Quantitative Modeling and Linear Programming Concepts

Vocabulary flashcards reviewing core concepts in quantitative modeling, linear programming, constraints, and network problems.

Probabilistic model

A model that uses probability because some data is uncertain.

Deterministic model

A model where all input values are known with certainty.

Redundant constraint

A constraint that does not change the feasible region, meaning the optimal solution and feasible region do not change when it is removed.

Alternate optimal solutions

Multiple feasible solutions that produce the same optimal objective value.

Unbounded linear programming problem

A problem where the objective can improve indefinitely without violating constraints.

Bounding an unbounded profit problem

The process of adding effective resource or production limits, such as $3X \le 500$ and $2Y \le 600$.

Linear programming acceptable objective function

An objective function where variables appear only to the first power, without products between variables.

Problems unsolvable by linear programming

A problem with a nonlinear objective function or nonlinear constraints.

Transportation network model objective

The usual objective to minimize total shipping cost while satisfying supply and demand.

Quantitative modeling process order

The sequence consisting of: formulate the problem, solve the model, and interpret the results.

Slack

The unused amount of a resource in a constraint.

Binding constraint

A constraint that is met exactly, whose final value equals its constraint limit in a Solver report, and its slack is zero.

Nonbinding constraint

A constraint that has nonzero slack because some resource remains unused.

Feasible region

The set of all solutions that satisfy every constraint.

Corner points

The vertices of the feasible region where optimal solutions can occur in linear programming.

Objective function

The equation representing the quantity to maximize or minimize, such as profit or cost.

Qualitative model

A model based mainly on descriptive judgments rather than numerical measurements.

Quantitative model

A model that uses numerical data and mathematical relationships.

Transportation problem

A network problem that determines how much to ship from sources to destinations.

Decision variable

A controllable quantity the model determines, such as units produced or shipped.

Constraints

Limits or requirements that decision variables must satisfy.

Maximization objective

An objective to choose feasible decision-variable values that make the objective as large as possible.

Minimization objective

An objective to choose feasible decision-variable values that make the objective as small as possible.

Sensitivity analysis

Examining how changes in model inputs affect the optimal solution.

RHS of a constraint

The right-hand-side value representing a resource limit or required minimum.

Positive slack ($\le$ constraint)

Indicates that the constraint is nonbinding and has unused capacity.

Negative net flow

An indication that there is more outgoing than incoming flow at a node under the worksheet's net-flow convention.