Key Concepts
Plain-language definitions and notation for the central ideas in V348, organized by week and alphabetically.
Use this as a map of the course, not a list to memorize. On each week page, dotted-underlined terms and selected notation open these same plain-language definitions on hover, keyboard focus, or tap. Details on any card opens a pop-out with a longer explanation, where the idea sits in the assigned chapter, and a worked example from a real organization, plus a second government or nonprofit example on the ideas where public work looks different. Each pop-out has its own link, so /concepts/#detail-shadow-price opens straight to that page.
Textbook alignment: the catalog is cross-checked against the in-scope material in Taylor, Introduction to Management Science (13e), Chapters 1, 2–4, 6, 8–9, 11–12, and 15. Definitions are concise original paraphrases, organized by the week in which each idea is first taught. Standard course extensions beyond Taylor are identified as such in the weekly lesson where they appear.
Break-even analysis
A method for finding the activity level where total revenue exactly equals total cost, so profit is zero.
Contribution margin
The selling price minus variable cost per unit; each unit contributes this amount toward fixed cost and then profit.
Decision variable
A mathematical symbol for a controllable activity level whose solved value provides a recommended decision.
Fixed cost
A cost that stays constant within the relevant activity range even when the number of units changes.
Linear function
A constant-rate relationship whose graph is a straight line, with a slope and an intercept.
Management-science model
An abstract representation of a problem situation, often expressed as a graph, chart, or set of mathematical relationships.
Management-science process
An ordered five-step approach of observation, problem definition, model construction, model solution, and implementation of the solution results.
Parameter
A fixed input supplied to a model, such as a price, cost, probability, capacity, or time estimate.
Profit equation
Profit is the amount left after subtracting total cost from total revenue; at break-even it equals zero.
Summation
Compact notation for adding a sequence of terms while an index runs over a stated range.
Variable cost
A per-unit cost that makes total cost rise with activity or production volume.
Addition rule
The rule for an “A or B” probability; it subtracts the overlap so outcomes are not counted twice.
Classical, relative-frequency, and subjective probability
The three places a probability can come from: counted from equally likely outcomes, observed as a share in past data, or judged by an informed expert. The first two are objective; the third is not.
Complement rule
A shortcut that finds an event through its opposite; “at least one” is often one minus “none.”
Conditional probability
The probability of one event after restricting attention to cases where another event occurred.
Dependent events
Events are dependent when learning that one occurred changes the probability of the other.
Expected value
The probability-weighted average outcome over many repetitions of an uncertain process.
Independence
Two events are independent when learning that one occurred does not change the probability of the other.
Joint probability
The probability that two events occur together.
Marginal probability
The probability of one event by itself, often found as a row or column total in a joint-probability table.
Multiplication rule
The rule for an “A and B” probability; it multiplies one event’s probability by the other event’s conditional probability.
Mutually exclusive events
Events that cannot occur on the same trial, so their joint probability is zero.
Probability
A number from 0 to 1 describing how likely an event is under a stated model or evidence base.
Probability distribution
A description of how probability is assigned across all possible outcomes or ranges of outcomes.
Probability experiment and event
A probability experiment is a repeatable chance process; an event is one specified outcome or set of outcomes from that process.
Random variable
A rule that assigns a numerical value to each outcome of a chance process.
Variance and standard deviation
Measures of spread around the expected value; standard deviation returns the spread to the outcome’s original units.
Coefficient of optimism
The Hurwicz weight placed on an alternative’s best payoff, with the remaining weight placed on its worst payoff.
Decision alternative
One controllable course of action available to the decision-maker, represented by a row in a payoff table.
Decision-making without probabilities (under uncertainty)
Choosing among alternatives when possible states are known but credible probabilities for those states are unavailable.
Dominance
Taylor calls an alternative dominant when it has a better payoff in every state; the standard weak form allows ties in some states if it is better in at least one.
Equal-likelihood (Laplace) criterion
A rule that averages an alternative’s payoffs as if all states were equally likely.
Hurwicz criterion
A compromise rule that blends each alternative’s best and worst payoffs using an optimism weight.
Maximax criterion
An optimistic rule that chooses the alternative with the largest possible payoff.
