2007 Jawaharlal Nehru Technological University B.E Electrical and Electronics OPERATIONS RESEARCH Question paper

Course: B.E Electrical and Electronics

University: Jawaharlal Nehru Technological University

1. A mining company owns two different mines that produces a given kind of ore in
grades A, B and C. The mining company has contracted to provide a smelting
plant 12 Tons of A, 8 Tons of B and 24 Tons of C grade ores per week. It costs
the company Rs. 2,000/- per day to run the first mine and Rs. 1,600/- per day to
run the second. In a day’s operation the first mine delivers 6 Tons of A, 2 Tons of
B and 4 Tons of C grade ores, where as the other mine delivers 2 tons of A and 6
tons of C grade ores. How many days in a week each mine should be operated to
fulfill the orders most economically?
(a) Formulate as an LPP
(b) Solve graphically. [6+10]
2. A Company has 4 warehouses and 6 stores, the cost of shipping one unit from
wareshouse i to store j is cij .
if c = (cij) =
2664
7 10 7 4 7 8
5 1 5 5 3 3
4 3 7 9 1 9
4 6 9 0 0 8
3775
and the requirements of the six stores are 40,40,60,20,40,20 and quantities at the
warehouse are 50,60,20,90. Find the minimum cost solution. [16]
3. Find the following sequencing problem to minimize the time elapsed with sequence
M1M2
Job 1 2 3 4 5
Maachine M1 7 10 8 9 7
Maachine M2 2 1 4 0 5
Also find the total elapsed time and idle times of each machine [16]
4. (a) Briefly explain the reasons for replacement.
(b) The following table gives the running costs /year and resale price of equipment
whose purchase price is Rs.8000.
Year 1 2 3 4 5 6 7 8
Running Cost(Rs.) 2500 2600 2800 3100 3500 3900 4400 5400
Resale Value(Rs.) 6500 5500 4700 4200 3800 3500 3500 3500
i. At what year is replacement due?
1 of 2
Code No: NR410301 NR
ii. If the resale value is zero, will there be any change in the replacement
policy? [4+12]
5. (a) Briefly explain
i. pure strategy
ii. mixed strategy
iii. optimal strategy
(b) Find the saddle point, optimum strategies and value of the game in the fol-
lowing pay off matrix [6+10]
Y
X
A B C D
I -3 4 2 9
II 7 8 6 10
III 6 2 4 -1
6. (a) What do you mean by the following
i. Queue discipline
ii. Input and holding times
(b) A service station operates a computerized order delivery service. The com-
puter can deliver an order every 20 minutes and actual delivery requires 30
minutes. Determine
i. the total number of orders that have been delayed after the start of day’s
work if 30 orders were placed prior to start up.
ii. the total elapsed time until the facility is idle. [6+10]
7. (a) Derive the Economic Order Quantity formula for the purchase model with
instantaneous replenishment and without shortages.
(b) Bata industry estimates that it will sell 24,000 units of its product for the
forthcoming year. The ordering cost is Rs. 150/- per order the carrying cost
per unit per year is 20% of the purchase price per unit. The purchase price
per unit is Rs. 50%. Find economic lot size, the number of orders per year
and the time between two successive orders. [8+8]
8. (a) State Belman’s principle of optimality and explain by an illustrative example,
how it can be used to solve multi stage decision problem.
(b) Define the following terms in dynamic programming :
i. Stage
ii. Decision variable
iii. Optimal return
iv. State transformation function. [8+8]

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