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Term End Examination - November 2012
Course : MEE437 - Operations Research Slot: B1+TB1
Class NBR : 2711 / 2712 / 3560 / 3565 / 5567
Time : Three Hours Max.Marks:100
(Use of Standard Normal and Random Number Tables are permitted)
Answer any FIVE Questions
(5 X 20 = 100 Marks)
1. a) An animal feed company must produce 200 kg of a mixture consisting of ingredients
type I and type II. The ingredient type I costs Rs.30 per kg and type II costs
Rs.50 per kg. Type I can be used 40kg and above but not more than 80 kg and at least
60 kg of type II must be used. Formulate a mathematical model of the problem for
optimization.
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b) Solve the following LP problem
Minimize Z = x1 – 3x2 + 2x3
Subject to 3x1 – x2 + 2x3 < 7
– 2x1 + 4x2 ≤ 12
– 4x1 + 3x2 + 8x3 ≤ 10
x1, x2, x3 > 0
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2. a) A company has four jobs to be processed by four mechanics. The following table gives
the return in rupees when the job is assigned to the mechanic. How should the jobs be
assigned to the mechanics so as to maximize the overall return?
Mechanic
15 12 10 13
Job 7 9 6 7
12 16 5 9
8 9 8 11
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b) Find the optimum solution to the following transportation problem in which the cells
contain the transportation cost in rupees.
Warehouse
W1 W2 W3 W4 W5 Available
Factory
F1 7 6 4 5 9 40
F2 8 5 6 7 8 30
F3 6 8 9 6 5 20
F4 5 7 7 8 6 10
Requirement 30 30 15 20 5
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3. a) Determine the optimal sequence of jobs that minimizes the total elapsed time based on
the following information processing time on machines is given in hours and passing is
not allowed.
Job A B C D E F
Machine M1 3 12 15 6 12 11
Machine M2 8 10 10 7 11 1
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b) A small project is composed of nine activities whole time estimates (in days) are listed
in the table below.
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Activity 1-2 2-3 2-4 3-4 3-5 3-6 4-5 4-6 5-6
Optimistic time 2 1 0.5 0 1 1 6 3 4
Most likely time 2 1.5 1 0 2.5 2 7 4 6
Pessimistic time 8 11 7.5 0 7 3 8 11 8
(i) Draw an arrow diagram and determine the expected activity time and variance.
(ii) Calculate earliest event time and latest event time.
(iii) Determine critical path and project duration.
(iv) What is the probability that the project will be completed in 20 days?
4. a) The probability density of demand of a item during a day is given below:
f(x) = 0.1 for 0≤ x ≤ 10
The demand is assumed to occur with instantaneous and set up cost is not allowed. The
carrying cost of the item in inventory is Re.0.5 per day and unit shortage cost is
Rs.4.5 per day. If Re.0.5 be the purchasing cost per unit, determine the optimum order
level of the inventory.
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b) The demand of an item in a company in 18000 units per year and the company can
produce the item at a rate of 3000 per month. The cost of set up in Rs.500 and the
holding cost of one unit per month is 15 paise. The shortage cost of the one unit is
Rs.20 per year. Determine (i) optimum production batch quantity and the number of
shortages, (ii) optimum cycle time and production time, (iii) maximum inventory level in
the cycle and (iv) total minimum cost per year if the cost of the item is Rs.20 per unit.
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5. A tax consulting firm has three counters in its office to receive people who have problems
concerning their income, wealth and sales taxes. On the average 48 persons arrive in an
8-hour day. Each tax adviser spends 15 minutes on an average on an arrival. If the arrivals
are Poisson distributed and service times are according to exponential distribution.
Determine (i) the average number of customers in the system, (ii) average number of
customers waiting to be served; (iii) average time a customer spends in the system,
(iv) average waiting time for a customer and (v) the expected number of idle tax advisers at
any specified time (vi) the utilization factor of the firm.
6. a) Enlist the solution methods for two-player zero-sum game. “Game theory bears a strong
relationship to linear programming”. Justify the statement.
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b) Use dominance rule to reduce the following game and hence find the optimal strategies
and the value of the game.
Player B
Player A 3 -2 4
-1 4 2
2 2 6
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7. The following failure rates have been observed for a certain type of transistors in a digital
computer:
End of week 1 2 3 4 5 6 7 8
Probability of
failure to date
0.05 0.13 0.25 0.43 0.68 0.88 0.96 1.00
There are 1000 transistors in use. The cost of replacing an individual failed transistor is
Rs.1.25. If the decision is made to replace all these transistors simultaneously at fixed
intervals, and to replace the individual transistors as they fail in service, then the cost of
group replacement is 30 paise per transistor. (i) Find out the best replacement policy.
(ii) What is the best interval between group replacements in the case of group replacement
policy? (iii) At what group replacement cost per transistor would a policy of strictly
individual replacement become preferable to the adopted policy?
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