Maximin criterion
A cautious rule that chooses the alternative with the best worst-case payoff.
Minimax regret criterion
A rule that minimizes the largest regret a decision could produce.
Payoff table
A grid showing the payoff from each decision alternative under each possible state of nature.
Regret (opportunity loss)
The payoff forgone because a chosen alternative was not the best one for the state that actually occurred.
State of nature
A future condition outside the decision-maker’s control, such as high demand, low demand, rain, or drought.
Week 4
EVPI) →Decision-making with probabilities (under risk)
Choosing among alternatives when the possible states and their probabilities are known or estimated.
Expected monetary value (EMV)
A decision alternative’s probability-weighted average monetary payoff across all states of nature.
Expected opportunity loss (EOL)
The probability-weighted average regret for an alternative; minimizing EOL gives the same choice as maximizing expected value.
Expected value of perfect information (EVPI)
The most a rational decision-maker should pay for perfectly accurate information before acting.
Expected value with perfect information
The expected payoff if the decision-maker could know the future state before choosing an action.
Decision and probability nodes
Squares mark decision alternatives; circles mark probability events, which are also commonly called chance nodes.
Decision strategy
A complete contingent plan that specifies the best action at every decision node that might be reached.
Decision tree
A left-to-right diagram of choices, uncertain events, probabilities, and payoffs in their actual sequence.
Sequential decision
A problem in which an early choice or observation changes the options available at a later decision point.
Working backward (foldback/rollback)
Solving a decision tree from right to left by averaging at chance nodes and keeping the best branch at decision nodes.
Week 6
EVSI & Utility →Bayes’ rule
A rule that combines prior and conditional probabilities to compute a revised posterior probability after new information.
Certainty equivalent and risk premium
The certainty equivalent is a sure amount valued like a gamble; EV minus that amount is the risk premium.
Expected utility
The probability-weighted average utility of uncertain outcomes, used when money alone does not represent the decision-maker’s preferences.
Expected value of sample information (EVSI)
The improvement in expected payoff from imperfect information before subtracting what that information costs.
Information efficiency
The share of perfect information’s potential value captured by an imperfect information source.
Likelihood
The probability of observing a particular signal if a given state is true.
Posterior probability
The revised probability of a state after combining the prior with observed evidence.
Prior probability
A belief about a state before observing the new signal or evidence.
Risk attitudes (averter, indifferent, taker)
Taylor distinguishes risk averters, risk takers, and people indifferent to risk by how they value uncertain outcomes relative to sure ones.
Sample information
Imperfect evidence from a test, survey, forecast, or sample that can revise probabilities before a decision is made.
Utility
A numerical measure of the satisfaction or value a decision-maker derives from an outcome, rather than its dollar amount alone.
Additivity
An LP assumption that total effects equal the sum of individual-variable effects, with no interaction terms.
Certainty assumption
An LP assumption that every objective coefficient, constraint coefficient, and right-hand side is known and fixed.
Constraint
A mathematical limit or requirement that every feasible decision must satisfy.
Corner point
A vertex of the feasible region; if a linear program has a finite optimum, at least one corner is optimal.
Divisibility
An LP assumption that decision variables may take fractional values unless a separate integer restriction is imposed.
Feasible solution area (feasible region)
The set of all decision-variable combinations that satisfy every constraint at the same time.
Infeasible problem
A model whose constraints have no common solution, so its feasible region is empty.
Linear programming (LP)
A method for maximizing or minimizing a linear objective while satisfying linear constraints.
Multiple optimal solutions
Two or more feasible solutions that share the same best objective value; in a two-variable LP an entire edge may tie.
Nonnegativity restriction
The common requirement that decision variables cannot take negative values.
Objective function
The mathematical expression a model seeks to maximize or minimize, such as profit, impact, time, or cost.
Proportionality
An LP assumption that each variable’s contribution to the objective and resource use changes at a constant per-unit rate.
Slack
Unused capacity in a less-than-or-equal constraint at a particular solution.
Surplus variable
The amount by which a greater-than-or-equal requirement is exceeded; subtracting it converts the inequality to an equation.
