CEE 201: Systems Analysis and Linear Programming Flashcards

Comprehensive vocabulary flashcards covering key terms and concepts across Systems Analysis, Model Building, Linear Programming, Feasible Region, Simplex Method, RHS Sensitivity, and Objective Function Sensitivity.

Systems Analysis

The application of mathematical models to quantitative decision-making problems for systems.

Descriptive Model

A model category that describes changes that have occurred based on historical data, characterized by the phrase "This is what has happened."

Predictive Model

A model category that forecasts outcomes based on a given set of inputs and conditions, characterized by the phrase "This is what will happen."

Prescriptive Model

A model category that leads directly to a decision, characterized by the phrase "This is what you should do."

Deterministic Model

A model that produces a single, certain outcome from a defined set of inputs and conditions without probability or randomness.

Stochastic Model

A model in which multiple outcomes are possible because inputs and conditions vary probabilistically.

Mathematical Programming

Another term for optimization, consisting of decision variables, parameters, constraints, and an objective function.

Decision Variables

Quantities representing all the decisions that must be made, including their components and consequences in an optimization problem.

Parameters

Given data and fixed values in an optimization model that cannot be affected or changed by decisions.

Constraints

Restrictions that connect decision variables to one another, acting as resource limits or logical rules.

Objective Function

A mathematical function defining the goal or criterion used to evaluate and compare different candidate solutions.

Linear Programming

An optimization technique where the objective function and all constraint equations or inequalities are additive and proportional linear combinations of decision variables.

Feasible Region

The set of all possible points or solutions that satisfy all constraints of a linear programming problem simultaneously.

Convexity

A geometric property where a line segment connecting any two points in a region lies entirely within or on the boundary of that region.

Bounded Feasible Region

A compact feasible region that is fully enclosed and does not extend to infinity in any direction.

Extreme Point

A corner point or vertex of the feasible region formed by the intersection of constraint boundary lines.

Extreme Point Theorem

A fundamental theorem stating that if an optimal solution exists for a linear program, at least one optimal solution occurs at a vertex or corner point of the feasible region.

Simplex Method

An algorithmic approach developed by George Dantzig in $1947$ that iteratively moves along adjacent extreme points of a convex polytope to locate the optimal solution.

Slack Variable

A non-negative variable added to a less-than-or-equal-to ($\\le$) inequality constraint to convert it into an equivalent equality equation.

Surplus Variable

A non-negative variable subtracted from a greater-than-or-equal-to ($\\ge$) inequality constraint to convert it into an equivalent equality equation.

Degeneracy

A condition in linear programming occurring when a vertex of the feasible region corresponds to more than one basic feasible solution.

Binding Constraint

A constraint satisfied exactly as an equality at the optimal solution, fully utilizing available resources and leaving zero slack or surplus.

Non-Binding Constraint

A constraint not satisfied as an equality at the optimal solution, having non-zero slack or surplus and a shadow price equal to $0$.

Right-Hand Side

The constant term in a constraint inequality or equality representing the limit or maximum availability of a resource.

Shadow Price

The dual value indicating the amount by which the optimal objective function value changes per unit increase in the right-hand side of a binding constraint.

Range of Feasibility

The range of values over which the right-hand side of a constraint can change without altering the optimal basis.

Allowable Increase

The maximum amount by which a parameter (such as right-hand side or objective coefficient) can increase before the shadow price changes or the optimal basis shifts.

Allowable Decrease

The maximum amount by which a parameter (such as right-hand side or objective coefficient) can decrease before the shadow price changes or the optimal basis shifts.

Objective Function Sensitivity Analysis

The study of how variations in the coefficients of decision variables in the objective function impact the optimal solution and objective value.

Range of Optimality

The range of values over which an objective function coefficient can vary without changing the optimal decision variables.

Binding Variable

A decision variable that directly influences the optimal solution, where changes to its objective function coefficient alter the optimal value of the objective function.

Non-Binding Variable

A variable that does not directly influence the optimal solution at its current value, having a shadow price of $0$ for small coefficient changes.