Busıness Decısıon Models Final 4. Deneme Sınavı
Toplam 20 Soru1.Soru
Who is the person who is recognized as the first to explore the field of operations research?
William W. Cooper |
George B. Dantzig |
Tjalling C. Koopmans |
Leonid V. Kantorovic |
Fraser Sherman |
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.
2.Soru
Which term is described by “decision to choose a course of action for each play in accordance with some particular probability”?
Pay-off |
Saddle point |
Mixed strategy |
Pure strategy |
Pay-off Matrix |
A mixed strategy is a decision to choose a course of action for each play in accordance with some particular probability.
3.Soru
⌈3 -2 -4⌉
|-5 -4 4|
|2 0 5|
⌊-3 -2 -4⌋
What is the maximin strategy for Player I in this game ?
-4 |
4 |
0 |
5 |
-5 |
lowest in rows : -4 -5 0 -4 ; max : 0 . pg. 158. Correct answer is C.
4.Soru
Which of the following is the most convenient method to initialize the solution of a transportation model?
Which of the following is the most convenient method to initialize the solution of a transportation model?
Northwest corner method |
Least-cost method |
Vogel’s approximation method |
Russel’s approximation method |
Hungarian method |
Vogel’s Approximation Method: Vogel’s approximation method (VAM) can be regarded as an improved version of the least-cost method. Instead of using the direct cost of the transportation, VAM utilizes the concept of the penalty cost. Each row or column has its own penalty cost, which is used for determining which variables are the basic ones. A penalty cost is the difference between the smallest cost of a row (or column) and the cost that is smaller than the others except the smallest one for that row (or column).
5.Soru
Which notion below can be individuals, organizations,teams or, in some cases, nature?
Strategy |
Players |
Pay-off |
Pay-off Matrix |
Saddle Point |
Players can be individuals, organizations, teams or, in some cases, nature itself. The
number of players must be finite and must be known.
6.Soru
"It is a state that can only return to itself after a fixed number of transitions greater than 1." Which notion below belongs to the given description?
Aperiodic state |
Periodic state |
Recurrent state |
Transient state |
Accessible state |
A state is called periodic, if it can only return to itself after a fixed number of transitions greater than 1. Otherwise, a state is said aperiodic.
7.Soru
A system of equations has six variables (n=6) in its three equations (m=3). How many basic solutions does the system have?
18 |
20 |
24 |
30 |
35 |
Thus, the solution space is presented by m linear equations and n variables. If the numbers of the linear equations and the variables are equal, the system has only one solution. However, the majority of linear programs have a greater number of variables compared equations n>m.
A basic solution whether it is feasible or not is a corner point of the solution space. The corner points of system of equations are obtained by setting n – m number of variables equal to zero and solving the equations for the remaining m number of variables. The number of basic solutions can be calculated as below:
Here, the system has two equations (m = 3) and four variables. (n = 6) Thus, there are 20 basic solutions:
8.Soru
Which of the following can not be said about the Dual of the Transportation Model?
The difference is that the constraints of the transportation model are in the form of equality. Thus, the duality relation here is asymmetric. |
For the problem of the production decision, a counterpart actor was assumed as if it provided a purchasing alternative. |
The original problem is to select the most economical distribution routes that meet the demands of the destinations. |
Total cost of the shipment depends on total costs of transportation for the selected routes. |
Dual transportation model is a transportation model, where the supply and demand constraints are equality, and the total supply equals total demand. |
The transportation problem, as it was formulated at the beginning of this chapter, is a minimization problem just as the one exemplified for the economic interpretation of the dual model. However, the difference is that the constraints of the transportation model are in the form of equality. Thus, the duality relation here is asymmetric.
The dual model interchanges costs and constraints of the primal model, and converts the objective from maximization to minimization. Hence, there is a dual variable y for each constraint. In the case of the transportation model, the dual variable y is defined with a pair of variables; u, for the constraints of origins and v, for the constraints of destinations.
