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Solving Transportation And Assignment Problems For Quantitative Techniques For Business Decisions Mcom Sem 2 Delhi University Notes

Solving Transportation And Assignment Problems For Quantitative Techniques For Business Decisions Mcom Sem 2 Delhi University Notes

Solving Transportation And Assignment Problems For Quantitative Techniques For Business Decisions MCOM Sem 2 Delhi University :   Here Cakart.in website team members provide direct download links for Solving Transportation And Assignment Problems For Quantitative Techniques For Business Decisions MCOM Sem 2 Delhi University Notes notes in pdf format. Download these Solving Transportation And Assignment Problems For Quantitative Techniques For Business Decisions MCOM Sem 2 Delhi University Complete Notes notes in pdf format and read well.

Solving Transportation And Assignment Problems For Quantitative Techniques For Business Decisions Mcom Sem 2 Delhi University Notes

Solving Transportation And Assignment Problems For Quantitative Techniques For Business Decisions MCOM Sem 2 Delhi University :  Quantitative techniques are needed to process the information needed for effective planning, leading organizing and controlling. Qualitative and quantitative methods are productive tools in solving organizational problems. They are behavioral and mathematical techniques respectively that can provide a diversity of knowledge. Quantitative analysis concentrates on facts, data and numerical aspects associated with the problem.

The emphasis is on the development of mathematical expression to describe the objectives and constraints connected with the problem. Thus, the administrator’s quantitative knowledge can help enhance the decision- making process. In this approach, past data is used in determining decisions that would prove most valuable in the future. The use of past data in a systematic manner and constructing it into a suitable model for future use comprises a major part of scientific management.

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For example, consider a person investing in fixed deposit in a bank, or in shares of a company, or mutual funds, or in Life Insurance Corporation. The expected return on investments will vary depending upon the interest and time period. We can use the scientific management analysis to find out how much the investments made will be worth in the future. There are many scientific method software packages that have been developed to determine and analyze the problems.

In case of non-availability of past data where quantitative data is limited, qualitative factors play a major role in making decisions. Qualitative factors are important in situations like the introduction of breakthrough technologies. In today’s complex and competitive global market, use of quantitative techniques with support of qualitative factors is paramount.

Application of scientific management and Analysis is more appropriate when there is not much of variation in problems due to external factors, and where input values are steady. In such cases, a model can be developed to suit the problem which helps us to take decisions faster. In today’s complex and competitive global marketplace, use of Quantitative Techniques with support of qualitative factors is necessary.

Today, several quantitative techniques are available to solve managerial problems and use of these techniques helps managers to become explicit about their objectives and provides additional information to select on optimal decision. This approach starts with data like raw material for a factory which is manipulated or processed into information that is valuable to people making decision. This processing and manipulating of raw data into meaningful information is the heart of scientific management analysis.

The methodology adopted in solving problems is as follows:

Solving Transportation And Assignment Problems For Quantitative Techniques For Business Decisions Mcom Sem 2 Delhi University Notes

Solving Transportation And Assignment Problems For Quantitative Techniques For Business Decisions MCOM Sem 2 Delhi University :  Quantitative Techniques may be defined as the tools used to make systematic means of analysis on the basis of quantitative data. It is a technical method used by the management in order to solve problems and make decisions.

The course includes several topics such as decision analysis, game theory, linear programming, transportation and assignment, etc. and it intends to furnish the management students with methodical, evaluative and rational tools necessary to be able to operate effectively and efficiently.

An individual who studies the course would be introduced to various tools of research and statistical analysis. And, by the end of the course, the participants should have clear understanding of concept and significance of quantitative techniques in any kind of decision making procedure.

The major aim of the course ‘Quantitative Technique’ is to acquaint students with essential concepts and skills to apply quantitative techniques and tools to solve problems and make decision. Apart from this, any participant who completes the course is expected to

  1. Identify quantifiable problems and design appropriate action plan.
  2. Translate a problem into simple mathematical model to help in understanding and solve problem easily.
  3. Employ suitable mathematical tools and techniques in problem solving process.
  4. Analyze, interpret and appreciate the statistical and mathematical values to business management.
  5. Carry out sample survey to draw and interpret results.
  6. Understand the basic concept of decision theory and apply the knowledge in various decision making process.
  7. Apply linear programming and network analysis with emphasis on limitations of the techniques.

Solving Transportation And Assignment Problems For Quantitative Techniques For Business Decisions Mcom Sem 2 Delhi University Notes

Solving Transportation And Assignment Problems For Quantitative Techniques For Business Decisions MCOM Sem 2 Delhi University : As we know, the transportation model is also used for solving assignment problems. In transportation model, the objective is to minimize the cost of transportation. For a maximization problem, the objective is to maximize the profit or returns. While entering the values the maximization matrix must be converted to minimization matrix by subtracting all the values with the highest value cell. This is shown by solving the solved problem Ex.  The given problem is maximization of sales.

