SPPU MBA II Semester III Past Papers - Decision Science PDF

Sadhu Vaswani Institute of Management Studies for Girls SPPU Question Papers MBA II Semester III 302 – Decision Science 1) October 2015 – 2013 Pattern 2) April 2016 – 2013 Pattern 3) October 2017 – 2016 Pattern 4) April 2018 – 2016 Pattern 5) Oct...

Sadhu Vaswani Institute of Management Studies for Girls SPPU Question Papers MBA II Semester III 302 – Decision Science 1) October 2015 – 2013 Pattern 2) April 2016 – 2013 Pattern 3) October 2017 – 2016 Pattern 4) April 2018 – 2016 Pattern 5) October 2018 – 2016 Pattern 6) April 2022 – 2019 Pattern 7) October 2022 – 2019 Pattern 8) October 2022 - 2021 Pattern 9) April 2023 – 2019 Pattern 10) April 2023 – 2021 Pattern 11) October 2023 – 2019 Pattern 12) October 2023 – 2019 Pattern Revised 13) May 2024 – 2019 Pattern 14) May 2024 – 2019 Pattern Revised  OCTOBER 2015 Total No. of Questions : 10] SEAT No. : P3793 -2004 [Total No. of Pages : 4 M.B.A. 204 : DECISION SCIENCE (2013 Pattern) (Semester - II) Time : 2½ Hours] [Max. Marks : 50 Instructions to the candidates: 1) Attempt Five questions. 2) Each question has an internal option. 3) Each question carries 10 marks. 4) Figures to the right indicate marks for question. 5) Graph will not be provided, draw neat diagrams on answer sheet only, if required. 6) Non scientific calculator is permitted. Q1) A company wants to give advertisements in two local news papers, one Hindi and one English. Expected coverage through the Ads, is 1000 and 1500 people per ads. respectively. Each Ads in a Hindi costs Rs. 3000/- and for an English is Rs. 5000/-. Company decided not to place more than 10 ads, in the Hindi and at least 6 ads. in the English daily. The Total advertisement budget is Rs, 50,000/-. Formulate the problem as L.P. Model. OR Q2) Four different machines have four different jobs. The following matrix gives the costs in rupees of job on machine. The set up and take down time costs are assumed to be prohibitively high for changovers. How should the jobs be assigned to the various machines so that the total costs is minimised. Machines M1 M2 M3 M4 J1 5 7 11 6 Jobs J2 8 5 9 6 J3 4 7 10 7 J4 10 4 8 3 P.T.O. Q3) A person wants to hire for repairing machines which breakdown at on average rate per hour, which following Poisson Distribution. A and B two repairmen interviewed. ‘A’ charges Rs. 100/- per hour and services breakdown machines at the rate of 6 per hour. B demands Rs. 125/- per hour and services at an average of 8 machines per hour. Downtime of a machine costs Rs. 25/- per hour, which repairman should be hired? OR Q4) Three brands of product P, Q and R are having market share as 30%, 30% and 40% respectively. Customers shifts their brands. Brand switching matrix every quarter is given below: From To A B C A 50% 30% 20% B 20% 70% 10% C 20% 20% 60% Find market share at the end of quarter. Q5) A production unit is not knowing the product acceptance probability and the data are given below: Anticipated 1st year profit Rs. ‘000 Accpetance Product Full Partial Minimal Good 8 70 50 Fair 50 45 40 Poor –25 –10 0 Determine the optimal decision under each of the following criteria : a) Maximax b) Maximin c) Minimax Regret OR -2004 2 Q6) Player A and B are playing with the following Matrix. Player B Player A 1 2 3 4 5 I 1 3 2 7 4 II 3 4 1 5 6 III 6 5 7 6 5 IV 2 0 6 3 1 Solve the following game by using Dominance Rule. Q7) Write short notes on (any two): [5 + 5 = 10] a) Concept of PERT and CPM. b) Concept of Network diagram with example. c) Dummy Activities and events with example. d) Floats and its types with example. OR Q8) Draw the network diagram for the following list of activities: Activity Immediate Activity Immediate Predecessor Predecessor A - L K B A M K C B N K D C O D E D P O F E Q B G E R N H C S L, M I C, F T S J G, H, I U P, Q K J V U -2004 3 Q9) a) A card is drawn from ordinary pack and a gambler bets that it is a spade or an ace. What are the odds against his winning this bet? b) What is the chance that a leap year, selected at random will contain 53 sundays? [5 + 5 = 10] OR Q10)Find the probability distribution of the number of sixes in three tosses of a dice. E E E -2004 4  APRIL 2016 Total No. of Questions : 10] SEAT No. : P3929 [Total No. of Pages : 4 - 2004 M.B.A. (Semester - II) 204 : DECISION SCIENCE (2013 Pattern) Time : 2½Hours] [Max. Marks : 50 Instructions to the candidates :- 1) Attempt 5(five) questions. 