Introduction to Operations Research

Introduction to Operations Research
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Frederick S. Hillier
6 نوفمبر 2021
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Introduction to Operations Research
Tenth Edition
Frederick S. Hillier
Stanford University
Gerald J. Lieberman
Late of Stanford University
Table of Contents
Preface Xxii
. The Origins of Operations Research
. The Nature of Operations Research
. The Rise of Analytics Together with Operations Research
. The Impact of Operations Research
. Algorithms and OR Courseware
Selected References
Overview of the Operations Research Modeling Approach
. Defining the Problem and Gathering Data
. Formulating a Mathematical Model
. Deriving Solutions from the Model
. Testing the Model
. Preparing to Apply the Model
. Implementation
. Conclusions
Selected References
Introduction to Linear Programming
. Prototype Example
. The Linear Programming Model
. Assumptions of Linear Programming
. Additional Examples
. Formulating and Solving Linear Programming Models on a Spreadsheet
. Formulating Very Large Linear Programming Models
. Conclusions
Selected References
Learning Aids for This Chapter on Our Website
Case . Auto Assembly
Previews of Added Cases on Our Website
Case . Cutting Cafeteria Costs
Case . Staffing a Call Center
Case . Promoting a Breakfast Cereal
Solving Linear Programming Problems: The Simplex Method
. The Essence of the Simplex Method
. Setting Up the Simplex Method
. The Algebra of the Simplex Method
. The Simplex Method in Tabular Form
. Tie Breaking in the Simplex Method
. Adapting to Other Model Forms
. Postoptimality Analysis
. Computer Implementation
. The Interior-Point Approach to Solving Linear Programming Problems
. Conclusions
Appendix . An Introduction to Using LINDO and LINGO
Selected References
Learning Aids for This Chapter on Our Website
Case . Fabrics and Fall Fashions
Previews of Added Cases on Our Website
Case . New Frontiers
Case . Assigning Students to Schools
The Theory of the Simplex Method
. Foundations of the Simplex Method
. The Simplex Method in Matrix Form
. A Fundamental Insight
. The Revised Simplex Method
. Conclusions
Selected References
Learning Aids for This Chapter on Our Website
Duality Theory
. The Essence of Duality Theory
. Economic Interpretation of Duality
. Primal–Dual Relationships
. Adapting to Other Primal Forms
. The Role of Duality Theory in Sensitivity Analysis
. Conclusions
Selected References
Learning Aids for This Chapter on Our Website
Linear Programming under Uncertainty
. The Essence of Sensitivity Analysis
. Applying Sensitivity Analysis
. Performing Sensitivity Analysis on a Spreadsheet
. Robust Optimization
. Chance Constraints . Stochastic Programming with Recourse
. Conclusions
Selected References
Learning Aids for This Chapter on Our Website
Case . Controlling Air Pollution
Previews of Added Cases on Our Website
Case . Farm Management
Case . Assigning Students to Schools, Revisited
Case . Writing a Nontechnical Memo
Other Algorithms for Linear Programming
. The Dual Simplex Method
. Parametric Linear Programming
. The Upper Bound Technique
. An Interior-Point Algorithm
. Conclusions
Selected References
Learning Aids for This Chapter on Our Website
The Transportation and Assignment Problems
. The Transportation Problem
. A Streamlined Simplex Method for the Transportation Problem
. The Assignment Problem
. A Special Algorithm for the Assignment Problem
. Conclusions
Selected References
Learning Aids for This Chapter on Our Website
Case . Shipping Wood to Market
Previews of Added Cases on Our Website
Case . Continuation of the Texago Case Study
Case . Project Pickings
Network Optimization Models
. Prototype Example
. The Terminology of Networks
. The Shortest-Path Problem
. The Minimum Spanning Tree Problem
. The Maximum Flow Problem
. The Minimum Cost Flow Problem
. The Network Simplex Method
. A Network Model for Optimizing a Project’s Time–Cost Trade-Off
. Conclusions
Selected References
Learning Aids for This Chapter on Our Website
CONTENTS xiiiProblems
Case . Money in Motion
Previews of Added Cases on Our Website
Case . Aiding Allies
Case . Steps to Success
Dynamic Programming
. A Prototype Example for Dynamic Programming
. Characteristics of Dynamic Programming Problems
. Deterministic Dynamic Programming
. Probabilistic Dynamic Programming
. Conclusions
Selected References
Learning Aids for This Chapter on Our Website
Integer Programming
. Prototype Example
. Some BIP Applications
. Innovative Uses of Binary Variables in Model Formulation
. Some Formulation Examples
. Some Perspectives on Solving Integer Programming Problems
. The Branch-and-Bound Technique and Its Application to Binary
Integer Programming
. A Branch-and-Bound Algorithm for Mixed Integer
. The Branch-and-Cut Approach to Solving BIP Problems
. The Incorporation of Constraint Programming
. Conclusions
Selected References
Learning Aids for This Chapter on Our Website
Case . Capacity Concerns
Previews of Added Cases on Our Website
Case . Assigning Art
Case . Stocking Sets
Case . Assigning Students to Schools, Revisited Again
Nonlinear Programming
. Sample Applications
. Graphical Illustration of Nonlinear Programming Problems
. Types of Nonlinear Programming Problems
. One-Variable Unconstrained Optimization
. Multivariable Unconstrained Optimization
. The Karush-Kuhn-Tucker (KKT) Conditions for Constrained Optimization
. Quadratic Programming
xiv CONTENTS . Separable Programming
. Convex Programming
. Nonconvex Programming (with Spreadsheets)
. Conclusions
Selected References
Learning Aids for This Chapter on Our Website
Case . Savvy Stock Selection
Previews of Added Cases on Our Website
Case . International Investments
Case . Promoting a Breakfast Cereal, Revisited
. The Nature of Metaheuristics
. Tabu Search
. Simulated Annealing
. Genetic Algorithms
. Conclusions
Selected References
Learning Aids for This Chapter on Our Website
Game Theory
. The Formulation of Two-Person, Zero-Sum Games
. Solving Simple Games—A Prototype Example
. Games with Mixed Strategies
. Graphical Solution Procedure
. Solving by Linear Programming
. Extensions
. Conclusions
Selected References
Learning Aids for This Chapter on Our Website
Decision Analysis
. A Prototype Example
. Decision Making without Experimentation
. Decision Making with Experimentation
. Decision Trees
. Using Spreadsheets to Perform Sensitivity Analysis on Decision Trees
. Utility Theory
. The Practical Application of Decision Analysis
. Conclusions
Selected References
Learning Aids for This Chapter on Our Website
Case . Brainy Business
CONTENTS xvPreview of Added Cases on Our Website
Case . Smart Steering Support
Case . Who Wants to be a Millionaire?
Case . University Toys and the Engineering Professor Action Figures
Queueing Theory
. Prototype Example
. Basic Structure of Queueing Models
. Examples of Real Queueing Systems
. The Role of the Exponential Distribution
. The Birth-and-Death Process
. Queueing Models Based on the Birth-and-Death Process
. Queueing Models Involving Nonexponential Distributions
. Priority-Discipline Queueing Models
. Queueing Networks
. The Application of Queueing Theory
. Conclusions
Selected References
Learning Aids for This Chapter on Our Website
Case . Reducing In-Process Inventory
Preview of an Added Case on Our Website
Case . Queueing Quandary
Inventory Theory
. Examples
. Components of Inventory Models
. Deterministic Continuous-Review Models
. A Deterministic Periodic-Review Model
. Deterministic Multiechelon Inventory Models for Supply
Chain Management
. A Stochastic Continuous-Review Model
. A Stochastic Single-Period Model for Perishable Products
. Revenue Management
. Conclusions
Selected References
Learning Aids for This Chapter on Our Website
Case . Brushing Up on Inventory Control
Previews of Added Cases on Our Website
Case . TNT: Tackling Newsboy’s Teaching
Case . Jettisoning Surplus Stock
Markov Decision Processes
. A Prototype Example
. A Model for Markov Decision Processes
xvi CONTENTS . Linear Programming and Optimal Policies
. Conclusions
Selected References
Learning Aids for This Chapter on Our Website
. The Essence of Simulation
. Some Common Types of Applications of Simulation
. Generation of Random Numbers
. Generation of Random Observations from a Probability Distribution
. Outline of a Major Simulation Study
. Performing Simulations on Spreadsheets
. Conclusions
Selected References
Learning Aids for This Chapter on Our Website
Case . Reducing In-Process Inventory, Revisited
Case . Action Adventures
Previews of Added Cases on Our Website
Case . Planning Planers
Case . Pricing under Pressure
. Documentation for the OR Courseware
. Convexity
. Classical Optimization Methods
. Matrices and Matrix Operations
. Table for a Normal Distribution
Author Index
Subject Index
Case . Cutting Cafeteria Costs
Case . Staffing a Call Center
Case . Promoting a Breakfast Cereal
Case . New Frontiers
Case . Assigning Students to Schools
Case . Farm Management
Case . Assigning Students to Schools, Revisited
Case . Writing a Nontechnical Memo
Case . Continuation of the Texago Case Study
Case . Project Pickings
Case . Aiding Allies
Case . Steps to Success
Case . Assigning Art
Case . Stocking Sets
Case . Assigning Students to Schools, Revisited Again
Case . International Investments
Case . Promoting a Breakfast Cereal, Revisited
Case . Smart Steering Support
Case . Who Wants to be a Millionaire?
Case . University Toys and the Engineering Professor Action Figures
Case . Queueing Quandary
Case . TNT: Tackling Newsboy’s Teachings
Case . Jettisoning Surplus Stock
Case . Planning Planers
Case . Pricing under Pressure
The LINGO Modeling Language
More about LINGO
Linear Goal Programming and Its Solution Procedures
Case S. A Cure for Cuba
Case S. Airport Security
A Case Study with Many Transportation Problems
xviii Using TreePlan Software for Decision TreesSUPPLEMENTS AVAILABLE ON THE TEXT WEBSITE xix
Derivation of the Optimal Policy for the Stochastic Single-Period Model
for Perishable Products
Stochastic Periodic-Review Models
A Policy Improvement Algorithm for Finding Optimal Policies
A Discounted Cost Criterion
Variance-Reducing Techniques
Regenerative Method of Statistical Analysis
The Art of Modeling with Spreadsheets
. A Case Study: The Everglade Golden Years Company Cash Flow Problem
. Overview of the Process of Modeling with Spreadsheets
. Some Guidelines for Building “Good” Spreadsheet Models
. Debugging a Spreadsheet Model
. Conclusions
Selected References
Learning Aids for This Chapter on Our Website
Case . Prudent Provisions for Pensions
Project Management with PERT/CPM
. A Prototype Example—The Reliable Construction Co. Project
. Using a Network to Visually Display a Project
. Scheduling a Project with PERT/CPM
. Dealing with Uncertain Activity Durations
. Considering Time-Cost Trade-Offs
. Scheduling and Controlling Project Costs
. An Evaluation of PERT/CPM
. Conclusions
Selected References
Learning Aids for This Chapter on Our Website
Case . “School’s out forever . . .”xx SUPPLEMENTS AVAILABLE ON THE TEXT WEBSITE
Additional Special Types of Linear Programming Problems
. The Transshipment Problem
. Multidivisional Problems
. The Decomposition Principle for Multidivisional Problems
. Multitime Period Problems
. Multidivisional Multitime Period Problems
. Conclusions
Selected References
Probability Theory
. Sample Space
. Random Variables
. Probability and Probability Distributions
. Conditional Probability and Independent Events
. Discrete Probability Distributions
. Continuous Probability Distributions
. Expectation
. Moments
. Bivariate Probability Distribution
. Marginal and Conditional Probability Distributions
. Expectations for Bivariate Distributions
. Independent Random Variables and Random Samples
. Law of Large Numbers
. Central Limit Theorem
. Functions of Random Variables
Selected References
. Structure Function of a System
. System Reliability
. Calculation of Exact System Reliability
. Bounds on System Reliability
. Bounds on Reliability Based upon Failure Times
. Conclusions
Selected References
The Application of Queueing Theory
. Examples
. Decision Making
. Formulation of Waiting-Cost Functions
. Decision Models
. The Evaluation of Travel Time
. Conclusions
Learning Aids for This Chapter on Our Website
. Some Applications of Forecasting
. Judgmental Forecasting Methods
. Time Series
. Forecasting Methods for a Constant-Level Model
. Incorporating Seasonal Effects into Forecasting Methods
. An Exponential Smoothing Method for a Linear Trend Model
. Forecasting Errors
. Box-Jenkins Method
. Causal Forecasting with Linear Regression
. Forecasting in Practice
. Conclusions
Selected References
Learning Aids for This Chapter on Our Website
Case . Finagling the Forecasts
Examples of Performing Simulations on Spreadsheets with Analytic
Solver Platform
. Bidding for a Construction Project
. Project Management
. Cash Flow Management
. Financial Risk Analysis
. Revenue Management in the Travel Industry
. Choosing the Right Distribution
. Decision Making with Parameter Analysis Reports and Trend Charts
. Conclusions
Selected References
Learning Aids for This Chapter on Our Website
Markov Chains
. Stochastic Processes
. Markov Chains
. Chapman-Kolmogorov Equations
. Classification of States of a Markov Chain
. Long-Run Properties of Markov Chains
. First Passage Times
. Absorbing States
. Continuous Time Markov Chains
Selected References
Learning Aids for This Chapter on Our Website
Simultaneous Linear Equations
Sears, Roebuck and Company,
Swift & Company,
Taco Bell Corporation,
Time Inc.,
United Airlines,
Waste Management, Inc.,
Welch’s Inc.,
Westinghouse Science and Technology Center,
approximation methods
quadratic, ,
Russell, ,
Vogel, –
basic, –
explanation of,
undirected, –
artificial problem construction,
artificial variable,
artificial-variable technique
equality constraints and, –
explanation of,
functional constraints in ≥ form and, –
ASPE Solver. See Analytic Solver Platform for Education
assignment problem
constraints and,
example of, –
explanation of, ,
Hungarian algorithm for, –
minimum cost flow problem and, –
model of, –
prototype example of, –
solution procedures for, –
assumption, cost,
additivity, –
certainty, ,
linear programming, –
AT&T Bell Laboratories,
augmented form, , –
augmented solution,
augmenting path
explanation of,
method to find, –
augmenting path algorithm
explanation of,
for maximum flow problem, –
Seervada Park maximum flow problem and, –
Auto Assembly (case), –
auxiliary binary variables, , , –
backward induction procedure,
balance equation, –
Bank Hapoalim Group,
Bank One Corporation,
barrier algorithms,
basic arcs, –
basic feasible (BF) solutions
explanation of, – , –
feasible spanning trees and, –
matrix form and, –
network simplex method and, –
optimality test for,
in simplex method, – , – , –
transportation problem and, –
basic solutions
explanation of, , ,
basic tabu search algorithm, –
basic variables,
Bayes’ decision rule
explanation of, –
sensitivity analysis with, –
Bayes’ theorem,
Better Products Company problem, –
bicycle example, –
big data,
Big M method
application of, –
explanation of,
binary integer programming (BIP). See also integer
programming (IP)
applications of, – ,
branch-and-bound technique for, –
branch-and-cut approach for, –
example of, –
explanation of,
software options for,
binary variables
auxiliary, , , – SUBJECT INDEX
binary representation of general integer variables and,

