BACHELOR'S DEGREE PROGRAMME (BDP) Term-End Examination December, 2015 (APPLICATION ORIENTED COURSE) AOR-01 : OPERATIONS RESEARCH

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1 01592 No. of Printed Pages : 16 I AOR-01 I BACHELOR'S DEGREE PROGRAMME (BDP) Term-End Examination December, 2015 (APPLICATION ORIENTED COURSE) AOR-01 : OPERATIONS RESEARCH Time : 2 hours Maximum Marks : 50 (Weightage : 70%) Note : Question no. 1 is compulsory. Answer any four questions out of questions no. 2 to 7. Calculators are not allowed. 1. Which of the following statements are True and which are False? Give a short proof or a counter-example in support of your answer. 5x2=10 (a) In an inventory model, the economic order quantity decreases with the increase in the shortage cost. AOR-01 1 P.T.O.

2 (b) In any assignment problem, the optimal assignments are always along the main diagonal. (c) A bound obtained by the branch-and-bound technique may not necessarily give a feasible point of the Integer Programming Problem. (d) The union of any two convex sets is convex. (e) In a queueing model, the arrival rate equals the mean of the exponential inter-arrival time. 2. (a) In the Central Railway Station, customers arrive at a counter following a Poisson distribution with an average time of five minutes between two arrivals. The time taken to process the ticket is on an average three minutes and it follows an exponential distribution. What is the probability that the counter is busy? What is the average waiting time of customer in queue? AOR-01 2

3 (b) A firm manufacturing a single product has three Plants I, II and III. Find the minimum possible transportation cost of shifting the manufactured product to the five customers. The net unit cost (in ) of transporting from the three plants to the five customers is given below : 6 Customer A B C D E Supply Plants I II III Demand (a) The daily demand for an item is 5000 units. Every time an order is placed, a fixed cost of 16 is incurred. Each unit costs 20 and the daily inventory carrying charge is 20%. Compute EOQ and the total variable cost. 4 AOR-01 3 P.T.O.

4 (b) A small project consists of seven activities for which the relevant data is given below : Activity Preceding activities Activity duration (in days) A 4 B 7 C 6 D A, B 5 E A, C 7 F C,D,E G C,D,E 5 (i) Draw the network and find the project's completion time. (ii) Find the critical path (a) Use the dual simplex method to solve the following L.P.P. 6 Maximize z = 2x 1 x3 subject to xi + x2 x3 5 x1 2x2 + 4x3 8 xl, x2, x3?-- 0. AOR-01 4

5 (b) A company has six jobs to perform on machines M 1 and M2. The time required for each job on each machine, in hours is given below A B C D E F M M Draw a sequence table for the six jobs on the two machines. Find the total elapsed time (a) Examine whether the following problem has an optimal solution graphically : Maximize z = 6x 1 2x2 subject to + x2 2 x1 x2 1 3x1 x2 6 x2?1 xl, x2?_ 0. AOR-01 5 P.T.O.

6 (b) Suggest optimum assignment of four workers A, B, C and D to four jobs I, II, III and IV. The time taken by different workers in completing the different jobs is given below : Job I II III IV A Worker B C D (a) A bank has two tellers working on saving accounts. The first teller handles withdrawals only. The second teller handles deposits only. It has been found that the service time distribution, both for the deposits and withdrawals, is exponentially distributed with mean service time three minutes per customer. Depositors are found to arrive according to Poisson distribution throughout the day with a mean arrival rate of 16 per hour. Withdrawers also arrive according to Poisson distribution with a mean arrival rate of 14 per hour. What would be the effect on the average waiting time for depositors and withdrawers if each teller could handle both withdrawals and deposits? AOR-01 6

7 (b) Find the shortest path from city "0" to city "6" in the following network design : 5 7. (a) A confectioner keeps stock of items. Past data of demand per week with associated probabilities is as follows : Demand/week Probability Use the following sequence of random numbers to simulate the demand for next five weeks : 44, 23, 10, 72, 85 AOR-01 7 P.T.O.

8 (b) Find the dual of the following Linear Programming Problem : Minimize z = 2xi + 3x2 + 4x3 subject to 12x 8x > xl + x2 8 8x1 + x3 12 xi, x2, x3 0. AOR-01 8

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16 () 1 1 i1i itrkg- 547rxr4 TrIR:tir *=t tth V c1 5 z = 2x1 + 3x2 + 4x3 1 1i.flchtul 12x1 8x2?_ 4 x1 + x2 8 8x1 + x3 12 xi, x2, x3?_ 0. AOR ,000