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PROVIDING
CASE STUDY SOLUTION, PROJECT REPORTS & ASSIGNMENT
By
DR.
PRASANTH S MBA PH.D. DME
MOBILE:
+91 9924764558 OR +91 9447965521
EMAIL:
prasanththampi1975@gmail.com
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UNIVERSITIES OR B-SCHOOLS
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ISBM,IIBM,
KSBM, XAVIER, ISMS, IGNOU, ALL B-SCHOOLS,
ALL INDIAN
& FOREIGN UNIVERSITIES
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COURSES
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DMS,
MBA,MCOM,MSW,BMS,BBA,BMS,BCOM
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MARKS : 80
SUB: QUANTITATIVE METHODS
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.
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.
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AN ISO 9001 : 2008 CERTIFIED INTERNATIONAL B-SCHOOL
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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 behaviour and
explain how the optimal time for replacement of an asset can be determined.
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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.
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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.
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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
Normal Crash Normal Crash
1 – 2 3 2 300 450
2 – 3 3 3 75 75
2 – 4 5 3 200 300
2 – 5 4 4 120 120
3 – 4 4 1 100 190
4 – 6 3 2 90 130
5 – 6 3 1 60 110
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.
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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.
No. of Area
Commercial Ads A B C D
0
0
0
0
0
1 9 13 11 7
2 15 17 1 15
3 1 21 23 25
4 25 23 21 29
5 31 25 27 33
Using dynamic programming, determine how the five commercial ads be
distributed between the four areas so as to maximize the estimated number of
votes.
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