İŞLETME KARAR MODELLERİ

LINEAR PROGRAMMING BASICS

Operations research is an analytical method for the management of organizations that provides mathematical solutions to decision-making problems. There are definitive steps of this approach that make it analytical:

1. Problem definition

2. System analysis for the problem and data gathering

3. Model construction

4. Model solution and testing

5. The decision of implementing the solution

The correct answer is E.

Operations research is an analytical method for the management of organizations that provides mathematical solutions to decision-making problems. There are definitive steps of this approach that make it analytical:

1. Problem definition

2. System analysis for the problem and data gathering

3. Model construction

4. Model solution and testing

5. The decision of implementing the solution

The correct answer is C.

A linear expression appears below; the powers of its variables x and y are equal to one.

2x – 3y

A linear constraint requires a linear expression to be equal to a number, to be less/greater than or equal to a number.

x + y = 4

x – 3y ≤ 2

x ≥ y

The last expression stated above is called a non-negativity constraint, which requires the value x to be greater or equal to zero. A linear program either minimizes or maximizes a linear expression subject to defined linear constraints. The correct answer is E.

An objective function is the function of a linear programming model that is desired to be maximized or minimized.

The correct answer is D.

The foundation of operations research is mostly cited to studies and applications in the U.S. Army right before The World War II. However, LeonidV. Kantorovich is recognized as the first to explore this area. In 1939, Kantorovich published a paper on a method for a production plan which he claimed to be the optimal way. This study included a linear program without a systematic solution. The systematic solution which is called “simplex algorithm” was later introduced by George B. Dantzig, who had planning experience in the U.S. Army Air Force. Tjalling C. Koopmans, who built a model for ship routes, was another contributor to the field. He and Kantorovich shared 1975 Nobel Prize in economics for their studies on the optimal allocation of resources. The correct answer is D.

x ≥ y

The last expression stated above is called a non-negativity constraint, which requires the value x to be greater or equal to zero. A linear program either minimizes or maximizes a linear expression subject to defined linear constraints. The correct answer is C.

An optimal solution is a feasible solution that reaches the most favorable value of the objective function. The correct answer is B.

The last assumption is certainty, which means that each parameter of a linear programming model is constant in all conditions. The correct answer is B.

Either it is the objective or the constraints, every function is the sum of the individual contribution of the respective variables. This is called the additivity assumption, which prohibits cross-product terms in the expressions of a linear program. This assumption restricts the model design as well.

The correct answer is B.

Proportionality assumption casts out any variable that has an exponent other than 1. The correct answer is A.

The foundation of operations research is mostly cited to studies and applications in the U.S. Army right before The World War II. However, Leonid V. Kantorovich is recognized as the first to explore this area. In 1939, Kantorovich published a paper on a method for a production plan which he claimed to be the optimal way. This study included a linear program without a systematic solution.

To get a solid grasp on modeling with linear programming, few other explanations have to be made about the program solution: Each feasible solution determines an objective value for the objective function that is being minimized or maximized. The smallest value for minimization program or the largest value for maximization program is the optimal value of the optimal solution. An optimal solution is a feasible solution that reaches the most favorable value of the objective function.

Operations research is an analytical method for the management of organizations that provides mathematical solutions to decision-making problems. There are definitive steps of this approach that make it analytical: 1. Problem definition 2. System analysis for the problem and data gathering 3. Model construction 4. Model solution and testing 5. The decision of implementing the solution

A linear expression is one where the powers of its variables x and y are equal to one.

This linear program has an objective function that is a maximization. An objective function is the function of a linear programming model that is desired to be maximized or minimized.

A feasible solution to this linear program is a value set of these decision variables which satisfy each of the constraints. The only values that satisfy all of the constraints in this linear program are (x,y) = (2,3).

Linear programming provides solutions under some assumptions. These are proportionality, additivity, divisibility and certainty assumptions. In both the objective function and constraints, the contribution of every decision variable is proportional to its value. As a result, proportionality assumption casts out any variable that has an exponent other than 1.

2x₁+1,5x₂+3x₃ ≤ 20 is one of the constraints for the problem above.

First and foremost, the non-negativity constraints of the model restrict the solution area to the first quadrant, which lies above the x1 axis and to the right of the x2 axis. Also the point (2,2) is inside the feasible region for the given constraints.

In the minimization models, the objective function is alternatively named cost function. The reason for this is the ultimate goal of minimizing something is to reduce loss or “cost”.