either-or constraints and, –
explanation of, ,
fixed-charge problem and, –
formulation techniques with, –
functions with N possible values and, –
K out of N constraints and, –
binding constraints,
bi parameters, –
birth-and-death process
analysis of, –
assumptions of, –
explanation of,
queueing models based on, –
results for, –
bisection method, –
bounding, – ,
Brainy Business (case), –
branch-and-bound algorithm, –
branch-and-bound technique
bounding and, –
branching and, –
explanation of, –
fathoming and, –
options available for, –
branch-and-cut technique
automatic problem processing and, –
background of, –
generating cutting planes and, –
branching, – , , ,
branching tree, , , , , –
branching variable,
Brushing Up on Inventory Control (case), –
business analytics. See analytics
California Manufacturing Company, – ,
calling population, , –
Canadian Pacific Railway (CPR),
Capacity Concerns (case), –
capacity-controlled discount fares model, –
Auto Assembly, –
Brainy Business, –
Brushing Up on Inventory Control, –
Capacity Concerns, –
Controlling Air Pollution,
Fabrics and Fall Fashions, –
Money in Motion, –
Reducing In-Process, –
Savvy Stock Selection, –
Shipping Wood to Market,
changing, –
data, –
certainty assumption, ,
Certified Analytics Professional,
chance constraints
explanation of, ,
form of, –
hard constraints and, –
stochastic programming and,
changing cells, –
chi-square distribution,
cj parameters, systemic changes in, –
coin-flipping game, –
column reduction,
column vector,
combinatorial optimization
commercial service systems,
complementarity constraint, ,
complementarity problem, –
complementary basic solutions
explanation of, ,
relationships between, –
complementary basic solutions property,
complementary optimal basic solutions property, ,