Unbounded problem
A model whose objective can improve without limit because the feasible region is open in that direction, often signaling a missing constraint.
Binding constraint
A constraint whose left-hand side equals its right-hand-side value at the solution, leaving zero slack or surplus.
Changing cells
Spreadsheet cells holding decision variables that Solver is allowed to adjust.
Excel Solver
Excel’s optimization add-in, which changes decision cells to optimize a target cell while enforcing constraints.
Optimal solution
A feasible decision that gives the best objective value among all feasible alternatives.
Solver Answer Report
A Solver report summarizing final variable values, the objective, constraint status, and remaining slack.
Objective-coefficient sensitivity range (allowable range)
For one objective-function coefficient, the interval over which the current optimal solution remains optimal while all other parameters stay fixed.
Objective-function coefficient
The per-unit contribution of a decision variable to the objective, such as profit per product or cost per shipment.
Reduced cost
For a zero-valued variable, the objective-coefficient improvement needed before that variable can enter the optimal solution.
RHS sensitivity range
The interval over which one constraint’s right-hand side may change while its current shadow price remains valid.
Right-hand side (RHS)
The constant limit or requirement on the right side of a constraint, often representing available capacity or minimum need.
Sensitivity analysis
Testing how a model’s solution or value changes when an input changes.
Shadow price
The change in the optimal objective value from one more unit of a constraint’s right-hand side, within its allowable range.
Solver Sensitivity Report
A Solver report containing objective and right-hand-side ranges, shadow prices, and reduced costs for an optimal linear program.
Technological coefficient
A constraint coefficient describing how much of a resource one unit of a decision activity uses or supplies.
Week 10
Transshipment & Assignment →Assignment model
A transportation special case that matches each person or resource to exactly one task, and each task to exactly one resource.
Balanced transportation problem
A transportation problem in which total supply equals total demand.
Binary (0-1) variable
A decision variable restricted to 0 or 1, used for yes/no choices such as opening a site or funding a project.
Branch and bound
The search Solver uses for integer models. It solves relaxed LPs and prunes branches that cannot beat the best whole-number answer found so far.
Flow balance
The accounting rule that inflow equals outflow at a pure transfer node, adjusted for any supply or demand located there.
Integer programming
A linear program with the extra requirement that some or all decision variables come out whole, used when fractional answers are meaningless.
LP relaxation
The same model solved with the whole-number requirement dropped. Its objective value bounds the true integer optimum, which can never beat it.
Mixed-integer model
A model in which some variables must be whole numbers while others may stay fractional.
Source and destination
A source is an origin with available supply; a destination is a receiving point with demand to be met.
Transportation model
A linear program that routes quantities from supply points to demand points at minimum total cost.
Transshipment
A network model that lets flow pass through intermediate locations such as hubs, warehouses, or transfer stations.
Unbalanced transportation problem
A transportation model in which total supply and total demand differ, so some supply or demand must remain slack or be represented explicitly.
Unit shipping cost
The cost of sending one unit along a specific source-to-destination route.
AHP consistency ratio
A comparison of observed pairwise inconsistency with random inconsistency; Taylor treats a ratio below 0.10 as satisfactory.
AHP preference scale
The reciprocal 1–9 scale AHP uses to express how strongly one item is preferred to another in a pairwise comparison.
Analytical Hierarchy Process (AHP)
A method that derives priorities from structured pairwise comparisons among criteria and alternatives.
Deviational variable
A variable measuring how far a result falls below or rises above a goal target.
Goal constraint
A target written as an equality by adding underachievement and overachievement deviation variables.
Goal programming
An optimization method that minimizes unwanted departures from several targets instead of optimizing one outcome alone.
Most satisfactory solution (satisficing)
The goal-programming solution that satisfies the stated goals as well as possible, even when not every goal can be achieved.
Normalization
Rescaling values to a common basis; min–max scoring maps raw values to 0–1, while Taylor’s AHP divides each matrix entry by its column total.
Pairwise comparison
A judgment made between two items at a time, used by AHP to build a full set of relative priorities.
Preemptive priority
A strict goal ranking in which a lower-priority goal is improved only after higher-priority performance is protected.
