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A situation in which more than one optimal solution
is possible. It arises when the angle or slope of the objective is the same as
the slope of the constraint.
Alternative Optimal Solution

Cells that represent the decision variables in Solver.
Changing Cell

A restriction (stated in the form of an inequality of
an equation) that inhibits (or binds) the value that can be achieved by the
objective function.
Constraint

A point that lies on one of the corner of the feasible
region. This means that it falls at the intersection of two constraint lines.
Corner (or Extreme) Point

The method of finding the optimal solution to an LP problem
that involves testing the profit or cost level at each corner point of the
feasible region. The theory of LP states that the optimal solution must lie at
one of the corner points.
Corner Point Method

The unknown quantities in a problem for which optimal
solution values are to be found.
Decision Variable

The area that satisfies all of a problem’s resource
restrictions—that is, the region where all constraint overlap. All possible
solutions to the problem lie in the feasible region.
Feasible Region

Any point that lies in the feasible region. Basically, it is
any point that satisfies all of the problem’s constraints.
Feasible Solution

Any point that lies outside the feasible region. It
violates one or more of the stated constraints.
Infeasible Solution

A straight line that represents all nonnegative combinations
of the decision variable for a particular profit (or cost) level.
Level (Iso) Line

The general category of mathematical modeling and
solution techniques used to allocate resources while optimizing a measurable
goal; LP is one type of programming model.
Mathematical Programming

A mathematical statement of the goal of an
organization, stated as an intent to maximize or minimize some important
quantity, such as profit or cost.
Objective Function

A common LP problem that involves a decision as to
which products a firm should produce given that it faces limited resources.
Product Mix Problem

A constraint that does not affect the feasible
solution region.
Redundant Constraint

An iterative procedure for solving LP problems.
Simplex Method

The difference between the righthandside and
lefthandside of a ≤ constraint. Slack typically represents
the unused resource.
Slack

An Excel addin that allows LP problems to be set up
and solved in Excel.
Solver

The difference between the lefthandside and
righthandside of a ≥
constraint. Surplus typically represents the level of oversatisfaction of a
requirement.
Surplus

The cell that contains the formula for the objective
function in Solver.
Target Cell

A condition that exists when the objective value can
be made infinitely large (in a maximization problem) or small (in a
minimization problem) without violating any of the problem’s constraints.
Unbounded Solution

The coefficient for a decision variable in the objective
function. Typically, this refers to unit profit or unit cost.
Objective Function Coefficient (OFC)

The difference between the marginal contribution to
the objective function value from the inclusion of a decision variable and the
marginal worth of the resources it consumes. IN the case of a decison variable
that has an optimal value of zero, it is also the minimum amount by which the
OFC of that variable should change before it would have a nonzero optimal value
Reduced Cost

The study of how sensitive an optimal solution is to
model assumptions and to data changes. Also referred to as postoptimality
analysis.
Sensitivity Analysis

The magnitude of the change in the objective function
value for a unit increase in the RHS of a constraint.
Shadow Price

The difference between the RHS and LHS of a ≤ constraint. Typically
represents the unused resource.
Slack

The difference between the LHS and RHS of a ≥ constraint. Typically
represents the level of oversatisfication of a requirement
Surplus

Decision variables that are required to have integer
values of either 0 or 1. Also called 01 variables.
Binary Variables

An algorithm used by Solver and other software to
solve IP problems. It divides the set of feasible solutions into subregions
that are examined systematically.
BranchandBound Method

Decision variables that are required to be integer
valued. Actual values of these variables are restricted only by the constraints
in the problem.
General Integer Variables

A mathematical programming technique that produces
integer solutions to LP problems.
Integer Programming (IP)

A category of problems in which some decision
variables must have integer values (either general integer or binary) and other
decision variables can have fractional values.
Mixed Integer Programming

The minimum guaranteed amount one is willing to accept to
avoid the risk associated with a gamble.
Certainty Equivalent

A number from 0 to 1 such that when α is close to 1, the decision criterion is optimistic, and when
α is close to zero, the
decision criterion is pessimistic.
Coefficient of Realism (α)

A course of action or a strategy that can be chosen
by a decision maker.
Decision Alternative

A decisionmaking environment in which several outcomes can
occur as a result of a decision or alternative. Probabilities of the outcomes
are known.
Decision Making Under Risk

A decisionmaking environment in which several
outcomes can occur. Probabilities of these outcomes, however, are not known
Decision Making under Uncertainty

A table in which decision alternatives are listed down
the rows and outcomes are listed across the columns. The body of the table
contain the payoff.
Decision Table

A ratio of the expected value of sample information and the
expected value of perfect information.
Efficiency of Sample Information

The average or expected monetary outcome of a decision if it
can be repeated many times. This is determined by multiplying the monetary
outcomes by their respective probabilities. The results are then added to
arrive at the EMV.
Expected Monetary Value (EMV)

The average or expected regret of a decision
Expected Opportunity Loss (EOL)

The average or expected value of information if it is
completely accurate.
Expected Value of Perfect Information (EVPI)

The average or expected value of the decision if the
decision maker knew what would happen ahead of time.
Expected Value with Perfect Information (EVwPI):

The average or expected value of imperfect or survey
information
Expected Value of Sample Information (EVSI)

An optimistic decisionmaking criterion. This is the
alternative with the highest possible return.
Maximax