complementary optimal solutions property,
complementary optimal solutions y, complementary slackness property explanation of, , use of, version of, complementary solutions property, , computer implementation, of simplex method, – computerized inventory systems, computers, operations research field and, concave function, convex set and, explanation of, of several variables, – of single variable, – concave set, connected networks, ConocoPhillips, CONOPT, , constrained optimization with equality constraints, – KKT conditions for, – linearly, constraint boundary, , constraint boundary equations explanation of, – indicating variables for, – constraint programming all-different constraints and, – background of, element constraints and, – nature of, – potential of, – research in, – constraints binding, chance, , – complementarity, , dual, – either-or, – , equality, , – , explanation of, functional, , – , , global, hard, , – inequality, introduction of new, – known, K out of N, – in linear programming model, nonnegativity, , , nonpositivity, redundant, soft, , upper-bound, , Continental Airlines, , contingent decisions, continuous simulation, Controlling Air Pollution (case), convex combination, convex function convex set and, explanation of, , , of several variables, – of single variable, – Convexity convex or concave functions of several variables, – convex or concave functions of single variable and, – convexity test, – , convex programming algorithms for, – explanation of, Frank-Wolfe algorithm for, – software options for, – SUMT and, – convex sets, cooperative game, corner-point feasible (CPF) solutions adjacent, , , – augmented, – explanation of, – integer programming and, optimality test and, , optimal solutions and, – properties of, – simplex method and, , – , , , , , – corner-point solution, , cost assumption, cost-benefit – trade-off problems, , , cost of ordering, cost tables, equivalent, – County Hospital problem, , – , – . See also queueing models CPF solutions. See corner-point feasible (CPF) solutions CPLEX explanation of, for integer programming, CPM (critical path method) explanation of, use of, , crashing, crashing activities, – crashing decisions for activities, – linear programming and, – crew scheduling problem, – CrewSolver, critical path explanation of, in time-cost trade-offs, – critical path method (CPM). See CPM (critical path method) cutting planes, for interger programming problems, – cut value, SUBJECT INDEX SUBJECT INDEX cycle length, cycles explanation of, – undirected, D database requirements, data cells, – data collection, data mining, decision analysis decision making with experimentation and, – decision making without experimentation and, – decision trees and, – game theory vs., overview of, – practical application of, – prototype example of, sensitivity analysis and, – utility theory and, – decision conferencing, decision making with experimentation posterior probabilities and, – prototype example of, value of experimentation and, – decision making without experimentation Bayes’ decision rule and, – formulation of prototype example of, maximum likelihood criterion and, – maximum payoff criterion and, – nature of, – sensitivity analysis and, – decision nodes, , decision-support system, decision trees construction of, – explanation of, illustration of, performing sensitivity analysis on, – problem analysis using, – decision variables duality and, examples of, explanation of, , in large linear programming problem, as parameter cell, – decreasing marginal utility for money, Deere & Company, defining equations, definite integral, degeneracy, D/Ek//s, demand, demand node, , , dependent demand, dependent-demand products, derivative, of definite integral, descendants, Descriptive analytics, determining reject allowances problem, – deterministic continuous-review models demand for products and, – EOQ model with planned shortages and, – EOQ model with quantity discounts and, – Excel and, explanation of, – illustration of, – just-in-time inventory management and, – observations about EOQ models and, – deterministic dynamic programming distribution of effort problem and, – example of, – explanation of, structure of, deterministic inventory model, deterministic multiechelon inventory models for supply chain management assumptions for serial multiechelon model and, – extensions of, – model for serial multiechelon system and, – , – overview of, – relaxation and, – revised problem solution and, – rounding procedure for n and, –
serial two-echelon model, –
deterministic periodic-review models
algorithm for, –
example of, –
explanation of,
Deutsche Post DHL,
directed arcs,
directed networks,
directed path, –
discount factor,
discount rate,
discrete-event simulation,
distributing scientists to research teams problem, –
distribution of effort problem, –
distribution systems, ,
Distribution Unlimited Co. problem, – , , – diversification,
divisibility, as linear programming assumption,
explanation of, ,
SOB method to determine form of constraints in, –
dual feasible solution, , –
duality properties,
duality theorem,
duality theory
adapting to other primal forms and, –
applications of, –
complementary basic solutions and, –
dual problem and, –
economic interpretations and, –
explanation of, –
nonlinear programming and,
primal-dual relationships and, – , –
sensitivity analysis and, , –
simplex method and, –
dual problem
applications of, –
construction of, ,
economic interpretation of, –
explanation of,
in linear programming,
in minimization form, ,
origin of, –
for other primal forms, –
relationship between primal problem and, –
summary of relationship between primal problem and,

dual simplex method
example of, –
explanation of, , –
summary of,
dummy demand node,
dummy destination, , –
dummy sink,
dummy source, , – ,
dynamic programming
deterministic, –
explanation of,
probabilistic, –
prototype example of, –
dynamic programming problems, –
echelon stock, ,
economic order quantity model. See EOQ models
efficient frontier,
either-or constraints, – ,
elementary row operations,
element constraints, –
EOQ formula, ,
EOQ models
basic, –
Excel templates for,
explanation of, –
observations about, –
with planned shortages, –
with quantity discounts, –
equality constraints, , – , , –
equivalence property,
equivalent cost tables, –
equivalent lottery method, –
Erlang distribution, , – ,
event node,
Evolutionary Solver,
Excel (Microsoft). See also Solver (Excel)
EOQ model and,
maximum flow problem and,
minimum cost flow problem and, –
OR applications for,
sensitivity analysis and, –
shortest-path problem and, –
for transportation problems, –
expected value of experimentation, –
expected value of perfect information (EVPI), –
exponential distribution
explanation of,
properties of, –
in queueing systems, – , ,
random observation generation and, –
exponential growth,
exponential service times,
exponential time algorithms,
Fabrics and Fall Fashions (case), –
fair game,
fathoming, , – , –
fathoming tests, – , ,
feasibility test,
feasible region
boundary of,
explanation of, ,
feasible solutions, ,
feasible solutions property, ,
feasible spanning trees, –
Federal Aviation Administration (FAA),
financial engineering,
financial risk analysis,
finite queue variation, –
fixed-charge problem, –
fixed-time incrementing, –
fractional programming, –
Frank-Wolfe algorithm, –
Franz Edelman Awards for Achievement in Operations
Research and the Management Science,
Frontline Systems, ,
functional constraints
duality and,
explanation of,
in ≥ form, –
slack variables and,
game theory
decision analysis vs.,
extensions and, –
for games with mixed strategies, –
graphical solution procedure for, –
linear programming to solve, –
overview of,
solving simple games with, –
two-person, zero-sum games and, –
gamma distribution, n
Gaussian elimination, – , ,
General Motors Corporation,
genetic algorithms
basic, –
basic concepts of, –
explanation of,
generating a child procedure and, –
integer version of nonlinear programming and, –
traveling salesman problem and, –
geometric programming,
GI/MI/s model,
global maximum, –
global minimum, ,
global optimization, –
Goferbroke Co. problem, – , – . See also
decision analysis
Good Products Company example, –
gradient algorithms, ,
gradient search procedure, – ,
Graphical Method and Sensitivity Analysis, , ,
graphical procedures
game theory and, –
linear programming and, –
nonlinear programming and, –
GRG Nonlinear,
hard constraints, , , –
health care applications, –
heuristic algorithms, ,
heuristic procedures,
Hewlett-Packard (HP), ,
hill-climbing procedure,
holding cost,
Hungarian algorithm
additional zero elements and, –
background of,
equivalent cost tables and, –
summary of,
hyperexponential distribution, –
hyperplanes, ,
identity matrix, –
independent demand,
indicating variables, –
inequality constraints,
infeasible solution,
infinite game,
infinite queues, –
influence diagram,
input cells,
installation stock, ,
Institute for Operations Research and the Management
Sciences (INFORMS), ,
integer programming (IP)
applications of, – , –
binary, – , –
binary variables in model formulation and, –
branch-and-bound algorithm and, –
branch-and-bound technique and, –
branch-and-cut approach and, –
explanation of,
incorporation of constraint programming and, – LP relaxation and, – , – ,
mixed, , , –
problem-solving perspectives on, –
prototype example of, –
software for,
integer solutions property, , ,
Intel Corporation,
interarrival time, , , ,
InterContinental Hotels Group (IHG),
interior-point algorithm
in augmented form, ,
centering scheme for implementing concept in,
example of,
overview of, –
projected gradient to implement concepts and and,