Preference vector
A set of AHP priority weights derived from a pairwise-comparison matrix and normalized to sum to one.
Scoring model
A multi-criteria method that rates each alternative on each criterion and combines the ratings with importance weights.
Weighted goals at one priority level
Taylor’s approach weights and sums unwanted deviations at the same priority level without allowing them to override a higher-priority goal.
Weighted scoring
A multi-criteria method that multiplies each criterion score by its importance weight and sums the results.
Activity-on-node and activity-on-arrow
AON represents activities as nodes, while AOA represents activities as arrows between milestone events.
Backward pass
Moving from project finish to start to compute each activity’s latest allowable start and finish.
Crash cost per time unit
The extra cost of an activity’s maximum feasible time reduction divided by the number of time units saved.
Critical path
The longest-duration path through a project network; its zero-slack activities determine the planned completion time.
Deadline z-score
The number of project standard deviations between an expected finish and a proposed deadline.
Dummy activity
A zero-duration arrow used in an AOA network only to preserve the correct precedence relationships.
Earliest and latest activity times
ES and EF show the soonest an activity can occur; LS and LF show the latest it can occur without delaying the project.
Forward pass
Moving through a project network from start to finish to compute each activity’s earliest start and finish.
Gantt chart
A calendar-style bar chart showing when project activities run, useful for timing but less explicit about network dependencies.
PERT
A project-scheduling method that represents each activity duration with optimistic, most-likely, and pessimistic estimates.
PERT expected time and variance
Formulas that turn three duration estimates into an activity mean and uncertainty measure.
Precedence relationship
A dependency specifying that one project activity must occur before another can begin or finish.
Project activity
A task that consumes time and possibly resources in a project network.
Project crashing
Reducing project duration at minimum added cost by shortening critical-path activities and recomputing the path as times change.
Project network
A directed project diagram showing tasks, durations, and precedence relationships.
Project-activity slack
The time an activity can slip without delaying the project’s planned finish.
Cumulative error and average error (bias)
Cumulative error sums signed errors; average error divides that sum by the number of periods. Positive values indicate forecasts biased low, and negative values indicate forecasts biased high.
Exponential smoothing
A recursive forecast that updates the previous forecast by a fraction of its latest error.
Forecast error
The difference between what actually happened and what the forecast predicted for the same period.
Mean absolute deviation (MAD)
The average absolute forecast error, expressed in the same units as the series.
Mean squared error (MSE)
The average squared forecast error, which penalizes large misses more heavily than small ones.
Moving average
A forecast equal to the average of the most recent fixed number of actual observations.
Smoothing constant
The number from 0 to 1 controlling how strongly an exponential-smoothing forecast reacts to the newest observation.
Time-series patterns
Trend, seasonality, cycles, and random variation are recurring shapes that guide the choice of forecasting method.
Weighted moving average
A moving-average forecast that assigns unequal weights to recent observations, with weights totaling one.
Adjusted exponential smoothing
Exponential smoothing with a trend factor added, so the forecast stops sitting permanently below a climbing series.
Coefficient of determination (R²)
The share of variation in the outcome explained by the fitted linear model.
Correlation coefficient
A number from −1 to +1 describing the direction and strength of a linear relationship.
Correlation versus causation
A strong association can support prediction without proving that changing one variable will cause the other to change.
Extrapolation
Predicting beyond the range of data used to fit a model, where the observed relationship may no longer hold.
Independent and dependent variables
The independent variable x is used to explain or predict the dependent response y.
Least squares
A fitting rule that chooses the line with the smallest sum of squared residuals.
Linear regression
A model that predicts an outcome from a related variable using a fitted straight line.
Linear trend
A straight-line model of how a time series changes by a roughly constant amount each period.
Residual
The vertical gap between an observed outcome and the value predicted by a fitted model.
Scatter diagram
A plot of paired x and y observations used to inspect a relationship’s direction, shape, spread, and unusual points.
Seasonal factor
One period's share of the total across all cycles observed. Multiply a forecast total by the factors to split it back into a seasonal shape; the factors sum to 1.
Trend factor
A smoothed estimate of how much the forecast itself moves each period, controlled by beta and added to the ordinary smoothed forecast.
