QUANTITATIVE MANAGEMENT

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Name:………………………….

Subject: QUANTITATIVE MANAGEMENT

Programme: Doctoral Programme in Management

N. B.: 1) Answer any Sixteen

1. What is a linear programming problem? Discuss the scope and role of linear programming in solving management problems. Discuss and describe the role of linear programming in managerial decision-making bringing out limitations, if any.

Ans: - Linear programming (LP) is a mathematical method for determining a way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model for some list of requirements represented as linear relationships. More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality linear equality and linear inequality constraints. Given a polytypic and

3. Linear programming is one of the most frequently and successfully employed Operations Research techniques to managerial and business decisions. Elucidate this statement with some examples.

Ans: A Linear (LP) is a problem that can be expressed as follows (the so-called Standard Form):

minimize cx

subject to Ax = b

x >= 0

where x is the vector of variables to be

5. What is an assignment problem? It is true to say that it is a special case of the transportation problem? Explain. How can you formulate an assignment problem as a standard linear programming problem? Illustrate. What do you understand by an assignment problem? Give a brief outline for solving it.

Ans: An Assignment Problem, is -- in which the number of sources (assignees) equals the number of designations (assignments) and each supply and each demand equals 1.

Assignment Problem

A special case of the transportation problem is the assignment problem which occurs when each supply is 1 and each demand is 1. In this case, the integrality implies that every supplier will be assigned one destination and every destination will have one supplier. The costs give the charge for assigning a supplier and destination to each other.

6. What are different types of inventories? Explain. What functions does inventory perform? State the two basic inventory decisions management must make as they attempt to accomplish the functions of inventory just described by you.

ANS:

TYPES OF INVENTORY

·         Raw materials: The purchased items or extracted materials that are transformed into components or products.

·         Components: Parts or subassemblies used in building the final product.

·         Work-in-process (WIP): Any item that is in some stage of completion in the manufacturing process.

·         Finished goods: Completed products that will be delivered to customers.

·         Distribution inventory: Finished goods and spare parts that are at various points in the distribution system.

·         Maintenance, repair, and operational (MRO) inventory (often called supplies): Items that are used in manufacturing but do not become part of the finished product.

INDEPENDENT VS. DEPENDENT DEMAND INVENTORY

Some inventory items can be

7. What is queuing theory? What type of questions are sought to be answered in analyzing a queuing system? Give a general structure of the queuing system and explain. Illustrate some queuing situations. What is queuing theory? In what types of problem situations can it be applied successfully? Discuss giving examples.

ANS:

·         It is a collection of mathematical models of various queuing systems.

·         It is used extensively to analyze production and service processes exhibiting random variability in market demand (arrival times) and

·          

8. What is a replacement problem? Describe some important replacement situations and policies. Briefly explain the costs which are relevant to decisions for replacement of depreciable assets. Illustrate their behavior and explain how the optimal time for replacement of an asset can be determined.

ANS: In any system , the efficiency of an item deteriorates With time. In such cases, either the old item should be replaced by a new item, or some kind of restorative action [ maintenance] is necessary to restore the efficiency of the whole system. The cost of maintenance depends upon a number of factors, and a stage comes at which the maintenance cost is so large ,it is more profitable to replace the old item.

THE VARIOUS TYPES OF REPLACEMENT PROBLEMS ARE:

9. What kinds of decision-making situations may be analysed using PERT and CPM techniques? State the major similarities between PERT and CPM. Under what circumstances is CPM a better technique of project management than PERT? A construction company has received a contract to build an office complex. It has frequently engaged itself in constructing such buildings. Which of the two network techniques, PERT and CPM, should in your opinion, be employed by the company? Why?

ANS : PERT and CPM, acronyms for "program evaluation and review technique" and "critical path method", respectively, are network techniques used to aid in the planning, scheduling, monitoring, and control of activities which are related to each other. For example, CPM is frequently used in the construction industry to help organize and schedule those activities which together constitute a given construction project. PERT was first used to help coordinate the activities in the development of the Polaris missle system. PERT and CPM differ from each

10. Describe the steps involved in the process of decision making. What are payoff and regret functions? How can entries in a regret table be derived from a pay-off table?

Ans: - Step 1: Define the “problem”

It is impossible to make a rational decision unless you can clearly define the problem or context in which the decision needs to be made. Why does a decision need to be made? What will be the outcome if no decision is made? What outcome is desired? What is preventing that outcome from being realized?

Step 2: Identify available alternative solutions to the problem

The key to this step is not to limit yourself to obvious alternatives or to what has worked in the past. Better decisions come from being open to multiple alternatives. It is often helpful to consult trusted adults or experts in the area in which the decision needs to be made.

