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QUANTITATIVE METHODS
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.
2. Explain the concept and computational steps
of the simplex method for solving linear programming problems. How would you
identify whether an optimal solution to a problem obtained using simplex
algorithm is unique or not?
a) What is the difference between a feasible
solution, a basic feasible solution, and an optimal solution of a linear
programming problem?
b) What is the difference between simplex
solution procedure for a `maximization’ and a `minimization’ problem?
c) Using the concept of net contribution,
provide an intuitive explanation of why the criterion for optimality for
maximization problem is different from that of minimization problems.
Outline the steps involved in the simplex
algorithm for solving a linear programming maximization problem. Also define
the technical terms used therein.
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.
4. Describe the transporation problem and give
its mathematical model. Explain, by taking an illustration, the North-West
Corner Rule, the Least Cost Method and the Vogel’s Approximation Method to
obtain the initial feasible solution to a transportation problem. Discuss the
various methods of finding initial feasible solution of a transportation
problem and state the advantages, disadvantages, and areas of application for
them.
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.
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.
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.
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.
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?
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?
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?
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?
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.
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?
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.
16. a) How do you distinguish between resource
leveling and resource allocation problems? State and explain an algorithm for
resource allocation.
b) Explain the following as they are used in
PERT/CPM
(i) Beta distribution, and (ii) Budget over-run.
17. The following table gives data on normal
time and cost, and crash time and cost for a project.
`Duration (Weeks) Total Cost (Rs) Activity
i) Draw the network and find out the critical
path and the normal project duration.
ii) Find out the total float associated with
each activity.
iii) If the indirect costs are Rs. 100 per week,
find out the optimum duration by crashing and the corresponding project costs.
iv) With the crash duration indicated, what
would be the minimum crash duration possible, ignoring indirect costs?
18. What is a `game’ in game theory? What are
the properties of a game? Explain the ``best strategy’’ on the basis of minimax
criterion of optimality. Describe the maximin and minimax principles 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
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.
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