Deterministic and probabilistic models
A deterministic model assumes no uncertainty in its parameters; a probabilistic model includes uncertainty and can produce more than one possible result.
Evidence-based recommendation
A decision statement that names the action, supporting result, important assumptions, uncertainty, and next step.
Model selection
Matching a real decision’s structure and available evidence to the management-science method that can answer it.
Sensitivity check
Re-running an analysis under plausible input changes to see whether the recommendation is robust or fragile.
Activity-on-node and activity-on-arrow
AON represents activities as nodes, while AOA represents activities as arrows between milestone events.
Addition rule
The rule for an “A or B” probability; it subtracts the overlap so outcomes are not counted twice.
Additivity
An LP assumption that total effects equal the sum of individual-variable effects, with no interaction terms.
Adjusted exponential smoothing
Exponential smoothing with a trend factor added, so the forecast stops sitting permanently below a climbing series.
AHP consistency ratio
A comparison of observed pairwise inconsistency with random inconsistency; Taylor treats a ratio below 0.10 as satisfactory.
AHP preference scale
The reciprocal 1–9 scale AHP uses to express how strongly one item is preferred to another in a pairwise comparison.
Analytical Hierarchy Process (AHP)
A method that derives priorities from structured pairwise comparisons among criteria and alternatives.
Assignment model
A transportation special case that matches each person or resource to exactly one task, and each task to exactly one resource.
Backward pass
Moving from project finish to start to compute each activity’s latest allowable start and finish.
Balanced transportation problem
A transportation problem in which total supply equals total demand.
Bayes’ rule
A rule that combines prior and conditional probabilities to compute a revised posterior probability after new information.
Binary (0-1) variable
A decision variable restricted to 0 or 1, used for yes/no choices such as opening a site or funding a project.
Binding constraint
A constraint whose left-hand side equals its right-hand-side value at the solution, leaving zero slack or surplus.
Branch and bound
The search Solver uses for integer models. It solves relaxed LPs and prunes branches that cannot beat the best whole-number answer found so far.
Break-even analysis
A method for finding the activity level where total revenue exactly equals total cost, so profit is zero.
Certainty assumption
An LP assumption that every objective coefficient, constraint coefficient, and right-hand side is known and fixed.
Certainty equivalent and risk premium
The certainty equivalent is a sure amount valued like a gamble; EV minus that amount is the risk premium.
Changing cells
Spreadsheet cells holding decision variables that Solver is allowed to adjust.
Classical, relative-frequency, and subjective probability
The three places a probability can come from: counted from equally likely outcomes, observed as a share in past data, or judged by an informed expert. The first two are objective; the third is not.
Coefficient of determination (R²)
The share of variation in the outcome explained by the fitted linear model.
Coefficient of optimism
The Hurwicz weight placed on an alternative’s best payoff, with the remaining weight placed on its worst payoff.
Complement rule
A shortcut that finds an event through its opposite; “at least one” is often one minus “none.”
Conditional probability
The probability of one event after restricting attention to cases where another event occurred.
Constraint
A mathematical limit or requirement that every feasible decision must satisfy.
Contribution margin
The selling price minus variable cost per unit; each unit contributes this amount toward fixed cost and then profit.
Corner point
A vertex of the feasible region; if a linear program has a finite optimum, at least one corner is optimal.
Correlation coefficient
A number from −1 to +1 describing the direction and strength of a linear relationship.
Correlation versus causation
A strong association can support prediction without proving that changing one variable will cause the other to change.
Crash cost per time unit
The extra cost of an activity’s maximum feasible time reduction divided by the number of time units saved.
Critical path
The longest-duration path through a project network; its zero-slack activities determine the planned completion time.
Cumulative error and average error (bias)
Cumulative error sums signed errors; average error divides that sum by the number of periods. Positive values indicate forecasts biased low, and negative values indicate forecasts biased high.
Deadline z-score
The number of project standard deviations between an expected finish and a proposed deadline.
Decision alternative
One controllable course of action available to the decision-maker, represented by a row in a payoff table.
Decision and probability nodes
Squares mark decision alternatives; circles mark probability events, which are also commonly called chance nodes.