11. What do you understand by Markov processes? In what areas of management can they be applied successfully? What do you understand by transition probabilities? Is the assumption of stationary transition probabilities realistic, in your opinion? Why or why not?

Ans:- A Markov analysis looks at a sequence of events, and analyzes the tendency of one event to be followed by another. Using this analysis, you can generate a new sequence of random but related events, which will look similar to the original. A Markov process is useful for analyzing dependent random events - that is, events whose likelihood

12. Explain how the probability tree helps to understand the problem of Markov processes. Explain the method of calculation of ending up in each absorbing state when a chain beings in a particular transient state. What is fundamental matrix of Markov chains? What does it calculate?

Ans: - A PROBABILITY TREE is a special type of graph used to determine the outcomes of an experiment. It consists of "branches" that are labeled with either frequencies or probabilities. Tree diagrams can make some probability problems easier to visualize and solve. The following example illustrates how to use a tree diagram.

Trees are excellent tools for helping you to choose between several courses of action. They provide a highly effective structure within which you can lay out options and investigate the possible outcomes of choosing those options. They also help you to form a balanced picture of the risks and rewards associated with each possible

13. What is simulation? Describe the simulation process. State the major two reasons for using simulation to solve a problem. What are the advantages and limitations of simulation? ``When it becomes difficult to use an optimization technique for solving a problem, one has to resort to simulation’’. Discuss. ``Simulation is typically the process of carrying out sampling experiments on the models of the system rather than the system itself.’’ Elucidate this statement by taking some examples.

Ans:- Simulation is the imitation of some real thing, state of affairs, or process. The act of simulating something generally entails representing certain key characteristics or behaviors of a selected physical or abstract system. The process of imitating a real phenomenon with a set of mathematical formulas. Advanced computer programs can simulate

14. A company has three offers for its existing equipment in one of the divisions. The first buyer is willing to pay Rs. 50,000 at the end of 8 years’ period. The second buyer offers Rs. 39,000—consisting of an immediate payment of Rs. 14,000 and Rs. 25,000 after 6 years. The third buyer agrees to buy the equipment for Rs. 29,000 payable right away. Which is the best offer for the company if it can earn an interest @ 8% per annum on the money received?

Ans: - A company has three offers.

FIRST OFFER

RS 50000 AFTER 8 YEARS.

AT THE END OF 8 YEARS ------RS 50,000.

15. What is the difference between qualitative and quantitative techniques of forecasting. When is a qualitative model appropriate? Briefly discuss the Delphi method of making forecasts.

Ans:- Forecasting can be broadly considered as a method or a technique for estimating many future aspects of a business or other operation. There are numerous techniques that can be used to accomplish the goal of forecasting. For example, a retailing firm that has been in business for

25 years can forecast its volume of sales in the coming year based on its experience over the

25-year period—such a forecasting technique bases

16. A) How do you distinguish between resource leveling and resource allocation problems? State and explain an algorithm for resource allocation.

Ans: - Resource allocation addresses the problem of the optimum use and timing of the assignment of these resources to the various project activities.

Resource aggregation involves determining the aggregate resources that will be needed, period by period, to complete all project activities.

Having identified the necessary resource requirements, the last stage in the process is resource leveling. In this stage, we attempt to ensure that the demand for resources does not exceed availability. Specifically, demand for resources is smoothed to ensure that the peaks and valleys are reduced. In this lesson, we will also learn about the "critical

18. What is a `game’ in game theory? What are the properties of a game? Explain the ``best strategy’’ on the basis of mini max criterion of optimality. Describe the maxim in and mini max principles of game theory.

Ans: - 'Game Theory'

A model of optimality taking into consideration not only benefits less costs, but also the interaction between participants. Game theory attempts to look at the relationships between participants in a particular model and predict their optimal decisions.

One frequently cited example of game theory

19. Explain the steps involved in solution to dynamic programming problems. Explain the following in the context of dynamic programming:

(a) Stages

(b) States

(c) Pay-off function

(d) Recursive relationship

Ans: - Dynamic programming is an optimization approach that transforms a complex problem into a sequence of simpler problems; it’s essential characteristic is the multistage nature of the optimization procedure.

20. A political campaign for election to the parliament is entering its final stage and pre-poll surveys are medicating a very close contest in a certain constituency. One of the candidates in the constituency has sufficient funds to give five full-page advertisements in four different areas. Based on the polling information, an estimate has been made of the approximate number (in thousands) of additional votes that can be polled in different areas. This is shown below.

Ans:- No. of Area

Commercial Ads A B C D

0

0

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