İŞLETME KARAR MODELLERİ - Deneme Sınavı - 4

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.

(based on the model on page 114)

As a linear algebraic property of balanced transportation model, the number of independent equations is m + n – 1. Therefore, a feasible basic solution has m + n – 1 basic variables.

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.

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. Northwest corner method is the most convenient method to initialize the solution of a transportation model as compared to least-cost and Vogel's approximation methods. so the answer for this question is A.

Decision Analysis generally deals with decision making in the face of uncertainty about one future event.

As a special form of the linear programming model, the transportation model and its solution method have been introduced thus far. This section introduces the assignment model, a special case of the transportation model. The term “Assignment” refers to the case of job allocations to a group of workers. In general, a worker has a single job and a job is done by a single worker. Similarly, the assignment model has the origin locations from where a single unit can be transported to a dedicated destination, and vice versa—the model has the destinations to which a single unit is sent solely from one origin location. Simply put, the number of the origins (represented by the workers) and the destinations (represented by the jobs) are equal, and the amount to be sent and received is strictly 1.

(see the relevant section in your book for more details.)

The assignment model has a tailored solution method such as the transportation model does. The solution method of the assignment model is called the Hungarian Method, named by the nationality of its developers. So, the correct answer is option B.

“Brand Switching” is basically a marketing application and deals with
the examination of customer’s commitment to a specific product type, store or supplier.

In stochastic processes, events occur over time, and time can be dealt with either in discrete fashion or continuous fashion.

The steps of Hungarian Method is given below.
1. Identify the smallest value of each row for the cost matrix of the assignment problem. Subtract each row’s smallest value from all the costs in the respective row.
2. Identify the smallest value of each column for this altered matrix. Subtract each column’s smallest value from all the costs in the respective column.
3. Mask the columns and rows out that have a zero value. The number of masked out rows and columns must be at a minimum.
4. If the number of masked out rows and columns is equal to n, then the optimum can be obtained from the present matrix; move on to the next step. If not, skip to Step 6.
5. Identify the optimal solution by the coordinates of the zero-valued elements in the present matrix.
6. Identify the smallest value except for the ones in masked out rows and columns. This value is then subtracted from the values of unmasked rows and columns and, added to the intersections of masked out rows and columns. Return to Step 3.

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

If the state space S of a stochastic process is discrete, the process is called discrete-state process often referred as a chain.

Familiar examples of stochastic processes are as follows:
• daily prices of a stock or exchange rate fluctuations,
• failures times of a machine,
• medical data such as a patient’s blood pressure or EKG,
• radar measurements for the position of an airplane,
• tossing a coin.

"Minting a coin" is not an example of a stochastic process.

The most common dependence structure is called Markov Property.

The probabilities of going from one state to another are called transition probabilities.

The n-step transition probability pij(n) is the probability that a process in state j will be in state i after n additional transitions.

A transition matrix is called regular if some power of the matrix includes all positive entries.

A state is called periodic, if it can only return to itself after a fixed number of transitions greater than 1.

They are used to analyse different decision situations.

It is a family of random variables.

If the state space S of a stochastic process finite, or countable, then the process is called a chain.