2) Each questions has an internal option. 3) Each question carry equal marks.(10) 4) Figures to the right indicate mark for questions. 5) Graph will not be provided, Draw a diagram on answer sheet. 6) Non Scientific calculator is allowed. Q1) Solve the following problem for maximizing the Production output. The data refers to the production of an article for the given operators and machines. Machines Operators A B C D 1 10 5 7 8 2 11 4 9 10 3 8 4 9 7 4 7 5 6 4 5 8 9 7 5 OR Q2) Solve the following L.P.P. using graphical method Minimize Z = 6X1 + 14X2 Subject to 5X1 + 4X2 > 60 3X1 + 7X2 < 84 X1 + 2X2 > 18 X1, X2 > 0 P.T.O. Q3) In a bank on an average every 15 min a customer arrives for cashing the cheque. The staff at the payment counter takes 10 min for serving a customer on an average. Calculate : a) Probability that system is busy. b) Average Queue Length. c) Average no of customers in the bank. d) Average waiting time of customer in queue before sevice. OR Q4) At a bus depo every bus should leave with driver. At the terminus they should keep two drivers as reserved if anyone on scheduled duty is sick and could not come following is the Probability distribution that driver become sick. No of Sick drivers 0 1 2 3 4 5 Probability 0.30 0.20 0.15 0.10 0.13 0.12 Simulate for 10 days and find utilization of reserved drivers. Also find how many days and how many buses cannot run because of non Availability of the drivers. Use following random numbers 30,54,34,72,20,02,76,74,48,22. Q5) Solve the following game using Principle of Dominance. Player B Player A I II III IV V VI 1 4 2 0 2 1 1 2 4 3 1 3 2 2 3 4 3 7 –5 1 2 4 4 3 4 –1 2 2 5 4 3 3 –2 2 2 OR -2004 2 Q6) A farmer wants to decide which of the 3 crops he should plant. The farmer has categorized the amount of rainfall as High, Medium and Low, Extimated profit is given below. Rainfall Estimated Profit (in Rs.) Crop A Crop B Crop C High 8000 3500 5000 Medium 4500 4500 4900 Low 2000 5000 4000 Farmer wishes to Plant one crop. Decide the best crop using. a) Hurwicz Alpha Criterion (Coefficient of Optimism a = 0.6) b) Laplace Criterion c) Minimax Regret Criterion Q7) The following information is gather for a project : Activity Preceding Activity Duration A - 1 B A 3 C A 4 D A 3 E D 2 F B,C,E 4 G D 9 H D 5 I H 2 J F,G,I 2 a) Draw the Network Diagram. b) Determine the Critical Path and Project Duration. OR Q8) Write short Notes on. a) Concept of Network diagram with example. b) Dummy Activities and events with example. -2004 3 Q9) a) What is the probability that a leap year selected at random will have 53 Mondays? b) The daily production (in number of units) for a week in a factory is 56,59,62,57,53,60,66 units. If it is checked at random on a day, what is the probability that it will be less than the average? OR Q10)a) There are three stock items, each of which can be substituted for the other. Each has stock out probability of 0.03 and is independent of others. The material manager wants to know the probability that i) All item are in stock ii) No item in stock. b) A card is drawn at random from a well shuffled Pack. Find the Probability that i) It is not a spade ii) It is a face card. eee -2004 4  OCTOBER 2017 Total No. of Questions : 5] SEAT No. : P3865 [Total No. of Pages : 3 - 2006 M.B.A. 204 : DECISION SCIENCE (2016 Pattern) (Semester - II) Time : 2¼ Hours] [Max. Marks :50 Instructions to the candidates: 1) Each question has an internal option. 2) Each question carries 10 marks. 3) Graph paper will not be provided. 4) Non Scientific calculator is allowed. Q1) A project manager has 4 subordinates and 4 task. His estimate of the time that each would take to perform each task is given in the matrix below. How should be the task allocated, so that the total man hours are minimized. I II III IV 1 8 26 17 11 2 13 28 4 26 3 38 19 18 15 4 19 26 24 10 OR Find the initial feasible solution for a given transportation matrix to reduce the cost using VAM method. D1 D2 D3 D4 Supply 01 5 3 6 2 19 02 4 7 9 1 37 03 3 4 7 5 34 90 Demand 16 18 31 25 90 Q2) Solve the given LPP using graphical method to maximize Z = 100x + 150y, Subject to, 2x + y ≤ 30, x + 3y ≤ 45 Where, x ≥ 0, y ≥ 0. OR P.T.O.  