exam 1
stochastic 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
Iconic model
a physical replica, or representation of a real object
Sing criterion decision problem
a problem in which the objective is to find the "best" solution with respect to just one crierion
Multicriteria decision problem
a problem that involves more than one criterion: the objective is to find the best solution, taking into account all the criteria
Nonnegativity constraints
a set of constraints that requires all varibales to be nonnegative
Feasible solution
a solution that satisfies all the contraints
slack varibale
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
surplus variable
a variable subtracted from the left-hand side of a greater than 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
constraints
restrictions or limitations imposed on a problem; an equation or inequality that rules out certain combinations of decision variables as feasible solutions
redundant constraint
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
relevant 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
sunk cost
a cost that is not affected by the decision made. it will be incurred no matter what values the decision variables assume
Infeasible solution
a decision alternative or solution that does not satisfy one or more constraints
Feasible solution
a decision alternative or solution that satisfies all contraints
standard form
a linear program in which all the constraints are certain 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
objective function
a math expression that describes the problem's objective
linear programming model
a math model with a linear objective function, a set of linear constraints, and nonnegative variables
deterministic model
a model in which all uncontrollable inputs are known and cannot vary
Model
a representation of a real object or situation
analog model
although physical in form, an analog model does not have a physical appearance similar to the real object or situation it represents
decision variable
another term for controllable input
linear program
another term for linear programming model
extreme point
graphically speaking, they are the feasible solution points occurring at the vertices or "corners" of the feasible region. with two-variable problems, extreme point
unbounded
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 constraints, the problem is said to be this
linear functions
math expressions in which the variables appear in the separate terms and are raised to the first power
Mathematical model
mathematical symbols and expressions used to represent a real situation
right-hand side allowable increase or decrease
the allowable increase or decrease of the right hand side of a constraint is the amount the right hand side may increase or decrease without causing any change int he dual value for that constraint. the allowable increase or decrease for the right hand side can be used to calculate the range of feasibility for that constraint
objective function allowable increase (decrease)
the allowable increase/decrease of an objective function coefficient is the amount the coefficient may increase or decrease without causing any change in the values of the decision variables in the optimal solution,
Decision
the alternative selected
alternative optimal solutions
the case in which more than one solution provides the optimal value for the objective function
dual value
the change in the value of the objective function per unit increase in the right-hand side of a constraint
reduced cost
the cost of a variable is equal to the dual value on the nonnegativity constraint for that variable
uncontrollable inputs
the environmental factors or inputs that cannot be controlled by the decision maker
controllable inputs
the inputs that are controlled or determined by the decision maker
fixed cost
the portion of the total cost that does not depend on the volume this cost remains the same no matter how much is produced
variable cost
the portion of the total cost that is dependent on and varies with the volume
Decision Making
the process of defining the problem, identifying the alternatives, determining the criteria, evaluating the alternatives, and choosing an alternative
problem solving
the process of identifying a difference between the actual and the desired state of affairs and then taking action to resolve
Problem formulation
the process of translating the verbal statement of a problem into a matematical statement called the mathematical model
range of optimality
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
marginal cost
the rate of change of the total cost with respect to volume
marginal revenue
the rate of change of total revenue with respect to volume
Feasible region
the set of all feasible solutions
infeasibility
the situation in which no solution to the linear programming problem satisfies all the constraints
Optimal solution
the specific decision-variable value or values that provide the best output for the model
sensitivity analysis
the study of how changes in the coefficients of a linear programming problem affect the optimal solution
breakeven point
the volume at which total revenue equals total cost