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### 66 Cards in this Set

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 The process of identifying a difference between the actual and the desired state of affairs and then taking action to resolve the difference. Problem solving The process of defining the problem, identifying the alternatives, determining the criteria, evaluating the alternatives, and choosing the alternative. Decision making A problem in which the objective is to find the "best" solution with respect to just one criterion. Single-criterion decision problem A problem that involves more than one criterion; the objective is to find the "best" solution, taking into account all the criteria. Multicriteria decision making The alternative selected. Decision A representation of a real object or situation. Model A physical replica, or representation, of a real object. Iconic model Although physical in form, an analog model does not have a physical appearance similar to the real object or situation it represents. Analog model Mathematical symbols and expressions used to represent a real situation. Mathematical model Restrictions or limitations imposed on a problem. Constraints A mathematical expression that describes the problem's objectives. Objective function The environmental factors or inputs that cannot be controlled by the decision maker. Uncontrollable inputs The inputs that are controlled or determined by the decision maker. Controllable inputs Another term for controllable input. Decision variable A model in which all uncontrollable inputs are known and cannot vary. Deterministic model A model in which at least one uncontrollable input is uncertain and subject to variation; stochastic models are also referred to as probabilistic models. Stochastic (probabilistic) model The specific decision-variable value or values that provided the "best" output for the mode. Optimal solution A decision alternative or solution that does not satisfy one or more constraints. Infeasable solution A decision alternative or solution that satisfies all constraints. Feasible solution The portion of the total cost that does not depend on the volume; this cost remains the same no matter how much is produced. Fixed cost The portion of the total cost that is dependent on and varies with the volume. Variable cost The rate of change of the total cost with respect to volume. Marginal cost The rate of change of total revenue with respect to volume. Marginal revenue The volume at which total revenue equals total cost. Breakeven point An equation or inequality that rules out certain combinations of decision variables as feasible solutions. Constraint The process of translating the verbal statement of a problem into a mathematical statement called the mathematical model. Problem formulation A controllable input for a linear programming model. Decision variable A set of constraints that requires all variables to be non-negative. Nonnegativity constraints A representation of a problem where the objective and all constraint conditions are described by mathematical expressions. Mathematical model A mathematical model with a linear objective function, a set of linear constraints, and nonnegative variables. Linear programming model Another term for linear programming model. Linear program Mathematical expressions in which the variables appear in separate terms and are raised to the first power. Linear functions A solution that satisfies all the constraints. Feasible solution The set of all feasible solutions. Feasible region A variable added to the left-hand side of a less-than-or-equal-to constraint to convert the constraint into an equality. The value of this variable can usually be interpreted as the amount of unused resource. Slack variable A linear program in which all the constraints are written as equalities. The optimal solution of the standard form of a linear program is the same as the optimal solution of the original formulation of the linear program. Standard form A constraint that does not affect the feasible region. If a constraint is redundant, it can be removed from the problem without affecting the feasible region. Redundant constraint Graphically speaking, extreme points are the feasible solution points occurring at the vertices or "corners" of the feasible region. With two-variable problems, extreme points are determined by the intersection of the constraint lines. Extreme point A variable subtracted from the left-hand side of a greater-tha-or-equal-to constraint to convert the constraint into an equality. The value of this variable can usually be interpreted as the amount over and above some required minimum level. Surplus variable The case in which more than one solution provides the optimal value for the objective function. Alternative optimal solutions The situation in which no solution to the linear programming problem satisfies all the constraints. Infeasibility If the value of the solution may be made infinitely large in a maximization linear programming problem or infinitely small in a minimization problem without violating any of the constraint, the problem is said to be unbounded. Unbounded The study of how changes in the coefficients of a linear programming problem affect the optimal solution. Sensitivity analysis The range of values over which an objective function coefficient may vary without causing any change in the values of the decision variables in the optimal solution. Range of optimality The improvement in the value of the objective function per unit increase in the right-hand side of a constraint. Dual price The amount by which an objective function coefficient would have to improve (increase for a maximization problem, decrease for a minimization problem) before it would be possible for the corresponding variable to assume a positive value in the optimal solution. Reduced cost The range of values over which the dual price is applicable. Range of feasibility A rule indicating when simultaneous changes in two or more objective function coefficients will not cause a change in the optimal solution It can also be applied to indicate when two or more right-hand-side changes will not cause a change in any of the dual prices. 100 percent rule A cost that is not affected by the decision made. It will be incurred no matter what values the decision variables assume. Sunk cost A cost that depends upon the decision made. The amount of a relevant cost will vary depending on the values of the decision variables. Relevant cost An algebraic procedure for solving linear programming problems. Simplex method Given a linear program in standard form, with n variables and m constants, is obtained by setting n-m of the variables equal to zero and solving the constraint equations for the values of the other m variables Basic solution One of the n-m variables set equal to zero in a basic solution. Nonbasic variable One of the m variables not required to equal zero in a basic solution. Basic variable A basic solution that is also feasible; that is, it satisfies the nonnegativity constraints. Basic feasible solution The form in which a linear program must be written before setting up the initial simplex tableau. Tableau form A table used to keep track of the calculations required by the simplex method. Simplex tableau A vector of column of a matrix that has a zero in every position except one. In the nonzero position there is a 1. There is a unit column in the simplex tableau for each basic variable. Unit column or unit vector The set of variables that are not restricted to equal zero in the current basic solution. The variables that make up the basis are termed basic variables, and the remaining variables are called nonbasic variables. Basis The row in the simplex tableau that contains the value of cj-zj for every variable (column). Net evaluation row The process of moving from one basic feasible solution to another. Iteration The element of the simplex tableau that is in both the pivot row and the pivot column. Pivot element The column in the simplex tableau corresponding to the nonbasic variable that is about to be introduced into solution. Pivot column The row in the simplex tableau corresponding to the basic variable that will leave the solution Pivot row When one or more of the basic variables has a value of zero. Degeneracy An associated linear programming problem to a linear programming problem. Deal problem