 Maximization Problem

Taking the highest value in the given maximization matrix, i.e., 41 and subtracting all other values, we get the following input matrix:

Input screen:

Solving Maximization Using TORA (Input Screen)

Part of the output screen is shown below in Figure.

Part of Output Screen (Enlarged)

The output given by TORA is the assignment schedule with the objective of minimization. The given problem is to maximize the sales. To arrive at the maximize sales value, add the assigned values from the given matrix, as shown in Table.

Assignment Schedule

Solving Transportation And Assignment Problems For Quantitative Techniques For Business Decisions Mcom Sem 2 Delhi University Notes

Solving Transportation And Assignment Problems For Quantitative Techniques For Business Decisions MCOM Sem 2 Delhi University : There is a type of linear programming problem that may be solved using a simplified version of the simplex technique called transportation method. Because of its major application in solving problems involving several product sources and several destinations of products, this type of problem is frequently called the transportation problem. It gets its name from its application to problems involving transporting products from several sources to several destinations. Although the formation can be used to represent more general assignment and scheduling problems as well as transportation and distribution problems. The two common objectives of such problems are either (1) minimize the cost of shipping m units to n destinations or (2) maximize the profit of shipping m units to n destinations.

Solving Transportation And Assignment Problems

Let us assume there are m sources supplying n destinations. Source capacities, destinations requirements and costs of material shipping from each source to each destination are given constantly. The transportation problem can be described using following linear programming mathematical model and usually it appears in a transportation tableau.

There are three general steps in solving transportation problems.

We will now discuss each one in the context of a simple example. Suppose one company has four factories supplying four warehouses and its management wants to determine the minimum-cost shipping schedule for its weekly output of chests. Factory supply, warehouse demands, and shipping costs per one chest (unit) are shown in Table 7.1


Table 7.1 ”Data for Transportation Problem”

At first, it is necessary to prepare an initial feasible solution, which may be done in several different ways; the only requirement is that the destination needs be met within the constraints of source supply.

The transportation matrix for this example appears in Table 7.2, where supply availability at each factory is shown in the far right column and the warehouse demands are shown in the bottom row. The unit shipping costs are shown in the small boxes within the cells (see transportation tableau – at the initiation of solving all cells are empty). It is important at this step to make sure that the total supply availabilities and total demand requirements are equal. Often there is an excess supply or demand. In such situations, for the transportation method to work, a dummy warehouse or factory must be added. Procedurally, this involves inserting an extra row (for an additional factory) or an extra column (for an ad warehouse). The amount of supply or demand required by the ”dummy” equals the difference between the row and column totals.

In this case there is:

Total factory supply … 51

Total warehouse requirements … 52

This involves inserting an extra row – an additional factory. The amount of supply by the dummy equals the difference between the row and column totals. In this case there is 52 – 51 = 1. The cost figures in each cell of the dummy row would be set at zero so any units sent there would not incur a transportation cost. Theoretically, this adjustment is equivalent to the simplex procedure of inserting a slack variable in a constraint inequality to convert it to an equation, and, as in the simplex, the cost of the dummy would be zero in the objective function.




Table 7.2 “Transportation Matrix for Chests Problem With an Additional Factory (Dummy)”

Initial allocation entails assigning numbers to cells to satisfy supply and demand constraints. Next we will discuss several methods for doing this: the Northwest-Corner method, Least-Cost method, and Vogel’s approximation method (VAM).

Table 7.3 shows a northwest-corner assignment. (Cell A-E was assigned first, A-F second, B-F third, and so forth.) Total cost : 10*10 + 30*4 + 15*10 + 30*1 + 20*12 + 20*2 + 45*12 + 0*1 = 1220($).

Inspection of Table 7.3 indicates some high-cost cells were assigned and some low-cost cells bypassed by using the northwest-comer method. Indeed, this is to be expected since this method ignores costs in favor of following an easily programmable allocation algorithm.

Table 7.4 shows a least-cost assignment. (Cell Dummy-E was assigned first, C-E second, B-H third, A-H fourth, and so on.) Total cost : 30*3 + 25*6 + 15*5 +10*10 + 10*9 + 20*6 + 40*12 + 0*1= 1105 ($).

Table 7.5 shows the VAM assignments. (Cell Dummy-G was assigned first, B-F second, C-E third, A-H fourth, and so on.) Note that this starting solution is very close to the optimal solution obtained after making all possible improvements (see next chapter) to the starting solution obtained using the northwest-comer method. (See Table 7.3.) Total cost: 15*14 + 15*10 + 10*10 + 20*4 + 20*1 + 40*5 + 35*7 + 0*1 = 1005 ($).



Table 7.3 ”Northwest – Corner Assignment





                                                                                                                            Table 7.4“Least – Cost Assignment”

Solving Transportation And Assignment Problems For Quantitative Techniques For Business Decisions Mcom Sem 2 Delhi University Notes

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