relevance of gradient for concepts and and, –
summary of, –
interior-point approach
background of, –
key solution concept and, ,
postoptimality analysis and,
simplex method vs., –
to solve linear programming problems, –
interior points,
internal service systems,
International Federation of Operational Research Societies
interrelated activity scheduling,
explanation of,
replenishment of, –
scientific management of, –
inventory models
components of, –
deterministic continuous-review, –
deterministic multiechelon, –
deterministic periodic-review, –
stochastic continuous-review, –
inventory policy
examples of, –
in stochastic continuous-review model, –
in stochastic single-period model, –
strategies to improve, –
inventory systems
management of,
multiechelon, –
serial multiechelon,
inverse transformation method, –
investment analysis, –
IOR Tutorial, –
IP programming. See integer programming (IP)
iteration, , , – , – , , –
iterative algorithms, , ,
Jackson networks, –
Job Shop Company problem, –
just-in-time (JIT) inventory management, , –
Karush-Kuhn-Tucker conditions. See KKT conditions
KKT conditions
application of,
for constrained optimization, –
explanation of,
for quadratic programming, –
known constant,
known constraints,
K out of N constraints, –
Lagrange multipliers, , , ,
Lagrangian function,
large linear programming models. See also linear
programming models
computer implementation of simplex method and,
example of, –
explanation of, –
interior-point algorithms and,
LINGO modeling language and, –
modeling languages for, –
lead time,
learning-curve effect,
LGO, ,
explanation of, ,
for integer programming,
for large linear programming models, – ,
for linear programming, –
use of, –
LINDO Systems, Inc.,
linear complementarity problem, ,
linear fractional programming,
linear functions, piecewise, –
linearly constrained optimization,
linear programming
additivity and, –
allowable range and,
applications of, –
assumptions of, –
certainty and,
crashing decisions and, –
divisibility and,
dual simplex method and, –
examples of, – , –
game theory and, –
goal of, –
interior-point algorithm and, –
optimal policies and, –
overview of, –
parametric, –
postoptimality analysis and, –
proportionality and, –
software for, –
terminology for, –
under uncertainty, – (See also uncertainty)
upper bound technique and, –
linear programming models
basic information about, –
Excel Solver to solve, –
explanation of, –
forms of, –
method to formulate large, –
parameters and,
spreadsheet use for, –
standard form of,
symbols use in, –
terminology for solutions of, –
linear programming problems
dual problem in,
formulation of, – , , –
network optimization models as,
simplex method to solve, , – (See also simplex
example using, –
explanation of,
for integer programming,
for linear programming, –
for nonlinear programming,
stochastic programming and,
use of, –
Little’s formula, ,
L.L. Bean, Inc.,
local improvement procedure, ,
local maximum,
local minimum,
local optima
Excel Solver to find, –
nonlinear programming problems with multiple,

systematic approach to finding, –
local search procedure,
long-run profit maximization,
LP relaxation, – , , – , – ,
management information systems, ,
manufacturing systems, –
marginal cost analysis, –
Markov chains
explanation of, –
steady-state probabilities and,
Markov decision process
explanation of,
linear programming and, –
model for, –
prototype example of, – , –
Markovian property, ,
Massachusetts Institute of Technology (MIT),
material requirements planning (MRP), –
mathematical models
advantages of,
deriving solutions from, –
explanation of,
formulation of, –
linear programming, –
pitfalls of,
retrospective test of,
validation of,
explanation of,
properties of, –
transition, ,
types of, –
vectors and, –
matrix form
dual problem and primal problem in, ,
notation in,
sensitivity analysis and,
simplex method and property revealed by,

simplex method in, , –
matrix multiplication,
max-flow min-cut theorem, –
maximization form, primal problem in, , – maximum flow problem
algorithm for, –
applications of, –
augmenting path algorithm for, –
Excel to formulate and solve,
explanation of,
finding augmenting path and, –
minimum cost flow problem and, –
Seervada Park problem and, –
maximum likelihood criterion, –
maximum payoff criterion,
M/D/s model,
M/Ek/s model, –
Memorial Sloan-Kettering Cancer Center (MSKCC),
Merrill Lynch, ,
development of,
examples of, –
explanation of,
genetic algorithms and, –
nature of, –
simulated annealing and, –
sub-tour reversal algorithm and, –
tabu search and, –
traveling salesman problem and, –
M/G/ model, , – ,
midpoint rule,
Midwest Independent Transmission System Operator, Inc.
military simulation applications,
minimax criterion, ,
minimax theorem, ,
minimization, simplex method and, –
minimization form, dual problem in, ,
minimum cost flow problem
applications of, –
example of, –
Excel to formulate and solve, –
explanation of, – ,
formulation of, –
special cases of, –
minimum cover,
minimum ratio test, ,
minimum spanning tree problem
algorithm for,
applications of, –
explanation of, , –
Seervada Park problem and, –
tabu search and, –
mixed congruential method, –
mixed integer programming (MIP). See also integer
programming (IP)
applications of, , ,
branch-and-bound algorithm for, –
explanation of,
mixed strategies, games with, – ,
M/M/ queueing system, ,
M/M/s/K model, –
M/M/s model
application of, – ,
birth-and-death process and, –
explanation of, , –
finite calling population variation of, –
finite queue variation of, –
multiple-server case and, –
single-server case and, –
model validation,
modified simplex method, –
Moneyball (Lewis), –
Money in Motion (case), –
move selection rule, ,
MPL (Mathematical Programming Language)
for convex programming, ,
example using, –
explanation of, , ,
for integer programming,
for large linear programming models, ,
multiple optimal solutions, , –
multivariable unconstrained optimization
explanation of, ,
gradient search procedure and, –
Newton’s method and, –
mutiplicative congruential method,
mutually exclusive alternatives, , ,
negative right-hand sides,
net flow, ,
Netherlands Railways,
net present value, ,
network design, minimum spanning tree problem
network optimization models
maximum flow problem and, –
minimum cost flow problem and, –
minimum spanning tree problem and, –
network simplex method and, –
to optimize project time-cost trade-off, –
overview of, –
prototype example of, –
shortest-path problem and, –
components of,
SUBJECT INDEX nonlinear programming
complementarity, –
convex programming, , –
explanation of,
fractional, –
graphical illustration of, –
KKT conditions for constrained optimization and,

linearly constrained optimization and,
with multiple local optima, –
multivariable unconstrained optimization and, –
nonconvex programming, , –
one-variable unconstrained optimization and, –
portfolio selection with risky securities problem, –
product-mix with price elasticity problem, –
quadratic programming and, – , –
sample applications of, –
separable programming, – , –
simulated annealing and, –
transportation problem with volume discounts on
shipping costs, ,
unconstrained optimization, –
nonnegativity constraints, , ,
nonpositivity constraints,
nonpreemptive priorities,
nonpreemptive priorities model, –
nonzero-sum game,
Nori & Leets Co. problem, –
normal distribution, , –
normal distribution table, –
n-person game,
null matrix,
null vector,
objective cells,
objective function
deterministic dynamic programming and,
explanation of, , ,
in large linear programming problem, –
OR model formulation and,
simplex method and,
slope-intercept form of,
objective function coefficients
allowable range for, –
percent rule for simultaneous changes in, – ,

simultaneous changes in, –
objectives, in problem definition,
explanation of,
flows in,
project, –
queueing, –
terminology of, –
time-cost trade-off optimization and, –
undirected, ,
network simplex method
BF solutions and feasible spanning trees and, –
completing process in, –
explanation of, ,
leaving basic variable and, –
minimum cost flow problem and,
selecting and entering basic variables and, –
upperbound technique and, –
newsvendor problem,
Newton’s method
explanation of,
of multivariable unconstrained optimization, –
one-variable unconstrained optimization and, –
next-event incrementing, –
no backlogging,
in decision trees,
demand, , ,
dummy demand,
explanation of, ,
transshipment, ,
nonbasic arcs,
nonbasic variables, , , – ,
nonconvex programming
challenges related to, –
Evolutionary Solver and,
Excel Solver to find local optima and, –
explanation of, ,
multiple local optima and, –
systematic approach to finding local optima and,

