Analytics Exam 2

Linear Program (LP)

A mathematical optimization model built entirely from linear equations and/or inequalities

Optimization

The process of finding the best (most efficient) way of using limited resources to achieve the objective(s) of an individual or organization

Decision Variables

values being determined by solution of the problem

Ex: X₁ = # of model A motors made in the production period

Parameters

values assumed to be known with “certainty” at the outset

Ex: Time required for wiring one Model A motor is 3 hours

Objective Function

Max or Min description of our purpose for solving the problem

Constraints

Limitations on our ability to achieve our objective

Ex: we only have 240 hours of employee time available during the production period for wiring motors

Corner Point Property/Fundamental Rule of Linear Program

An optimal solution must lie at one or more corner points

Slack

How much is left unused

• ≤

• RHS - LHS

• 210 available -120 used = 90

Surplus

How much you exceed the minimum required

• ≥

• LHS - RHS

• 120 produced - 100 required = 20

Redundant Constraint

Can be removed from the system without changing the feasible region

Does not determine the feasible region

Feasible region

The set of points that satisfies all constraints

Corner points

intersections between constraints that define the feasible region

Optimal solution

The point(s) that result in the best objective function value

Unique Optimal

Exactly one point gives the best value

Multiple Optimal

more than one point ties for the best

Infeasible

No point satisfies all the constraints, so there is no valid solution

Unbounded

The objective keeps improving forever, theres no finite best value

Binding (Active) Constraint

A constraint with no slack or surplus

LHS = RHS

shadow price ≠ 0

Non-binding constraint

LHS ≠ RHS

shadow price = 0

Sensitivity Analysis

allows us to determine how (responsive) the optimal solution is to changes in data values

Allowable Change in OFC

the amount by which a coefficient in the objective function can change before the optimal solution changes

Adjacent points

the corner points connected to the optimal solution by line segments

Indifference points

points that produce the same objective function

an adjacent point creates indifference

Multiple optimal solutions occur when what ?

Relaxing or loosening a non-redundant constraint

What makes the feasible region larger in RHS?

Tightening a non-redundant constraint

What makes the feasible region smaller in RHS?

Shadow price

indicates the amount by which the objective function value changes given a unit increase in the RHS value of the constraint, assuming all other coefficients remain constant

no impact on the feasible region

Changes in OFC have what?

changes the slope of the objective function line

changing an objective function value does what?

at least

≥

no more than

≤