The dual of the transportation model can be interpreted as the dual model explained in the previous subsection. For the problem of the production decision, a counterpart actor was assumed as if it provided a purchasing alternative. A similar assumption can be made to interpret the dual of the transportation model. The original problem is to select the most economical distribution routes that meet the demands of the destinations. Total cost of the shipment depends on total costs of transportation for the selected routes. The decision variables for the primal model are the amounts to be carried from the origins (e.g. production locations) to the destinations (e.g. retailing locations).
According to these information, the correct answer is option E.
9.Soru
Min Z = x1 – 3 x2 + 2 x3 + 0 s1 + 0 s2 is the objective function of a linear program. The initial basic feasible solution for this program is (0, 0, 0, 5, 26). Which of the following is the 1st variable that enters to basic variables ?
x2 |
s2 |
x1 |
s1 |
x3 |
Max -Z = -x1 + 3 x2 - 2 x3 - 0 s1 - 0 s2 ; x2 : it has the maximum positive coefficient . pg. 95 . Correct answer is A.
10.Soru
_______ is the most convenient method to initialize the solution of a transportation model.
Which of the following completes the sentence above best?
Northwest Corner Method |
Dual Model |
Modified Distribution Method |
Vogel's Approximation Method |
Least-Cost Method |
Northwest Corner Method: The first basic variable is the one that is at the northwest on the transportation tableau. The value allocated to this variable is the value of the smaller one of the supply and demand. If the respective origin has any supply remaining after the allocation, then move one column to the right and allocate the value in the same manner as the first one. Otherwise, move one row down and repeat the allocation process with the remaining demand. The process is finalized when there is nothing left to allocate at the last row. The correct answer is A.
11.Soru
The dual of a balanced transportation problem is interpreted as a problem of ____________.
Which of the following completes the defintion given above?
a counterpart who provides an alternative to transportation. |
the total cost of each route. |
linear optimization |
minimizing the total transportation cost. |
feasibility of the transportation. |
The dual of a balanced transportation problem is interpreted as a problem of a counterpart who provides an alternative to transportation. The decision variables of the dual model are the prices of the alternative service offered by the counterpart actor. The correct answer is A.
12.Soru
Selecting a variable to be basic means allocating the greatest value possible to the respective variable, under the constraints of the total supply and demand for the origins and destinations, respectively. There are various methods for selecting an arbitrary variable. In which of the following, these methods are given correctly?
1. Balanced transportation method |
1. Northwest corner method |
1. Northwest corner method |
1. Northwest corner method |
1. Northwest corner method |
Selecting a variable to be basic means allocating the greatest value possible to the respective variable, under the constraints of the total supply and demand for the origins and destinations, respectively. There are various methods for selecting an arbitrary variable; the most prominent ones are:
1. Northwest corner method
2. Least-cost method
3. Vogel’s approximation method
The correct answer is C.
13.Soru
Which of the following cannot be said about the Least-cost Method?
The Least-cost method considers the respective costs of the variables so as to find a basic feasible solution that approximates the optimum solution more. |
Unlike the Northwest Method, the Leastcost algorithm begins with selecting the route that has the smallest unit cost of transportation. |
If there is more than one variable that has the smallest cost, any variable among these can be selected arbitrarily. |
The value allocated to this variable is the value of the smaller one of the supply and demand. |
The value allocated to the selected route is the greater one of the values of the supply and demand. |
The Least-cost method considers the respective costs of the variables so as to find a basic feasible solution that approximates the optimum solution more. Unlike the Northwest Method, the Leastcost algorithm begins with selecting the route that has the smallest unit cost of transportation. If there is more than one variable that has the smallest cost, any variable among these can be selected arbitrarily. The value allocated to the selected route is the greater one of the values of the supply and demand. In this sense, the correct aswer is the option D.
14.Soru
Which model do the steps given below belong to ?