Decision strategy
A complete contingent plan that specifies the best action at every decision node that might be reached.
Decision tree
A left-to-right diagram of choices, uncertain events, probabilities, and payoffs in their actual sequence.
Decision variable
A mathematical symbol for a controllable activity level whose solved value provides a recommended decision.
Decision-making with probabilities (under risk)
Choosing among alternatives when the possible states and their probabilities are known or estimated.
Decision-making without probabilities (under uncertainty)
Choosing among alternatives when possible states are known but credible probabilities for those states are unavailable.
Dependent events
Events are dependent when learning that one occurred changes the probability of the other.
Deterministic and probabilistic models
A deterministic model assumes no uncertainty in its parameters; a probabilistic model includes uncertainty and can produce more than one possible result.
Deviational variable
A variable measuring how far a result falls below or rises above a goal target.
Divisibility
An LP assumption that decision variables may take fractional values unless a separate integer restriction is imposed.
Dominance
Taylor calls an alternative dominant when it has a better payoff in every state; the standard weak form allows ties in some states if it is better in at least one.
Dummy activity
A zero-duration arrow used in an AOA network only to preserve the correct precedence relationships.
Earliest and latest activity times
ES and EF show the soonest an activity can occur; LS and LF show the latest it can occur without delaying the project.
Equal-likelihood (Laplace) criterion
A rule that averages an alternative’s payoffs as if all states were equally likely.
Evidence-based recommendation
A decision statement that names the action, supporting result, important assumptions, uncertainty, and next step.
Excel Solver
Excel’s optimization add-in, which changes decision cells to optimize a target cell while enforcing constraints.
Expected monetary value (EMV)
A decision alternative’s probability-weighted average monetary payoff across all states of nature.
Expected opportunity loss (EOL)
The probability-weighted average regret for an alternative; minimizing EOL gives the same choice as maximizing expected value.
Expected utility
The probability-weighted average utility of uncertain outcomes, used when money alone does not represent the decision-maker’s preferences.
Expected value
The probability-weighted average outcome over many repetitions of an uncertain process.
Expected value of perfect information (EVPI)
The most a rational decision-maker should pay for perfectly accurate information before acting.
Expected value of sample information (EVSI)
The improvement in expected payoff from imperfect information before subtracting what that information costs.
Expected value with perfect information
The expected payoff if the decision-maker could know the future state before choosing an action.
Exponential smoothing
A recursive forecast that updates the previous forecast by a fraction of its latest error.
Extrapolation
Predicting beyond the range of data used to fit a model, where the observed relationship may no longer hold.
Feasible solution area (feasible region)
The set of all decision-variable combinations that satisfy every constraint at the same time.
Fixed cost
A cost that stays constant within the relevant activity range even when the number of units changes.
Flow balance
The accounting rule that inflow equals outflow at a pure transfer node, adjusted for any supply or demand located there.
Forecast error
The difference between what actually happened and what the forecast predicted for the same period.
Forward pass
Moving through a project network from start to finish to compute each activity’s earliest start and finish.
Gantt chart
A calendar-style bar chart showing when project activities run, useful for timing but less explicit about network dependencies.
Goal constraint
A target written as an equality by adding underachievement and overachievement deviation variables.
Goal programming
An optimization method that minimizes unwanted departures from several targets instead of optimizing one outcome alone.
Hurwicz criterion
A compromise rule that blends each alternative’s best and worst payoffs using an optimism weight.
Independence
Two events are independent when learning that one occurred does not change the probability of the other.
Independent and dependent variables
The independent variable x is used to explain or predict the dependent response y.
Infeasible problem
A model whose constraints have no common solution, so its feasible region is empty.
Information efficiency
The share of perfect information’s potential value captured by an imperfect information source.
Integer programming
A linear program with the extra requirement that some or all decision variables come out whole, used when fractional answers are meaningless.
Joint probability
The probability that two events occur together.
Least squares
A fitting rule that chooses the line with the smallest sum of squared residuals.
Likelihood
The probability of observing a particular signal if a given state is true.
Linear function
A constant-rate relationship whose graph is a straight line, with a slope and an intercept.
