Roll No. :... Invigilator s Signature :.. CS/B.TECH(IT)/SEM-5/M(CS)-511/ OPERATIONS RESEARCH AND OPTIMIZATION TECHNIQUES

Size: px

Start display at page:

Download "Roll No. :... Invigilator s Signature :.. CS/B.TECH(IT)/SEM-5/M(CS)-511/ OPERATIONS RESEARCH AND OPTIMIZATION TECHNIQUES"

Lawrence Ward
6 years ago
Views:

1 Name : Roll No. :.... Invigilator s Signature :.. CS/B.TECH(IT)/SEM-5/M(CS)-511/ OPERATIONS RESEARCH AND OPTIMIZATION TECHNIQUES Time Allotted : 3 Hours Full Marks : 70 The figures in the margin indicate full marks. Candidates are required to give their answers in their own words as far as practicable. Graph sheet(s) will be supplied by the Institution on demand. GROUP A ( Multiple Choice Type Questions ) 1. Choose the correct alternatives for any ten of the following : 10 1 = 10 i) If in the simplex algorithm, the basis column of the final simplex table contains an artificial variable, then the problem has ii) iii) a) unbounded solution b) degenerate solution c) feasible solution d) infeasible solution. If the primal problem of an LPP has an unbounded solution, then the dual problem has no a) Basic solution b) Feasible solution c) Unbounded solution d) Bounded solution. If some basic variables are zero, then the solution to the corresponding LPP is called a) Non-degenerate b) Optimal c) Non-optimal d) Degenerate 5302 [ Turn over

2 iv) If there are n workers and n jobs, the number of solutions is a) n! b) (n 1)! c) (n 1) d) n. v) In an assignment problem involving four workers and three jobs, the total number of assignments possible is vi) a) 4 b) 3 c) 7 d) 12. The number of non-basic variables in the balanced TP with 4 rows and 5 columns is a) 4 b) 5 c) 12 d) 20. vii) An activity is said to be critical activity if a) its free float is zero b) its total float is zero c) its independent float is zero d) its time duration is zero. viii) In an (M/M/1) : ( /FIFO) model, the average number of customers E (n) is given by ix) a) " n b) c) " 2 1#" d) " 1#" " 1+" The EOQ formula under lotsize model without shortage is a) 2c 3 c 1 R b) 2c 3 R c 1 c) 2c 1 c 3 R d) 2c 1 R c

3 x) The point of intersection of pure strategies in a game is called xi) a) value of the game b) saddle point c) mixed strategy d) optimal strategy An assignment problem can be solved by a) Hungarian Method b) VAM c) Matrix Minima Method d) Dominance Principle. xii) Full form of PERT is a) Program Estimation and Review Techniques b) Project Evaluation and Review Techniques c) Project Estimation and Research Techniques d) Project Evaluation and Research Techniques. GROUP B ( Short Answer Type Questions ) Answer any three of the following. 3 5 = Write the LPP in its standard form : Max (Z) = x 1 3x 2 + 5x 3 subject to x 1 + x 2 + x 3 "7 x 1 " x 2 + x 3 # 2 3x 1 " x 2 +2x 3 = "5 x 1, x 2 " 0 and x 3 is unrestricted. 3. A manufacturing company purchases 9000 parts of a machine for its annual requirements, ordering one month usage at a time. Each part costs Rs. 20. The ordering cost per order is Rs. 15 and the carrying charges are 15% of the average inventory per year. It has been assigned to suggest a more economical purchasing policy for the company. What advice would you offer and how much would it save the company per year? [ Turn over

4 4. Find out the initial basic feasible solution of the following transportation problem by Vogel s Approximation method. D E F G Available A B C Demand jobs A, B,C,D are to be assigned to workers and 1,2,3 and 4 and the respective profits in rupees of these assignments is given in the following matrix. Determine the optimal assignment to the profit. Calculate the maximum profit resulting from the assignment. A B C D Solve the following game problem : Player B I II III IV I II III IV Player A

5 GROUP C ( Long Answer Type Questions ) Answer any three of the following = a) A manufacturer produces TVs and VCRs in a factory. Each TV requires 4 hours to assemble in workstation 1 and 2 hours in workstation 2. Each VCR requires 2 hours to assemble in workstation 1 and 5 hours in workstation 2. Workstations 1 and 2 function for 40 hours and 60 hours respectively in a week. The profit on each TV is Rs and on each VCR is Rs Assuming that all the TVs and VCRs are sold, what should be the strategy of the manufacturer so as to earn maximum profit using LPP? b) Solve the following integer programming problem using Gomory s cutting plane algorithm : Max Z = x 1 +x 2 subject to 3x 1 + 2x 2 " 5 x 2 " 2 x 1 " 0, x 2 " 0 and are integers. 8. a) A particular item has annual requirement of 3000 units. The ordering cost is Rs. 100 per order. The per unit cost is Rs. 10. The carrying cost per unit per year is 30% of the unit cost. (i) Find EOQ. (ii) By using better organizational methods the ordering cost per order is brought down to Rs. 80 per order, but the same quantity as determined above was ordered. If new EOQ is found by using the ordered cost as Rs. 80, what would be further savings in the cost? [ Turn over

6 b) A T.V. repairman finds that the time spent on his jobs have an exponential distribution with mean 30 minutes. If he repairs sets in the order in which they came in, and if the arrival of sets is approximately Poisson with average rate of 10 per 8-hour day, what is repairman s expected idle time each day? How many jobs are ahead of the average set just brought in? 9. a) Three persons are being considered for three open positions. Each person has been given a rating for each position as shown in the following table : position person A B C Assign each person to one and only one position in such a way that the sum of ratings for three persons is maximum. b) Solve the following Transportation Problem using the Vogel s Approximation Method : D 1 D 2 D 3 O O O O Also test the optimality of the solution obtained using Modified Distribution Method

7 10. a) Find out the shortest path and distance between node 1 and node 9 of the following network using Dijkstra s algorithm. b) Using Floyd-Warshall s algorithm, calculate the shortest distance and the shortest path between node 1 to node 4 of the following network [ Turn over

8 11. A small project is composed of seven activities whose time estimates are listed in the table as follows : Estimated duration (weeks) Activity Optimistic Most Likely Pessimistic You are required to : a) Draw the project network b) Find the expected duration and variance of each activity c) Calculate the early and late occurrence for each event and the expected project length d) Calculate the variance and standard deviations of project length e) What is the probability that the project will be completed- (i) 4 weeks earlier than expected (ii) Not more than 4 weeks later than expected (iii) If the project due date is 19 weeks, what is the probability of meeting the due late?

Babu Banarasi Das National Institute of Technology and Management

Babu Banarasi Das National Institute of Technology and Management Department of Computer Applications Question Bank Masters of Computer Applications (MCA) NEW Syllabus (Affiliated to U. P. Technical University,