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Business Decision Models Dersi 4. Ünite Sorularla Öğrenelim

Linear Programming

1. Soru

What does identity matrix of an refer to?

Cevap

Identity matrix of n is the n×n square matrix with ones on the main diagonal and zeros elsewhere. An identity matrix is also called a unity matrix.


2. Soru

Who was the concept of linear programming and its solution method “simplex” first presented by?

Cevap

The concept of linear programming and its solution method “simplex” was first introduced by George Dantzig.


3. Soru

What are the four main steps of the simplex algorithm?

Cevap

  • Initialization
  • Test for optimality
  • Determining the entering variable
  • Determining the leaving variable


4. Soru

What does the simplex tableau refer to?

Cevap

As a compact form of the model, the simplex tableau provides the essential information required by the simplex method.


5. Soru

How is the solution space presented?

Cevap

The solution space is presented by m linear equations and n variables.


6. Soru

What does the minimum value mean?

Cevap

The minimum value means limiting the entering variable the most.


7. Soru

What does initialization refer to?

Cevap

Initialization is an augmentation of the model by slack, surplus and artificial variables to obtain a system of equations.


8. Soru

What does an iterative algorithm aims to do?

Cevap

An iterative algorithm aims to obtain successively closer approximations to the
solution.


9. Soru

How many variables do linear programs have and how does this affect the solution space?

Cevap

The majority of linear programs have a greater number of variables compared
equations n>m. This yields an infinite number of solutions, which creates the solution space. 


10. Soru

How is a slack or surplus utilized?

Cevap

A slack or surplus is utilized to reconstruct a constraint to obtain equation format.


11. Soru

What does a slack variable represent?

Cevap

A slack variable represents the remainder of an expendable resource and applies to less than or equal constraints.


12. Soru

What does a surplus represent?

Cevap

A surplus represents the excess amount of a restricted resource and applies to greater than or equal constraints.


13. Soru

When do cornerpoint feasible solutions become adjacent?

Cevap

If two corner-point feasible solutions are connected by a line segment, these cornerpoint feasible solutions are adjacent. Two corner-point feasible solutions are adjacent if all but one of their respective variables have the same value.


14. Soru

What does iteration refer to?

Cevap

Iteration is a repetition of a mathematical procedure applied to the result of a previous application.


15. Soru

When does a corner-point feasible solution become the optimum corner-point feasible solution?

Cevap

A corner-point feasible solution is the optimum corner-point feasible solution only if it has no adjacent corner-point feasible solutions with a more desirable Z value.


16. Soru

When are the two BF solutions adjacent?

Cevap

Similar to the definition of adjacent CPF solutions, two BF solutions are adjacent if their basic variables are equal except one. As the basic and non-basic variables are interchangeable only with each other, two adjacent BF solutions have the same non-basic variables with a single exception. Inherently, all but one
of their basic variables are the same. 


17. Soru

Which basic variables is determined as the leaving variable?

Cevap

The one that first decreases to zero as the value of entering variable increases


18. Soru

What is pivotal number?

Cevap

The value at the intersection of the pivotal column and row is called the pivotal number. It is alternatively called as pivot number or pivot element.


19. Soru

What are the key solution concepts of the method before moving to the algebra of the simplex method?

Cevap

• The method solely focuses on CPF solutions, i.e., BF solutions.
• It is an iterative algorithm, as described in Figure 5.2.
• The preferred initial BF solution is the CPF solution at the origin, where all decision variables are set to zero.
• Optimality test subject changes from a BF solution to an adjacent one.
• The selection between the adjacent BF solutions is based on the improvement in Z.
• If there are many adjacent BF solutions that improve the Z, the one providing the largest
improvement is selected.
• If none of the adjacent BF solutions improve Z, the current BF solution is optimal.


20. Soru

How is the entering variable determined?

Cevap

The criteria is the rate of improvement of Z. The coefficients of the variables in the objective function refer to the effect of one unit increase of respective variable on the function output Z.


21. Soru

What are the steps of determining the pivotal row?

Cevap

1. Take each positive coefficient in the pivotal column.
2. Divide each of these into the right-hand side constant for the corresponding row.
3. Identify the row that has the minimum ratio.
4. Pivotal row is the row that is identified in the previous step.


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