問題一覧
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extreme points of the feasible region
CORNER POINTS
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Indicate that here is something wrong with the formulation of the LP model • Example: one or more constraints were omitted from the formulation, or a less than constraint was erroneously entered as a greater than constraint.
UNBOUNDED SOLUTION
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Lines representing the two objective function values; represent different levels or values of the objective.
LEVEL CURVES
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Field of management science that finds the optimal, or most efficient way of using limited resources to achieve the objectives of an individual or a business.
MATHEMATICAL PROGRAMMING
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Other feasible point that maximizes (or minimizes) the value of the objective function
ALTERNATE OPTIMAL SOLUTION
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to find the values of the decision variables that maximize (or minimize) the objective function without violating any of the constraints.
THE GOAL IN OPTIMIZATION
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The process of taking a practical problem and expressing it algebraically in the form of an LP model
FORMULATING THE MODEL
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Set of points or values that the decision variables can assume and simultaneously satisfy all the constraints in the problem.
FEASIBLE REGION
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This function expresses the mathematical relationship between the decision variables in the model to be maximized or minimized.
STATE THE OBJECTIVE FUNCTION AS A LINEAR COMBINATION OF THE DECISION VARIABLE
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The objective function identifies some function of the decision variables that the decision maker wants to either
MAXIMIZE OR MINIMIZE
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What are the fundamental decisions that must be made in order to solve the problem?
IDENTIFY THE DECISION VARIABLES
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some function of the decision variables that must be less than or equal to, greater than or equal to, or equal to some specific value (represented by the letter b).
CONSTRAINTS
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The technique of linear programming is so-named because the MP problems to which it applies are
LINEAR IN NATURE
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constraint to ensure that the total amount of money withdrawn from a person’s retirement accounts is at least the minimum amount required by the IRS.constraint to ensure that the total amount of money withdrawn from a person’s retirement accounts is at least the minimum amount required by the IRS.
GREATER THAN OR EQUAL TO
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Without this, it is unlikely that your formulation will be correct.
UNDERSTANDING THE PROBLEM
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An LP problem is infeasible if there is no way to simultaneously satisfy all the constraints in the problem
INFEASIBILITY
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Constraint that plays no role in determining the feasible region of the problem
REDUNDANT CONSTRAINT
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Additional constraints in the problem. • Non-negativity conditions
IDENTIFY ANY UPPER OR LOWER BOUNDS ON THE DECISION VARIABLE
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SPECIAL CONDITION IN LP MODEL
ALTERNATE OPTIMAL SOLUTION, REDUNDANT CONSTRAINT , UNBOUNDED SOLUTION, INFEASIBILITY
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Limitations on some values that can be assumed by the decision variables in an LP model
STATE THE CONSTRAINT AS LINEAR COMBINATION OF THE DECISION VARIABLE
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constraint to ensure that the total labor used in producing a given number of products does not exceed the amount of available labor.
LESS THAN OR EQUAL TO
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Involves creating and solving optimization problems with linear objective functions and linear constraints.
LINEAR PROGRAMMING
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If an LP problem has an optimal solution with a finite objective function value, this solution will always occur at a point in the feasible region where two or more of the boundary lines of the constraints intersect.
CORNER POINTS OR EXTREME POINTS OF THE FEASIBLE REGION
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APPLICATIONS OF MATHEMATICAL PROGRAMMING one space
DETERMINING PRODUCT MIX MANUFACTURING ROUTING LOGISTIC FINANCIAL PLANNING