Northwest- Corner Method |
Balanced Transportation Model |
Modified Distribution Model |
The Hungarian Method |
Least-Cost Method |
Also known as the method of simplex multipliers or the u-v method, MODI is a tailored version of the simplex method for the transportation model. MODI determines whether a basic feasible solution is optimal or not, and if not, identifies the entering variable by following these steps: 1. Denote the simplex multipliers, ui for each row and vi for each column alongside the transportation tableau 2. Write down the equations ui + vi = cij for each basic variable xij 3. Set one of the multipliers to zero and find the values of other multipliers on this system of equations 4. Calculate the values of cij – (ui + vi ) for each non-basic variable 5. If any of these values is greater than or equal zero, then the solution is optimal 6. If not, the non-basic variable that has the most negative value is the entering variable. The correct answer is C.
15.Soru
'E0' represents no earthquake during the year in a seismically active zone, and 'E1' represents the at least one-earthquake during the year. The matrix shows the transition between the states through the years respectively. What is the probability in the long run, there will be an earthquake?
%50 |
%87 |
%13 |
%17 |
%83 |
then the following explanation is obtained
and
Because of the
the result is
The answer is E.
16.Soru
- Identify the corners (corner point feasible solution) of the feasible region, of which one is expected to be the optimum.
- Use iso-profit (iso-cost) lines based on the maximum (minimum) objective function to determine the optimum corner point feasible solution.
- Represent the problem with a system of equations, which has m equations and n non-negative variables.
- Determine the basic feasible solutions of the equations, of which one is expected to be the optimum.
- Use the objective function to determine the optimum basic feasible solution.
Considering the items above, which of the followings does include the right phases of the algebraic solution?
I and II only |
I, II, and III |
II and IV only |
II, III, and IV |
III, IV, and V |
The phases of algebraic method are these:
- Represent the problem with a system of equations, which has m equations and n non-negative variables.
- Determine the basic feasible solutions of the equations, of which one is expected to be the optimum.
- Use the objective function to determine the optimum basic feasible solution.
17.Soru
Which term completes the blank in the following sentence best? ............... generally deals with decision making in the face of uncertainty about one future event.
Decision Analysis |
Discrete-state process |
Brand Switching |
Markov analysis |
Stochastic process |
Decision Analysis generally deals with decision making in the face of uncertainty about one future event.
18.Soru
Who proposed the game theory for the first time?
Emil Borel |
John von Neumann |
Oskar Morgenstern |
John Nash |
Albert Einstein |
Historically, the game theory was first proposed by the French mathematician Emil Borel in 1921.
19.Soru
I. Check the optimality of the basic feasible solution as the simplex method does. If it is not, optimal, then move to the next step. If optimal, stop.
II. Iterate to the next basic feasible solution by determining the entering and leaving variable using the rate of improvement on the objective value.
III. Determine a basic feasible solution to initiate.
Which of the following is the correct order of the steps of solution of a transportation model?
I,II,III |
I,III,II |
II,III,I |
III,I,II |
III,II,I |
The solution of a transportation model follows the steps that the simplex method offers:
1. Determine a basic feasible solution to initiate,
2. Check the optimality of the basic feasible solution as the simplex method does. If it is not, optimal, then move to the next step. If optimal, stop.
3. Iterate to the next basic feasible solution by determining the entering and leaving variable using the rate of improvement on the objective value.
20.Soru
According to the above transition diagram, which of the following shows the communication classes of the diagram?
{A, B} |
{A, B} and {C, D} |
{A, B} and {D, E} |
{A, B} and {C, D, E} |
{A, B, C, D, E} |
For the structure and analysis of transitions in a Markov chain, it is necessary to classify the states. Some states, after being visited once, are certain to be visited again, while some other states this may not to be case. States i and j are in the same communicating class if each state is accessible from the other, i.e., i-j. According to the diagram there are two communication classes. The answer is D.
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