noncooperative game,
nonexponential distributions involving queueing
hyperexponential distribution and, –
M/Ek/s, –
M/G/ , –
phase-type distribution and, –
without Poisson input, – percent rule
for simultaneous changes in objective function
coefficients, – , –
for simultaneous changes in right-hand sides,
one-variable unconstrained optimization
bisection method and, –
explanation of, –
Newton’s method and, –
Operation Desert Storm,
operations research modeling approach
conclusions related to,
defining the problem and gathering data in, –
deriving solutions from, –
implementation of, –
mathematical model formulation in, –
model application in, –
model testing in, –
operations research (OR)
analytics and, –
applications of, described in vignettes, –
impact of,
nature of, –
origins of, –
team in, ,
OPL-CPLEX Development System,
optimality principle,
optimality test
for basic feasible solution, ,
for corner-point feasible solution, ,
sensitivity analysis and,
simplex method and, , –
optimal policies, in Markov decision process, –
optimal solutions
CPF solutions and, –
example of,
explanation of, ,
iteration and, –
multiple, –
search for,
classical methods of, –
constrained, , – , –
global, –
robust, –
with simulation and ASPE’s Solver, –
unconstrained, – , – , –
Optimization Programming Language (OPL),

optimizing, satisficing vs.,
OR. See operations research (OR)
OR Courseware
Analytic Solver Platform for Education,
Excel files,
explanation of,
IOR Tutorial, –
OR Tutor,
use of, –
order quantity Q,
OT Tutor,
output cells, ,
overall measure of performance,
overbooking model, –
Pacific Lumber Company (PALCO),
P & T Company problem, – . See also
transportation problem
parameter analysis report
two-way, –
use of, – ,
parameter cell, –
explanation of,
of linear programming model,
parameter table, , , ,
parametric linear programming
explanation of, – ,
for systemic changes in bi parameters, –
for systemic changes in cj parameters, –
critical, –
directed, –
undirected, –
payoff table, – , , ,
performance, overall measure of,
perishable products, – . See also stochastic single
period model for perishable products
phase-type distributions, –
piecewise linear functions, –
pivot column,
pivot number,
pivot row,
planned shortages, EOQ model with, –
Poisson distribution,
Poisson input
explanation of, ,
models without, –
Poisson input process, , ,
Poisson process, –
policy decision,
political campaign problem, –
Pollaczek-Khintchine formula, ,
polynomial time algorithms, –
portfolio selection, with risky security, –
positive semidefinite matrix,
posterior probabilities, – ,
postoptimality analysis
combining simplex method with interior-point approach
Excel and, –
explanation of, , ,
parametric linear programming and, –
reoptimization and,
sensitivity analysis and, –
shadow prices and, –
use of,
predictive analytics,
preemptive priorities, , –
preemptive priorities model,
prescriptive analytics,
price-demand curve,
price elasticity, product-mix problem with, –
primal-dual relationships. See also duality theory; dual
problem; primal problem
complementary basic solutions and, –
explanation of,
relationships between complementary basic solutions
and, –
primal-dual table,
primal feasible solution, ,
primal problem
applications of, –
economic interpretation of,
explanation of,
in maximization for, –
in maximization form, , –
relationship between dual problem and, –
summary of relationship between dual problem and,

principle of optimality,
prior distribution, –
priority-discipline queueing models
example of, –
explanation of,
nonpreemptive priorities model and, –
preemptive priorities model and,
single-server variation of, –
types of, –
prior probabilities, ,
probabilistic dynamic programming
examples of, –
explanation of, –
probability distribution
explanation of, –
generation of random observations from, –
probability tree,
problem definition,
Procter & Gamble (P&G),
product demand, –
production and distribution network design,
product-mix problem
explanation of, ,
with price elasticity, –
perishable, –
profit function, ,
profit maximization, long-run,
profits, goal of satisfactory,
project deadlines, –
project networks, –
auxiliary binary variables and, –
explanation of,
as linear programming assumption, –
pseudo-random numbers,
pure strategies, ,
quadratic approximation, ,
quadratic programming
explanation of, – , –
KKT conditions for, –
modified simplex method and, –
software options for, –
quantity discounts, with EOQ model, –
quasi-Newton methods,
queue, ,
queue discipline, ,
queueing models
basic structure of, –
birth-and-death process and, –
M/M/s, –
nonexponential distributions and, – priority discipline, –
queueing networks
explanation of, –
infinite queues in series and, –
Jackson networks and, –
Queueing Simulator, –
queueing systems
classes of, –
design and operation of, – ,
explanation of,
exponential distribution and, –
queueing theory
applications of, , –
background of,
explanation of,
prototype example of,
terminology and notation for, –
R, Q policy (reorder-point, order-quantity policy),
radiation therapy, two-phase method and, –
radiation therapy example
illustration of, –
primal-dual form and,
simplex method and, –
RAND() function (Excel), ,
random digits table,
random integer numbers
converted to uniform random numbers,
explanation of,
generation of,
probability distributions and,
randomized policy, –
random number generation
computers for,
congruential methods for, –
simulation and,
random number generators,
random numbers
categories of,
characteristics of, –
explanation of,
move selection rule and,
uniform, , ,
random observations from probability distribution
explanation of,
generation of, –
range names, ,
range of uncertainty,
rate in = rate out principle, –
recursive relationship, ,
Reducing In-Process (case), –
regional planning problem, –
explanation of,
inventory and, , –
LP, – , , – , –
Reliable Construction Co. problem, – . See also
time-cost trade-offs
in postoptimality analysis,
sensitivity analysis and,
reorder point, , –
residual capacities, ,
residual network, ,
resource-allocation problems, ,
results cell,
retrospective test,
revenue management
in airline industry, –
background of, –
capacity-controlled discount fares and, –
considerations for models used in, –
explanation of,
overbooking model and, –
reverse arc,
revised simplex method
applications of,
explanation of, –
Rijkswaterstaat (Netherlands) study, , –
risk seekers,
robust optimization
explanation of, –
extension of,
with independent parameters, –
recourse and,
stochastic programming and,
row reduction,
row vector,
Russell’s approximation method, ,
saddle point, –
salvage value, ,
Samsung Electronics Corp.,
Save-It Company problem, –
Savvy Stock Selection (case), –
scheduling employment levels problem, –
scientific inventory management,

Sears, Roebuck and Company,
Seervada Park problem
algorithm for shortest-path problem and, –
maximum flow problem and, –
minimum spanning tree problem and, –
overview of, –
sensible-odd-bizarre method (SOB), –
sensitive parameters
explanation of, ,
sensitivity analysis to identify,
sensitivity analysis
application of, , –
with Bayes’ decision rule, –
changes in bi and, –
changes in coefficients of basic variable and, –
changes in coefficients of nonbasic variable and,

duality theory and, , –
example of, –
explanation of, , ,
introduction of new constraint and, –
introduction of new variable and,
in postoptimality analysis, , , –
procedure for, – , –
purpose of,
sensitivity report to perform, –
on spreadsheets, – , –
types of,
sensitivity reports, –
separable programming
explanation of, – , –
extensions of, –
key property of, –
reformulation as linear programming problem and,

sequences of numbers,
sequential-approximation algorithms, –
sequential linear approximation algorithm (Frank-Wolfe),

sequential unconstrained algorithms,
sequential unconstrained minimization technique. See
serial multiechelon system
assumptions for, –
model for, –
serial two-echelon model, –
service industry simulation applications,
service level, ,
service time, – , , ,
set covering problems,
set partitioning problems,
shadow price
duality theory and, ,
explanation of, –
sensitivity analysis and,
shipment dispatch, –
shipping costs, ,
Shipping Wood to Market (case),
shortage cost,
shortest-path problem
algorithm for,
applications for, –
Excel to formulate and solve, –
minimum cost flow problem and,
overview of,
Seervada Park, –
simple discrete distributions,
simplex method. See also dual simplex method; network
simplex method
algebra of, –
basic feasible solutions in, – , – , –
computer implementation of, –
CPF solutions and, , – , , , , ,

direction of movement and, –
duality and, – ,
equality constraints and, –
examples in, – , –
explanation of, , , –
extensions to augmented form of problem and, –
functional constraints in ≥ form and, –
geometric concepts in, –
interior-point approach and, –
key solution concepts in, –
in matrix form, , –
maximum flow problem and,
method to set up, –
minimization in, –
modified, –
negative right-hand sides and,
no feasible solutions and, –
optimality test and, , –
postoptimality analysis and, –
property revealed by matrix form of, –
revised, – summary of, –
in tabular form, –
terminology for, –
tie breaking in, –
for transportation problem, –
two-phase method in, –
use of,
with variables allowed to be negative, –
simplex tableau, , , , – ,
simulated annealing
basic concepts of, –
basic simulated annealing algorithm and, –
nonlinear programming and, –
traveling salesman problem and, –
simulated annealing algorithm, –
examples of, –
explanation of, –
fixed-time incrementing and, –
next-event incrementing and, –
optimization with, –
in OR studies, –
random number generation and, –
random observation generation from probability
distribution and, –
software for, – , –
spreadsheets for, –
steps in OR research studies based on applying,

