309 Terms Flashcards
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 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 iteractive procedure for solving LP problems.
Simplex Method
The difference between the right-hand-side and left-hand-side of a ≤ constraint. Slack typically represents the unused resource.
Slack
An Excel add-in that allows LP problems to be set up and solved in Excel.
Solver
The difference between the left-hand-side and right-hand-side 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
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 0-1 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.
Branch-and-Bound 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
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
A course of action or a strategy that can be chosen by a decision maker.
Decision Alternative
A decision-making 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 decision-making 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 decision-making criterion. This is the alternative with the highest possible return.
Maximax
A pessimistic decision-making 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 risk-neutral 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 decision-making process.
Utility Curve
A theory that allows decision makers to incorporate their risk preference and other factors into the decision-making 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.
Two-person 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.
Zero-sum 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.
Minimal-Spanning Tree Model
A model that determines the shortest path or route through a network.
Shortest-Path 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.
First-In First-Out (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 customers 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
A simulation model in which we need to keep track of the passage of time by using a simulation clock.
Discrete-Event 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 real-world 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
