İŞLETME KARAR MODELLERİ - Deneme Sınavı - 5

Pivot number is 2 in this tableau.

the dual problems are imaginary and thus, purchasing is not a real option for the Factory. The purchasing price concept in the text is sometimes called shadow price so as to stress the virtuality. The real alternative for this factory is “not to produce”, no purchasing.

Historically, the game theory was first proposed by the French mathematician Emil Borel in 1921.

In a degenerate basic feasible solution, a degenerate basic variable acts as a non-basic variable, however, it does not prevent reaching to the optimal.

The game theory was developed extensively by John Nash in the 1950s.

There are various methods for selecting an arbitrary variable; the most prominent ones are:

Northwest corner method

Least-cost method

Vogel’s approximation method

Each individual (interested party) is called a player who makes decisions that are interdependent.

A transportation problem is a linear optimization problem, which seeks to minimize the total costs of shipment of items from certain origins to a number of destinations while fulfilling the requirements of destinations and emptying the origins. The decision variables of this problem are the amounts to be shipped for each origin-destination pairs.

Some transportation problems may be less restrictive; the total supply may exceed aggregate demand. In such a case, a dummy destination must be defined to fictionally absorb an excessive amount of the supply. Thus, the model becomes balanced and fits the general form of the transportation model. Note that a transportation problem has a feasible solution only if the total availability meets all the requirements.

According to these, the correct answer is given in the option C.

A strategy is a complete description of a player’s course of action during the game.

A pure strategy is an unconditional decision always to select a particular course of action. For example, in the game of Rock-Paper-Scissors, if a player would choose to only play Rock for each interdependent trial, regardless of the other player’s strategy, it would be the player’s pure strategy.

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. Return to step 2.

In this sense, the correct answer is A.

A mixed strategy is a decision to choose a course of action for each play in accordance with some particular probability.

The dual model interchanges costs and constraints of the primal model, and converts the objective from maximization to minimization. Moreover, the values of the decision variables of the dual model reveal the prices for the constraints of the original problem
for a basic feasible solution. This interpretation provides an economic perspective for solving the primal problem. Combining this economic insight and the properties of duality allows for an easier method altering the regular version of the simplex algorithm for the solution of a balanced transportation model. According tı these, the correct answer is given in the option B.

A pay-off is a numerical value which indicates the amount gained or lost by a player at the end of the game contingent upon the course of actions all of other players.

A payoff matrix shows the gains and losses that result from a combination of players’ strategy choices.

Battle of the Sexes is a two-person game in the game theory. In this game, a couple Mark and Kelly wish to go out together, but they have different preferences. Mark prefers to go to the football match while Kelly wants to go to the opera. In this game both players wish to coordinate their behavior, but they have conflict interests. That is, there are two steady states: one in which Mark and Kelly always choose football match and one in which they always choose opera.

Some of the properties of duality contribute solving of the primal problem by considering primal-dual model relationships. Before getting into these, recall that x’s are the components of a feasible solution for the primal model and, whereas the corresponding dual solution comprises of y’s. For a basic feasible solution of the primal model, the objective value, Z is equal or greater than W, the objective value of the corresponding dual solution. This is called weak duality property: the researcher begins at any point, then reaches the optimum at a level by lowering the costs and thus increasing the revenues simultaneously. In this sense the correct answer is E.

The Odds and Evens Game: In this game, two players (called Odd and Even) show simultaneously either one finger or two fingers. If the sum of the fingers put out both players is odd, the Odd wins $1 from the Even. If the sum of the fingers is even, the Even wins $1 from the Odd.

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.

The solution of a transportation problem begins with determining a basic feasible solution to proceed to the next phase. A balanced transportation problem has m + n – 1 basic variables in its basic feasible solution, whereas the number of the constraint equations is m + n. The correct answer is given in option A.