simulation applications
distribution system design and operation,
financial risk analysis,
health care, –
innovative new,
inventory system management,
manufacturing systems design and operation, –
project completion deadline, –
queuing systems design and operation,
service industry,
simulation models
checking accuracy of,
explanation of,
formulation of, –
planning simulations for, –
preparing recommendations based on,
simulation run for, –
software for, –
testing validity of,
site selection, –
slack variables, , , ,
slope-intercept form, of objective function,
SOB (sensible-odd-bizarre method), –
social service systems,
soft constraints, ,
linear programming, –
nonlinear programming, – , –
operations research background and development of,
for simulation, – , –
for solving BIP models,
solid waste reclamation problem, –
solutions. See also basic feasible (BF) solutions; optimal
corner-point feasible,
optimal, , ,
Solver (Excel). See also Analytic Solver Platform for
Education (ASPE)
application of,
description of, –
to find local optima, –
for integer programming,
for linear programming,
sensitivity analysis and,
Southern Confederation of Kibbutzim problem, –
Southwestern Airways example, –
spanning trees
explanation of, – ,
feasible, ,
minimum, –
ASPE’s Solver and, –
formulating linear programming models on, –
sensitivity analysis on, – , –
software for,
Solver use and, –
stable products, –
stable solution,
stagecoach problem, –
stages, in dynamic programming problems,
standard form, for linear programming model,
state of nature,
states, in dynamic programming problems,
stationary, deterministic policy,
statistic cells,
steady-state condition, , ,
steepest ascent/mildest descent approach,
stochastic continuous-review model
assumptions of,
example of,
explanation of, –
order quantity Q and,
reorder point R and, –
stochastic inventory model,
stochastic process,
stochastic programming with recourse
applications of, –
example of, –
explanation of, –
stochastic single period model for perishable products
analysis of, –
application of, – , –
assumptions of, –
example of, –
explanation of, –
optimal policy and, –
types of perishable products and, –
stock portfolios, –
strong duality property,
structural constraints. See functional constraints
suboptimal solutions,
sub-tour reversal, –
sub-tour reversal algorithm, –
example of, –
explanation of, , –
summary of,
superoptimal basic solution,
Supersuds Corporation example, –
supply chain,
supply chain management. See deterministic multiechelon
inventory models for supply chain management
supply node,
surplus variable, –
Swift & Company,
symbols, use in linear programming models, –
symmetry property,
system service rate, –
table lookup approach,
tabular form, simplex method in, –
tabu list,
tabu search
basic tabu search algorithm and, –
explanation of,
minimum spanning tree problem with constraints and,

traveling salesman problem and, –
Taco Bell Corporation,
tasks, ,
teams, ,
technological coefficients,
time advance methods,
time-cost trade-offs
crashing decisions and, –
critical path and, –
for individual activities, –
network model and,
project networks and, –
prototype example of, –
Time Inc.,
transient condition, ,
transition matrix, ,
transition probabilities,
transportation problem
basic feasible (BF) solutions and, –
with dummy destination, –
with dummy source, –
Excel to formulate and solve, –
explanation of,
generalizations of,
minimum cost flow problem and,
model of, –
prototype example of, –
streamlined simplex method for, –
with volume discounts on shipping costs, ,
transportation service systems,
transportation simplex method
application of, –
drawback of,
explanation of,
features of example of, –
initialization of, –
iteration for, –
optimality test for, –
set up for, –
summary of,
transportation simplex tableau, , –
transpose operation,
transshipment node, ,
transshipment problem, minimum cost flow
problem and, traveling salesman problem
example of, –
genetic algorithms and, –
simulated annealing and, –
tabu search and, –
trend charts,
two-bin system,
constant-sum game,
zero-sum games
explanation of, –
formulation of, –
two-phase method
explanation of, –
use of, –
unbounded Z, ,
chance constraints and, –
overview of, –
robust optimization and, –
sensitivity analysis and, –
sensitivity analysis application and, –
sensitivity analysis on spreadsheets and, –
stochastic programming with recourse and,

unconstrained optimization
explanation of, –
multivariable, – ,
one-variable, – , –
undirected arcs, –
undirected networks, ,
undirected path, –
uniform random numbers, , ,
Union Airways problem, –
United Airlines,
unstable solution,
upper bound technique
example of, –
explanation of, –
network simplex method and, –
utility function (U/M) for money M, –
utility theory
application of, –
equivalent lottery method and, –
estimating U/M and, –
overview of, –
utility functions for money and, –
utilization factor, – ,
value of game,
binary, , , –
with bound on negative values allowed,
decision, , , , ,
negative, –
in network simplex method, –
with no bound on negative values allowed,

nonbasic, , , – ,
slack, , , ,
surplus, –
variance-reducing techniques,
of basic variables,
explanation of, –
Vogel’s approximation method, –
waiting cost,
warm-up period,
Waste Management, Inc.,
Welch’s, Inc.,
Westinghouse Science and Technology Center,
what-if analysis,
winning in Las Vegas problem, –
Winter Simulation Conference,
World Health Council problem, –
Worldwide Corporation problem, –
Wyndor Glass Co. problem
additivity assumption and, –
approach to, –
background of,
certainty assumption and,
chance constraints and, ,
complementary basic solutions for,
conclusions about, , ,
constraint boundary equations for, –
constraints in,
CPF solutions for, , , –
divisibility assumption and,
dual simplex method and, –
formulation of mathematical model for, –
graphical solution to, –
interior-point algorithm and,
LINDO and LINGO use and, –
nonlinear programming and, – , –
primal and dual problems for, ,
proportionality assumption and, –
sensitivity analysis and, – , – , – ,

simplex method and, – , , – , – ,
, , – , ,
spreadsheets for, – , –
stochastic programming and, –
uncertainty and, ,
Xerox Corporation,
yes/no decisions, , , ,
zero elements, –
Abbink, E., n
Abellan-Perpiñan, J. M.,
Acharya, D.,
Achterberg, A.,
Ahmed, S., n,
Ahn, S.,
Ahrens J. H., n
Ahuja, R. K., n
Akgun, V.,
Alden, H., n
Alden, J. M., , n,
Alexopoulos, C.,
Allan, R.,
Allen, S. J., n
Almroth, M.,
Altschuler, S., , n
Ambs, K.,
Anderson, E. T., n
Anderson, P. L.,
Andrews, B.,
Angelis, D. P., n
Appa, G. L.,
Argüello, M., n,
Armacost, A. P.,
Aron, I. D.,
Asmussen, S.,
Assad, A. A.,
Aumann, R. J.,
Avis, D., n
Avriel, M., n, n
Axsäter, S., n,
Azaiez, M. N.,
Bagchi, S.,
Baker, K. R.,
Banks, J.,
Baptiste, P.,
Barabba, V.,
Barkman, M., n
Barnes, E. R., n
Barnhart, C.,
Barnum, M. P., n
Batavia, D., , n
Bayes, T., – , n, – , , , , ,
Bazarra, M. S., , ,
Beis, D. A.,
Benjamin, A. T., n
Ben-Khedher, N.,
Bennett, J., , n
Benson, R. F.,
Ben-Tal, A.,
Berk, G. L., n
Berkey, B. G., n
Bertsimas, D., , , n, ,
Best, M. J.,
Best, W. D.,
Bielza, C., n
Bier, V. M.,
Billington, C.,
Birge, J. R.,
Bixby, A., , n
Bland, R., n
Blatt, J. A., n
Bleichrodt, H.,
Bleuel, W. H.,
Blyakher, S., n
Board, J.,
Bohm, W.,
Bollapragada, S.,
Bookbinder, J. H.,
Boucherie, R. J.,
Bowen, D. A., n
Boyd, S.,
Braklow, J. W.,
Brennan, M., n
Brenner, D. A.,
Brigandi, A. J., ,
Brinkley, P. A.,

