Linear Programing

product mix problem

a common LP problem that involve a decision as to which products a firm should produce given that it faces limited resources.

unbounded solution

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.

redundant constraint

a constraint that does not affect the feasible solution region.

inequality

a mathematical expression that contains a greater than or equal to relation or a less than or equal to relation between the left-hand side and the right-hand side of the expression.

objective function

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.

linear programming

a mathematical technique used to help management decide how to make the most effective use of an organization's resources.

corner (or extreme) point

a point that lies on one of the corners of the feasible region. This means that if falls at the intersection of two constraint lines.

pricing out

a procedure by which the shadow price information in the sensitivity report can be used to gauge the impact of the addition of a new variable in the LP model.

iterative procedure

a process (algorithm) that repeats the same steps over and over.

answer report

a report created by Solver when it solves an LP model. This report presents the optimal solution in a detailed manner.

Constraint

a restriction (stated in the form of an inequality or an equation) that inhibits (or binds) the value that can be achieved by the objective function.

100% rule

a rule used to verify the validity for the information in the sensitivity report when dealing with simultaneous changes to more than one RHS value or more than one OFC value.

non-negativity constraints

a set of constraints that requires each decision variable to be non-negative; that is, each decision variable must be greater than or equal to 0.

alternate optimal solution

a situation in which more than one optimal solution is possible. It arises when the angle or slope of the objective function is the same as the slope of the constraint.

Iso line

a straight line that represents all non-negative combinations of the decision variables for a particular profit or cost level.

Solver

an Excel add-in that allows LP problems to be set up and solved in Excel.

SUMPRODUCT function

an Excel function that allows users to easily model formulas for the objective function and constraints.

simplex method

an iterative procedure for solving LP problems.

assume non-negative

an option available in Solver that automatically enforces the nonnegativity constraint.

assume linear model

an option available in Solver that forces Solver to solve the model as a linear program by using the simplex procedure.

feasible solution

any point that lies in the feasible region. Basically, it is any point that satisfies all of the problem's constraints.

infeasible solution

any point that lies outside the feasible region. It violates one or more of the stated constraints.

changing cells

cells that represent the decision variable in Solver.

simultaneous equation method

the algebraic means of solving for the intersection point of two or more linear constraint equations.

right-hand side (RHS) value

the amount of resource available (for a less than or equal to constraint) or the minimum requirement of some criterion (for a greater than or equal to constraint). typically expressed as a constant for sensitivity analysis.

feasible region

the area that satisfies all of a problem's resource restrictions- that is, the region where all constraints overlap. All possible solutions to the problem lie in the feasible region.

constraint LHS

the cell that contains the formula for the left-hand side of a constraint in Solver. There is one such cell for each constraint in a problem.

target cell

the cell that contains the formula for the objective function in Solver.

constraint RHS

the cell that contains the value (or formula) for the right-hand side of a constraint in Solver. There is one such cell for each constaint in a problem.

objective function coefficient (OFC)

the coefficient for a decision variable in the objective function. Typically, this refers to unit profit or unit cost.

surplus

the difference between the LHS and RHS of a greater than or equal to constraint. represents the level of oversatisfaction of a requirement.

slack

the difference between the LHS and RHS of a less than or equal to constraint. represents the unused resource.

surplus

the difference between the left-hand and right-hand side of a greater than or equal to constraint. surplus typically represents the level of over satisfaction of a requirement.

reduced cost

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 decision 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.

slack

the difference between the right-hand side and left-hand side of a les than or equal to constraint. Slack typically represents the unused resource.

mathematical programming

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.

shadow price

the magnitude of the change in the objective function value for a unit increase in the RHS of a constraint.

allowable decrease for an OFC

the maximum amount by which the OFC of a decision variable can decrease for the current optimal solution to remain optimal.

allowable increase for an OFC

the maximum amount by which the OFC of a decision variable can increase for the current optimal solution to remain optimal.

allowable decrease for a RHS value

the maximum amount by which the RHS value of a constraint can decrease for the shadow price to be valid.

allowable increase for a RHS value

the maximum amount by which the RHS value of a constraint can increase for the shadow price to be valid.

Corner Point Method

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 potimal solution must lie at one the the corner points.

sensitivity analysis

the study of how sensitive an optimal solution is to model assumptions and to data changes. also referred to as postoptimality analysis.

decision variables

the unknown quantities in a problem for which optimal solution values are to be found.