Linear programming (LP)
A method for maximizing or minimizing a linear objective while satisfying linear constraints.
Linear regression
A model that predicts an outcome from a related variable using a fitted straight line.
Linear trend
A straight-line model of how a time series changes by a roughly constant amount each period.
LP relaxation
The same model solved with the whole-number requirement dropped. Its objective value bounds the true integer optimum, which can never beat it.
Management-science model
An abstract representation of a problem situation, often expressed as a graph, chart, or set of mathematical relationships.
Management-science process
An ordered five-step approach of observation, problem definition, model construction, model solution, and implementation of the solution results.
Marginal probability
The probability of one event by itself, often found as a row or column total in a joint-probability table.
Maximax criterion
An optimistic rule that chooses the alternative with the largest possible payoff.
Maximin criterion
A cautious rule that chooses the alternative with the best worst-case payoff.
Mean absolute deviation (MAD)
The average absolute forecast error, expressed in the same units as the series.
Mean squared error (MSE)
The average squared forecast error, which penalizes large misses more heavily than small ones.
Minimax regret criterion
A rule that minimizes the largest regret a decision could produce.
Mixed-integer model
A model in which some variables must be whole numbers while others may stay fractional.
Model selection
Matching a real decision’s structure and available evidence to the management-science method that can answer it.
Most satisfactory solution (satisficing)
The goal-programming solution that satisfies the stated goals as well as possible, even when not every goal can be achieved.
Moving average
A forecast equal to the average of the most recent fixed number of actual observations.
Multiple optimal solutions
Two or more feasible solutions that share the same best objective value; in a two-variable LP an entire edge may tie.
Multiplication rule
The rule for an “A and B” probability; it multiplies one event’s probability by the other event’s conditional probability.
Mutually exclusive events
Events that cannot occur on the same trial, so their joint probability is zero.
Nonnegativity restriction
The common requirement that decision variables cannot take negative values.
Normalization
Rescaling values to a common basis; min–max scoring maps raw values to 0–1, while Taylor’s AHP divides each matrix entry by its column total.
Objective function
The mathematical expression a model seeks to maximize or minimize, such as profit, impact, time, or cost.
Objective-coefficient sensitivity range (allowable range)
For one objective-function coefficient, the interval over which the current optimal solution remains optimal while all other parameters stay fixed.
Objective-function coefficient
The per-unit contribution of a decision variable to the objective, such as profit per product or cost per shipment.
Optimal solution
A feasible decision that gives the best objective value among all feasible alternatives.
Pairwise comparison
A judgment made between two items at a time, used by AHP to build a full set of relative priorities.
Parameter
A fixed input supplied to a model, such as a price, cost, probability, capacity, or time estimate.
Payoff table
A grid showing the payoff from each decision alternative under each possible state of nature.
PERT
A project-scheduling method that represents each activity duration with optimistic, most-likely, and pessimistic estimates.
PERT expected time and variance
Formulas that turn three duration estimates into an activity mean and uncertainty measure.
Posterior probability
The revised probability of a state after combining the prior with observed evidence.
Precedence relationship
A dependency specifying that one project activity must occur before another can begin or finish.
Preemptive priority
A strict goal ranking in which a lower-priority goal is improved only after higher-priority performance is protected.
Preference vector
A set of AHP priority weights derived from a pairwise-comparison matrix and normalized to sum to one.
Prior probability
A belief about a state before observing the new signal or evidence.
Probability
A number from 0 to 1 describing how likely an event is under a stated model or evidence base.
Probability distribution
A description of how probability is assigned across all possible outcomes or ranges of outcomes.
Probability experiment and event
A probability experiment is a repeatable chance process; an event is one specified outcome or set of outcomes from that process.
Profit equation
Profit is the amount left after subtracting total cost from total revenue; at break-even it equals zero.
Project activity
A task that consumes time and possibly resources in a project network.
Project crashing
Reducing project duration at minimum added cost by shortening critical-path activities and recomputing the path as times change.
Project network
A directed project diagram showing tasks, durations, and precedence relationships.
Project-activity slack
The time an activity can slip without delaying the project’s planned finish.