Page numbers followed by n indicate footnotes. AUTHOR INDEX
Brown, D. B.,
Brown, G. G.,
Brown, S. M.,
Buckley, S.,
Bunday, B. D., n
Burman, M.,
Burns, L. D., , n,
Busch, I. K., n
Byers, S.,
Cahn, M. F.,
Cai, X.,
Caixeta-Filho, J. V.,
Callioni, G.,
Camm, J. D., n
Canbolat, B.,
Cao, B., n
Caramanis, C.,
Carlson, B., n
Carlson, W., n
Carr, W. D.,
Carson, J. S., II,
Case, R., n
Cavalier, T. M., n
Chalermkraivuth, K. C.,
Chandrasekaran, S.,
Chao, X., n
Chatterjee, K.,
Chelst, K.,
Chen, E. J., n
Chen, H., , n
Cheng, R.,
Chinneck, J. W., n
Chiu, H.W.C.,
Choi, T.-M.,
Chorman, T. E., n
Chu, L. Y., n
Cioppa, T. M.,
Clark, M. C.,
Clemen, R. T.,
Clerkx, M., ,
Coello, C.,
Cohen, M.,
Cooke, F.,
Copeland, D., n
Corner, J. L.,
Cosares, S.,
Costy, T., , n,
Cottle, R. W., n
Coveyou, R. R., n
Crane, B.,
Cremmery, R.,
Cunningham, J.,
Cwilich, S.,
Dakin, R. J., , n
Dantzig, G. B., , , , , , ,
Dargon, D. R., ,
Darnell, C.,
Darrow, R., ,
Darwin, Charles,
Davenport, T. H., ,
Deaton, J.,
De Lascurain, M., n
del Castillo, E.,
De los Santoz, L., n
Dempsey, J. F., n
Denardo, E. V., , , , , ,
Deng, M.,
Denton, B. T.,
Desaulniers, G.,
De Schuyter, N.,
Desrosiers, J.,
Deutsch, D. N.,
DeWitt, C. W.,
Dieter, V., n
Diewert, W. E., n
Dikin, I. I., n
Dill, F. A., n
Dodge, J. L.,
Doig, A. G., , n
Downs, B., , n
Drew, J. H.,
Dumas, Y.,
Dyer, J. S., n
Earl, M. A., n
Ecker, J. G.,
Ehrgott, M.,
Eidesen, B. H., n
Eilon, S., , n
Einarsdottir, H.,
Eister, C., n
Eklund, M.,
El Ghaoui, L.,
Elhallaoui, I.,
Elieson, J.,
El-Taha, M.,
Epstein, R.,
Erlang, A. K., , , – ,
Erlenkotter, D., n
Eschenbach, T. G., n
Ettl, M.,
Etzenhouser, M. J., n
Evans, J. R., n
Eveborn, P.,
Everett, G.,
Fallis, J., n
Farasyn, I.,
Fattedad, S. O., n
Feinberg, E. A.,
Feitzinger, E. G.,
Ferris, M. C., n
Feunekes, A.,
Feunekes, U.,
Fiacco, A. V.,
Figueira, J. R.,
Filomena, T. P., n
Fioole, P.-J., n
Fischer, M.,
Fischetti, M., n
Fishburn, P. C.,
Fishman, G. S.,
Fitzsimons, G. J., n
Fletcher, L. R., n
Fletcher, R.,
Fleuren, H., ,
Fodstad, M., n
Fogel, D. B.,
Folger, J.,
Forrest, J.,
Fossett, L., n
Fourer, R., , n
Frank, M., n
Frank, M. Z., n
Freedman, B. A., n
Freundt, T.,
Fry, M. J.,
Fu, M.,
Fu, M. C.,
Gal, T.,
Gass, S. I., , ,
Gautam, N.,
Gavirneni, S.,
Geckil, I. K.,
Gen, M.,
Gendreau, M.,
Geoffrion, A. M., n, n
Geraghty, M. K., ,
Gershwin, S. B.,
Geyer, E. D., Sr.,
Ghosh, D.,
Giehl, W.,
Gill, P. E.,
Girgis, M.,
Gjessing, R.,
Glover, F.,
Glynn, P. W.,
Goeller, B. F.,
Goetschalckx, M.,
Goh, J.,
Golabi, K.,
Goldring, L.,
Goldsman, D.,
Gomory, Ralph,
Goossens, C.,
Gorman, M. F.,
Gould, G.,
Graham, W. W.,
Granfors, D. C.,
Graves, S.,
Greco, S.,
Greenberg, F.,
Gross, D.,
Gryffenberg, I.,
Guenther, D.,
Guo, X.,
Gutin, G.,
Haag, K. R.,
Hahn, G. J.,
Hall, J.A.J., n
Hall, R. W., , ,
Hammond, J. S.,
Han, J., , ,
Hanschke, T.,
Harris, C. M.,
Harris, J. G.,
Harrison, G., n
Harrison, T. P.,
Harsanyi, J. C.,
Hasegawa, T., Hassler, S. M.,
Haupt, R. L.,
Haupt, S. E.,
Haviv, M.,
Hazelwood, R. N., n
Hellemo, L., n
Henderson, S. G.,
Hendriks, M.,
Hernandez-Lerma, O.,
Herrería, F., n
Hicks, R.,
Higbie, J. A., n
Higle, J. L., ,
Hilliard, M. C., n
Hilliard, M. S.,
Hillier, F. S., , , , , , , , n,
Hillier, M. S., , , , , , ,
Holcomb, R.,
Holmberg, K., n
Holmen, S. P., n
Hong, C.-F.,
Hooker, J. N., , ,
Hordijk, A., n
Houck, D. J.,
Howard, K., n
Howard, R. A., ,
Hu, N.-Z.,
Huang, C.-H.,
Huber, C.,
Hueter, J., n,
Huh, W. T., n
Huisingh, J. L.,
Huisman, D., n
Hunsaker, B., n
Hutton, R. D., , n,
Huxley, S. J.,
Iancu, D. A., n
Infanger, G.,
Ireland, P., n
Jackson, C. A., , n, ,
Jackson, J. R.,
Jacobs, B. I., n
Jain, J. L.,
Janakiraman, B., n
Janakiraman, G., n
Janssen, F., ,
Jarvis, J. J., ,
Johnson, E., ,
Jones, D.,
Kaczynski, W. H.,
Kall, P.,
Kamber, M., ,
Kamesam, P. V.,
Kanaley, M.,
Kang, J., , n
Kaplan, A.,
Kaplan, E. H.,
Karlof, J. K.,
Karmarkar, N., – , , n, , – ,
Karush, H. W., , n
Karush, W., , n
Katz, D., n
Kaya, A., n
Keefer, D. L.,
Keeney, R. L.,
Kelton, W. D., n
Kempf, K., , n
Kennington, J. L., n
Khouja, M.,
Kiaer, L.,
Kim, B.-I., n
Kim, D. S., , n,
Kim, K.,
Kim, S., n
Kimbrough, S.,
King, P. V., n
Kintanar, J.,
Kirkwood, C. W., n,
Kleijnen, J. P. C.,
Kleindorfer, P.,
Klingman, D.,
Kobayashi, S., n
Koenig, L.,
Kohls, K. A., , n,
Kok, T. de, ,
Konno, H., n
Koschat, M. A., n
Koshizuka, T., n
Kotha, S. K., n
Kotob, S.,
Koushik, D., n
Kraemer, R. D., nAUTHOR INDEX
Krass, B., n
Krishnamurthy, N., n
Kroon, L., n
Kücükyavuz, S., n
Kuehn, J., n
Kumar, A., n
Kunz, N. M., n
Labe, R., , n
Lacroix, B.,
Laguna, M.,
Lai, K.-K.,
Lambrecht, M. R.,
Lamont, G. B.,
Land, A. H., , n
Larson, R. C.,
Lasdon, L. S.,
Lau, E. T., n
Law, A. M.,
Leachman, R. C., , , n
LeBlanc, L. J., n
L’Ecuyer, P., n
Lee, E. K., n
Lee, H.,
Lee, H. L.,
Leemis, L. M.,
Lehky, M., n
Leimkuhler, J. F.,
Lejeune, M. A., n
LePape, C.,
LePore, M. H., n
Leung, E.,
Levi, R., n
Levy, K. N., n
Lew, A.,
Lewis, M.,
Leyton-Brown, K.,
Li, D.,
Li, H.-L.,
Liao, B., , n
Liberatore, M. J., ,
Liden, K.,
Lim, G. J., n
Lin, G.,
Lin, V.,
Lin, Y., n
Liou, K.,
Lipsky, L.,
Little, J. D. C.,
Liu, C., , n
Liu, J.,
Liu, Y., n
Lo, F., n
Lombard, M.-C.,
Loucopoulos, P.,
Louveaux, F.,
Lu, H.-C.,
Lucas, T. W.,
Luenberger, D., , , , ,
Luo, W.,
Lustig, I., , ,
Lynch, D. F.,
Ma, L., n
MacNaughton, J.,
