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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 behaviour 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
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.
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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