DOEACC Society 2006 DOEACC B Level B10 Applied Operations Research ( ) - Question Paper

BE10-R3: APPLIED OPERATIONS RESEARCH
NOTE:
Time: three Hours Total Marks: 100
1.
a) In Operations Research (OR) there are 2 distinct kinds of computations: those
involving simulation and those dealing with mathematical models. explain them briefly.
Why are calculations in OR mathematical models typically iterative?
b) A paper mill produce 2 grades of paper namely X and Y. Because of raw material
restrictions, it cannot produce more than 400 tons of grade X and 300 tons of grade Y in
a week. There are 160 production hours in a week. It requires 0.2 and 0.4 hours to
produce a ton of products X and Y respectively with corresponding profits of Rs. 200 and
Rs. 500 per ton. Formulate the above as a linear programming issue to maximize
profit.
c) Consider the subsequent problem:
minimize z = 3x1+4x2-5x3
subject to
2x1+3x2-5x3 ³ 10
x1-2x2-3x3 £ 8
x1,x2,x3 ³ 0
describe the dual issue.
d) What is Critical Path Method (CPM)? elaborate its main objectives?
e) Arrivals at a telephone both are considered to be subsequent Poisson process with an
avg. time of 10 minute ranging from 1 arrival and the next. Length of a phone call is
presumed to be distributed exponentially with mean three minutes.
i) What is the probability that a person arriving at the booth will have to wait?
ii) What is the avg. length of queue?
f) Determine the optimal sequence of jobs, which minimizes the total elapsed time based
on the subsequent info.
Processing times on the machines A, B, C
Job A B C
1 three 3 5
2 eight four 8
3 seven two 10
4 five one 7
5 two five 6
g) The demand rate for an item in a company is 18000 units per year. The company can
produce at the rate of 3000 per month. The set-up-cost is Rs. 500 per order and the
holding cost is Rs. 0.15 per unit per month. Calculate:
i) optimum manufacturing volume
ii) maximum inventory.
(7x4)
BE10-R3 Page one of four July, 2006
1. ans ques. one and any 4 ques. from two to 7.
2. Parts of the identical ques. should be answered together and in the identical
sequence.
2.
a) The network in the subsequent figure represents the distances in miles ranging from different
cities i, i =1, 2, …., 8. obtain the shortest routes ranging from the subsequent pairs of cities:
i) City one and city 8.
ii) City two and City 6.
4
2 one three 2
2
1 six 5
3 7
1 two 6
5 8
b) Determine the maximum flow ranging from nodes one and five for the network provided below:
(9+9)
3. Consider the integer linear programming problem:
maximize Z = 7x1+9x2
subject to
-x1+3x2 £ 6
7x1+x2 £ 35
x1, x2 nonnegative integers.
a) Using branch-and-bound algorithm (B&B), find the optimal solution.
b) Outline briefly the steps of B&B algorithm

Earning:   Approval pending.