operation optimum solution period primal Problem set production cost raw material Reddy Mikks model represent requires result right-hand side route satisfy schedule Section sensitivity analysis shortest shows simplex algorithm simplex method simplex tableau slack solution space Solve stage starting basic subproblem summarized Suppose tion TORA TOYCO transportation model unrestricted vector yields z-row zero