Finance & Accounting

Most management decisions cannot be made by simply applying personal experience guesswork or intuition because the consequences of wrong decisions are serious and costly. OR techniques help decision makers make rational and effective decisions by having a basic knowledge of mathematics and statistics as well as the use of computer software needed for computational purposes. OR is one of the quantitative aids to Decision Making Process. In general while solving a problem, decision makers must examine it both from quantitative as well as qualitative perspective.

Certain Qualitatives factors such as: Weather, State and Central policies, New Technology, Political situation need to be considered, but these factors are difficult to quantify. It is also very time consuming. Because of the amount of and complexity of information that must be processed. Secondly, the number of alternative solutions could be so large that a decision maker simply cannot evaluate all of things and select an appropriate one. So decision makers turn to quantitative methods and use computer to arrive at the optimal solution to problems involving a large number of alternatives.

The study of this method and how decision makers use them in decision process, in the essence of operations research approach. Balanced Transportation Problem In Operation research problem we are given supply to meet the demand. When the total supply equals total demand the problem is called a balanced transportation problem, otherwise an unbalanced transportation problem. If in case of unbalanced transportation problem -Supply exceeds total demand, an additional column – a dummy demand centre is added to absorb the excess supply. The unit is zero as they represent product items that are not being made nor being sent.

In case of demand exceeds – a dummy row – a dummy supply centre is added to account for the excess demand quality. Q. Which are the Common Methods to obtain IBFS in Transportation Problem? In T.P to obtain an initial basic feasible solution there are three methods 1. North West Corner Rule 2. Least Cost Method 3. Vogels' Approximation Method. Step Wise Procedure to Solve Problem:- Vogels Approximation Method VAM is a heuristic method and is preferred to the other 2 methods. The advantage of this method is that it gives an initial solution which is nearer to an optimal solution or is the optimal solution itself.

Steps:- 1. Calculate the difference between the smallest and next smallest unit transportation cost from each row and then each column. 2. Select the row or column with the largest difference and allocate in the cell having the least cost in selected row or column. If there is a tie in values then select the cell where maximum allocation can be made. 3. Adjust the Supply and Demand and cross out the satisfied row or column. 4. Repeat Steps 1 to 3 until the entire available supply at various sources and demand at various destinations are satisfied.

Q. What is meant by an Optimality Test in a Transportation Problem? Once an initial solution is obtained, the next step is to check its optimality. An optimal solution is one where there is no other set of transportation routes (allocation) that will further reduce the total transportation cost. Thus, we have to evaluate each unoccupied cell (unused route) in the transportation table in terms of an opportunity of reducing total transportation cost. An unoccupied cell with the largest negative opportunity cost is selected to include in the new set of transportation routes known as Incoming Variable.

The Outgoing Variable in the current solution is the occupied cell (basic variable) in the unique closed path (loop) whose allocation will become zero first as more units are allocated to the unoccupied cell with the largest negative opportunity cost. Such an exchange reduces total transportation cost. The process is continued until there is no negative opportunity cost. That is, the current solution cannot be improved further.

This is Optimal Solution. Q. What is Degeneracy in T.P? How such problems are solved ? In Transportation problem, when the number of positive allocation ( value of decision variables) at any stage of the feasible solution is less then the required number ( row+ column -1) i.e. number of independent constraint equations, the solution is said to be degenerate, otherwise non-degenerate.