A pessimistic decisionmaking criterion that maximizes
the minimum outcome. It is the best of the worst possible outcomes
Maximin

A decision criterion that minimizes the maximum
opportunity loss.
Minimax Regret

The amount you would lose by not picking the best
alternative. For any outcome, this is the difference between the consequences
of any alternative and the best possible alternative. Also called regret.
Opportunity Loss

: A person who avoids risk. As the monetary value
increases on the utility curve, the utility increases at a decreasing rate.
This decision maker gets less utility for a greater risk and higher potential
returns
Risk Avoider

A person who is indifferent toward risk. The utility
curve for a riskneutral person is a straight line.
Risk Neutral

The monetary amount that a person is willing to give up in
order to avoid the risk associated with a gamble.
Risk Premium

A person who seeks risk. As the monetary values
increases on the utility curve, the utility increases at an increasing rate.
This decision maker gets more pleasure for a greater risk and higher potential
returns.
Risk Seeker

Decisions in which the outcome of one decision influences
other decisions.
Sequential Decisions

A graph or curve that illustrates the relationship between
utility and monetary values. When this curve has been constructed, utility
values from the curve can be used in the decisionmaking process.
Utility Curve

A theory that allows decision makers to incorporate
their risk preference and other factors into the decisionmaking process.
Utility Theory

A game in which the optimal strategy for both players
involves playing more than one strategy over time. Each strategy is played a
given percentage of the time
Mixed Strategy game

A game in which both players will always play just one
strategy.
Pure Strategy

A game that has a pure strategy
Saddle Point Game

A game that has only two players
Twoperson Game

The expected winning of the game if the game is played
a large number of times
Value of the Game

A game in which the losses for one player equal the gains
for the other player.
Zerosum Game

A specific class of network models that involves
determining the most efficient assignment of people to projects, salespeople to
territories, contracts to bidders, jobs to machines and so on
Assignment Model

A problem that finds the maximum flow of any quantity
or substances through a network
Maximal Flow Model

A model that determines the path through the network that
connects all the nodes while minimizing total distance.
MinimalSpanning Tree Model

A model that determines the shortest path or route
through a network
ShortestPath Model

: A specific case of network models that involves
scheduling shipment from origins to destination so that total shipping costs
are minimized.
Transportation Model

An extension of the transportation model in which some
points have both flows in and out of them.
Transshipment Model

The population from which arrivals at the queuing system
come. Also known as the calling population.
Arrival Population

The case in which arriving customer refuse to join the
waiting line.
Balking

A probability distribution that is often used to describe
random service times in a queuing system.
Exponential Distribution

A case in which the number of customers in the system is
significant proportion of the calling population.
Finite (or Limited) Population

A queue that cannot increase beyond a specific size.
Finite (or Limited) Queue Length

A queue discipline in which the customers are served
in the strict order of arrival.
FirstIn FirstOut (FIFO)

: A system in which service is received from more than
one station, one after the other.
Multiphase System

Descriptive characteristics of a queuing system,
including the average number of customers in a line and in the system, the
average waiting times in a line and in the system, and the percentage of idle
time.
Operating Characteristics

A probability distribution that is often used to
describe random arrivals in a queue.
Poisson distribution

One or more customers or units waiting to be served.
Also called a waiting line.
Queue

The rule by which customer in a line receive services.
Queue Discipline

: The case in which customer enter a queue but then
leave before being served.
Reneging

A queue discipline in which the customers are served
in the strict order of arrival
FirstIn FirstOut (FIFO):

A system in which service is received from more than
one station, one after the other
Multiphase System

Descriptive characteristics of a queuing system,
including the average number of customers in a line and in the system, the
average waiting times in a line and in the system, and the percentage of idle
time.
Operating Characteristics

A probability distribution that is often used to
describe random arrivals in a queue
Poisson distribution

One or more customers or units waiting to be served.
Also called a waiting line.
Queue

The rule by which customer in a line receive services
Queue Discipline

The case in which customer enter a queue but then
leave before being served.
Reneging

The proportion of time that the service facility is in
use
Utilization Ratio (ρ)

: A simulation model in which we need to keep track of the
passage of time by using a simulation clock.
DiscreteEvent Simulation

An excel function that can be used to randomly
generate values from discrete general probability distributions.
LOOKUP

A simulation that experiments with probabilistic
elements of a system by generating random numbers to create value for those
elements.
Monte Carlo Simulation

An Excel function generates a random number between 0
and 1 each time it is computed.
RAND

A number (typically between zero and one in most
computer programs) whose values is selected completely at random.
Random Number

A single run of a simulation model. Also known as a
run or trial
Replication

A technique that involves building a mathematical
model to represent a realworld situation. The model is then experimented with
to estimate the effects of various actions and decisions
Simulation

: A state then, when entered, cannot be left. The
probability of going from an absorbing state to any other state is 0.
Absorbing State

A condition that exists when the state probabilities
for a future period are the same as the state probabilities for a previous
period.
Equilibrium Condition

A type of analysis that allows us to predict the
future by using the state probabilities and the matrix of transition
probabilities.
Markov Analysis

A matrix containing all transition probabilities for a
certain process or system.
Matrix of Transition Probabilities

The probability of an event occurring at a point in
time. Examples include the probability that a person will be shopping at a
given grocery store during a given month
State Probability

The condition probability that we will be in a future
state given a current or existing state.
Transition Probability