Madrid, R.,
Markowitz, H.,
Markowitz, H. M., n
Maros, I.,
Maróti, G., n
Marshall, S., n
Marsten, R.,
Marsten, R. E.,
Mason, R. O., n
Mathisen, K.,
Mauch, H.,
Mayer, J.,
McAllister, W. J., n
McCormick, G. P.,
McCowan, S. M., n,
McGrayne, S. B.,
McKenney, J. L., n
McKinnon, K. I. M., n
Meents, I.,
Mehrotra, S., n
Meiri, R., n
Meketon, M., n, n
Melhem, S. A.,
Mendelson, E.,
Mendez-Martinez, I.,
Menezes, F.,
Metrane, A.,
Metty, T.,
Meuffels, I.,
Meyer, M., n
Meyer, R. R., n
Meyerson, R. B.,
Michalewicz, Z.,
Milligan, C.,
Milne, R. J.,
Miser, H. J.,
Mitchell, M.,
Mohammadian, M.,
Mohanty, S. G.,
Morahan, G. T., n
Morales, R.,
Morgan, C.,
Morison, R.,
Morris, W. T.,
Muckstadt, J.,
Muir, C. T.,
Mukuch,W. M.,
Mulvey, J. M.,
Muñoz, D., n
Murdzek, J. P.,
Murphy, F. H.,
Murray, W.,
Murty, K. G., , , , , , ,
Naccarato, B. L.,
Nagali, V.,
Nagata, Y., n
Nahmias, S.,
Nair, S. K., n
Nash, J. F., Jr.,
Nazareth, J. L.,
Neale, J. J.,
Neeves, W.,
Nelson, B. L.,
Nemhauser, G., n,
Nemhauser, G. L.,
Nemirovski, A.,
Newton, Isaac, n, – , – ,
Neyman, J., n
Nicol, D. M.,
Nigam, R., , n
Nuijten, W.,
Nydick, R. L.,
Oh, J., , n
Ohlmann, J. W.,
Oiesen, R., n
O’Keefe, E.,
Owen, J. H., , n, n,
Ozaltin, O. Y., n
Paich, M.,
Palacios-Brun, A., n
Palmer, S.,
Pang, J.-S., n
Parsons, H.,
Patchak, W. M.,
Pearson, J. N., n
Peck, K. E.,
Peck, L. G., n
Pedersen, B., n
Pederson, S. P., n
Peeters, W., ,
Pei, J., ,
Pekgün, P.,
Pennings, J. M. E., n
Perdue, R. K., n
Peretz, A., n
Pfeil, G.,
Phillips, N.,
Philpott, A.,
Pidd, M.,
Pinto-Prades, J. L.,
Pitsoulis, L.,
Poole, D.,
Popov, A., Jr., n
Poppelaars, J.,
Potvin, J.-Y.,
Powell, W. B., ,
Prabhu, N. U., n
Prior, R. C.,
Pri-Zan, H., n
Pruneau, R.,
Pudar, N.,
Puget, J.-F.,
Punnen, A.,
Puterman, M. L., n,
Pyrgiotis, Y.,
Queille, C.,
Quillinan, J. D.,
Quinn, P.,
Raar, D. J.,
Raiffa, H.,
Rakshit, A., n
Ramaswami, V., AUTHOR INDEX
Randels, D., Jr., n
Rao, B. V.,
Rapp, J. U.,
Rash, E., , n
Reeves, C. R.,
Reilly, T.,
Reiman, M., n
Reinfeld, N. V., n
Rinnooy Kan, A.,
Romeijn, H. E., n
Romeo-Hernandez, O., n
Rømo, F., n
Ronnqvist, M.,
Rosenthal, R. E.,
Roundy, R., , n, , n,
Ruark, J. D.,
Russell, E. J., , – , n
Sabuncuoglu, I.,
Sahoo, S., n
Saltzman, M.,
Samuelson, D. A.,
Samuelson, W. F.,
Sanchez, S. M.,
Saniee, I.,
Sarker, R.,
Sasaki, T.,
Saxena, R.,
Schaefer, A. J., n
Schaible, S., n
Scheff, R. P., Jr.,
Schelling, T. C.,
Schmidt, U.,
Scholz, B. J.,
Schrage, L., ,
Schrijver, A., n
Schriver, A.,
Schuster, E. W., n
Scraton, R. E., n
Seelen, L. P., n
Self, M., , n
Sellers, D.,
Selton, R.,
Sen, S.,
Sennott, L. I.,
Serón, J.,
Seshadri, S., n
Shang, H. K., n
Shanno, D.,
Shanthikumar, J. G., n, n
Sharpe, W.,
Sheehan, M. J., ,
Shell, M. C.,
Shen, Z.-J., n,
Shenoy, P. P., n
Shepard, D. M., n
Shepard, R.,
Sherali, H. D., , ,
Shetty, C. M.,
Shmoys, D. B., n
Shoham, Y.,
Shortle, J. F.,
Shwartz, A.,
Siegel, A. F., n
Sierksma, G.,
Sim, M.,
Simard, R., n
Simchi-Levi, D.,
Simester, D., n
Simon, H.,
Slavens, R. L.,
Smidts, A., n
Smith, B. C., ,
Smith, J., n,
Smith, J. Q.,
Sniedovich, M.,
Solanki, R. S., n
Solis, F., n
Song, C., n
Song, G.,
Song, L.-S., n
Soucy, R.,
Soumis, F., ,
Soyster, A. L., n
Spencer, T., III, ,
Srinivasan, A.,
Srinivasan, M. M.,
Steenbeck, A., n
Steiger, D.,
Stepto, D.,
Stidham, S., Jr., ,
Stone, R. E., n
Stripling, W.,
Subramanian, R., ,
Sud, V. P., n,
Sun, X.,
Sutcliffe, C.,
Suyematsu, C.,
Swain, J.,
Swann, T. K., n AUTHOR INDEX
Swart, W., n,
Sweeney, D. J., n
Swersy, A. J.,
Taj, S.,
Talbi, E.,
Talluri, G.,
Tamiz, M.,
Tang, C. S.,
Tanino, M., n
Taylor, P. E.,
Tayur, S., n
Tekerian, A.,
Tekin, E.,
Teo, C.-P.,
Thapa, M. N., , , , ,
Thiele, A.,
Thompson, J. M.,
Tijms, H. C., n, n
Tiwari, V.,
Todd, M. J., n
Toledano, D.,
Tomasgard, A., n
Trench, M. S., n
Tretkoff, C.,
Trimarco, J.,
Troyer, L., n
Tseng, M. M.,
Tucker, A. W., , n
Turnquist, M. A., , n,
Tuy, H., n
Urbanovich, E., n
Vandaele, N. J.,
Vandenberghe, L.,
Vanderbei, R. J., , , , n, ,
Vander Veen, D. J., n,
van Dijk, N. M.,
van Doremalen, J., ,
Van Dyke, C., n
Van Hoorn, M. H., n
van Ryzin, K.,
van Swaay-Neto, J. M.,
Van Veldhuizen, D. A.,
van Wachem, E., ,
Vatn, K.,
Veen, D. J. V.,
Vielma, J. P., n,
Villaseñor, J., n
Vogel, W. R., – , n
Wagemaker, A. de P.,
Wagner, H. M., n
Wallace, S. W.,
Walls, M. R., n
Wan, Y.-w.,
Wang, H., n
Wang, K.,
Wang, K. C. P.,
Wang, Z., n
Ward, J., n
Ware, K. A.,
Waren, A. D.,
Wasem, O. J.,
Washburn, A.,
Webb, J. N.,
Wegryn, G. W., n
Wei, K. K.,
Weigel, D., n
Wein, L. M.,
Weintraub, A.,
Wetherly, J., n
Wheeler, B. R.,
White, A., n,
White, D. J.,
White, R. E., n
White, T.,
Whitt, W.,
Whittle, P.,
Willems, S. P.,
Williams, H. P., , ,
Wilson, A. M.,
Wilson, J. R., n,
Wiper, D. S.,
Wolfe, P., n, n
Wolsey, L. A.,
Wong, C. K.,
Woodgate, A., n
Wright, M. H.,
Wright, P. D.,
Wright, S. J., n
Wu, O. Q., n
Wu, S. D., Y
Yaman, H., n
Yamauchi, H. M.,
Yan, D.,
Yaniv, E., n
Yao, D. D., ,
Yao, X.,
Ybema, R., n
Ye, Y., , , , ,
Yildirim, E. A., n
Yoshino, T.,
Young, E. E., n
Young, W.,
Yu, G., n, n,
Yu, O. S., n, n
Yunes, T.,
Zaider, M., n
Zang, I., n
Zaniewski, J. P.,
Zank, H.,
Zhang, M., n
Zheng, Y.-S., n
Zhou, S. X., n
Ziemba, W. T.,
Zimmerman, R.,
Zipken, P. H.,
Zisgen, H.,
Zografos, K. G.,
Zouaoui, F.,

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