Proportionality
An LP assumption that each variable’s contribution to the objective and resource use changes at a constant per-unit rate.
Random variable
A rule that assigns a numerical value to each outcome of a chance process.
Reduced cost
For a zero-valued variable, the objective-coefficient improvement needed before that variable can enter the optimal solution.
Regret (opportunity loss)
The payoff forgone because a chosen alternative was not the best one for the state that actually occurred.
Residual
The vertical gap between an observed outcome and the value predicted by a fitted model.
RHS sensitivity range
The interval over which one constraint’s right-hand side may change while its current shadow price remains valid.
Right-hand side (RHS)
The constant limit or requirement on the right side of a constraint, often representing available capacity or minimum need.
Risk attitudes (averter, indifferent, taker)
Taylor distinguishes risk averters, risk takers, and people indifferent to risk by how they value uncertain outcomes relative to sure ones.
Sample information
Imperfect evidence from a test, survey, forecast, or sample that can revise probabilities before a decision is made.
Scatter diagram
A plot of paired x and y observations used to inspect a relationship’s direction, shape, spread, and unusual points.
Scoring model
A multi-criteria method that rates each alternative on each criterion and combines the ratings with importance weights.
Seasonal factor
One period's share of the total across all cycles observed. Multiply a forecast total by the factors to split it back into a seasonal shape; the factors sum to 1.
Sensitivity analysis
Testing how a model’s solution or value changes when an input changes.
Sensitivity check
Re-running an analysis under plausible input changes to see whether the recommendation is robust or fragile.
Sequential decision
A problem in which an early choice or observation changes the options available at a later decision point.
Shadow price
The change in the optimal objective value from one more unit of a constraint’s right-hand side, within its allowable range.
Slack
Unused capacity in a less-than-or-equal constraint at a particular solution.
Smoothing constant
The number from 0 to 1 controlling how strongly an exponential-smoothing forecast reacts to the newest observation.
Solver Answer Report
A Solver report summarizing final variable values, the objective, constraint status, and remaining slack.
Solver Sensitivity Report
A Solver report containing objective and right-hand-side ranges, shadow prices, and reduced costs for an optimal linear program.
Source and destination
A source is an origin with available supply; a destination is a receiving point with demand to be met.
State of nature
A future condition outside the decision-maker’s control, such as high demand, low demand, rain, or drought.
Summation
Compact notation for adding a sequence of terms while an index runs over a stated range.
Surplus variable
The amount by which a greater-than-or-equal requirement is exceeded; subtracting it converts the inequality to an equation.
Technological coefficient
A constraint coefficient describing how much of a resource one unit of a decision activity uses or supplies.
Time-series patterns
Trend, seasonality, cycles, and random variation are recurring shapes that guide the choice of forecasting method.
Transportation model
A linear program that routes quantities from supply points to demand points at minimum total cost.
Transshipment
A network model that lets flow pass through intermediate locations such as hubs, warehouses, or transfer stations.
Trend factor
A smoothed estimate of how much the forecast itself moves each period, controlled by beta and added to the ordinary smoothed forecast.
Unbalanced transportation problem
A transportation model in which total supply and total demand differ, so some supply or demand must remain slack or be represented explicitly.
Unbounded problem
A model whose objective can improve without limit because the feasible region is open in that direction, often signaling a missing constraint.
Unit shipping cost
The cost of sending one unit along a specific source-to-destination route.
Utility
A numerical measure of the satisfaction or value a decision-maker derives from an outcome, rather than its dollar amount alone.
Variable cost
A per-unit cost that makes total cost rise with activity or production volume.
Variance and standard deviation
Measures of spread around the expected value; standard deviation returns the spread to the outcome’s original units.
Weighted goals at one priority level
Taylor’s approach weights and sums unwanted deviations at the same priority level without allowing them to override a higher-priority goal.
Weighted moving average
A moving-average forecast that assigns unequal weights to recent observations, with weights totaling one.
Weighted scoring
A multi-criteria method that multiplies each criterion score by its importance weight and sums the results.
Working backward (foldback/rollback)
Solving a decision tree from right to left by averaging at chance nodes and keeping the best branch at decision nodes.