A bakery keeps stock of branded cake. Daily demand based on the past experience and its probability is given below. Demand 0 15 25 35 45 50 Probability 0.01 0.15 0.20 0.50 0.12 0.02 Consider the following sequence of random number - and 48, 78, 9, 51, 56, 77, 15, 14, 68 and 09. a) Simulate the demand for next 10 days. b) Find the Average demand of Cake. c) Find the stock situation of cake at the end of each day, if the owner of bakery decides to make 35 cakes every day. Q3) For the given profit matrix, find the optimal strategy using, a) Max Mini criteria. b) Laplace criteria. c) Hurwicz criteria (α = 0.7). N1 N2 N3 N4 S1 30 10 10 8 S2 40 –15 5 7 S3 50 20 –6 10 OR Solve the following game using dominance rule. Player B Strategy 1 2 3 4 5 I 1 3 2 7 4 Player A II 3 4 1 5 6 III 6 5 7 6 5 IV 2 0 6 3 1 Q4) We have 5 jobs each of which must go through the machines A, B & C. in the order ABC. Processing time in (hrs.) is as follows : Job 1 2 3 4 5 Machine A 5 8 6 9 5 Machine B 2 1 4 5 3 Machine C 3 7 5 6 7 Determine the sequence of the jobs that will minimize the total elapsed time. Also find the idle time for all machines as well. OR - 2006 2  Write short notes on (any Two) : a) Concept of PERT and CPM. b) Concept of Network diagram with example. c) Dummy activities and events with example. d) Floats and its types with example. Q5) A box contains 6 white and 8 red balls. The Second box contain 9 white and 10 red balls. One ball is drawn at random from the first box and put in the second box without noticing its colour. A ball is drawn at random from Second box. What is a probability that it is red? OR In an intelligence test administered to 1000 students, the average score was 42 and the standard deviation 24. Find - a) The number of students lying between 30 and 54 marks. b) The value of score exceeded by top 100 students. (Given Z at 0.5 = 0.1915, Z at 1.28 = 0.4). llll - 2006 3  APRIL 2018 Total No. of Questions : 5] SEAT No. : P1430 [Total No. of Pages : 4 -2004 M.B.A. 204: DECISION SCIENCE (2016 Pattern) (Semester-II) Time : 2¼Hours] [Max. Marks : 50 Instructions to the candidates: 1) Each question carry equal marks. 2) Each question has an internal option. 3) Graph paper will not be provided. 4) Non-Scientific calculator is allowed. Q1) a) A computer center has four expert programmers. The center needs. four application programs to be developed. The head of computer center after carefully studying, estimates. The time required (in minutes) by the expert to develop the application programm. Find the assignment schedule so that time will be minimized. A B C D Programes 1 120 100 80 90 Expert 2 80 90 110 70 3 110 140 120 100 4 90 90 80 90 OR a) Discuss the role of quantitative techniques in decision making. Give an example. b) Find the initial feasible solution using North-West corner method for the given matrix. Store A B C D Supply I 10 20 5 7 10 Warehouse II 13 9 12 8 20 III 4 15 7 9 30 IV 14 7 1 0 40 V 3 12 5 19 50 Demand 60 60 20 10 150 150 -2004 1 P.T.O. Q2) Solve the following LPP graphically to maximize Z =3x+4y, subject to, x + y ≤ 6, and 2x + y ≤ 8, where x ≥ 0, y ≥ 0. OR The rainfall distribution of monsoon season is as follows. Rainfall(in cm) 0 1 2 3 4 5 Frequency 50 25 15 5 3 2 Using the following random number-67,63,39,55,29,78,70,6,78, and 76, simulate the rainfall for next 10 days and find the average rainfall. Q3) A businessman has three alternative actions that he can take. Each of the action can be followed by any of the four posible events. The conditional payoff for each action-event combination are as under. Nature N1 N2 N3 N4 S1 4 0 -5 3 action S2 -2 6 9 1 S3 7 3 2 4 Find the optimal strategy using: a) Maxmini criteria b) Laplace criteria and c) Hurwicz criteria (α = 0.6) OR In a service department manned by one server, on an average one customer arrives every 10 minutes. It has been found that each customer requires 6 minutes to be served find out. a) Probability that the server is idle. b) Average queue length. c) Average time spent by each. Customer in the system. d) Probability that there would be 2 customers in the queue. -2004 2 Q4) Following information is gathered for a project. Activity Preceding activity Duration(weeks) A - 1 B A 3 C A 4 D A 3 E D 2 F B,C,E 4 G D 9 H D 5 I H 2 J F,G,I 2 a) Draw network diagram. b) Determine critical path and its duration. OR We have seven jobs, each of which has to go through two machines A&B in the order AB. The processing time for the jobs on the two machines (in hrs) are given as, Job 1 2 3 4 5 6 7 Machine A 3 12 15 6 10 11 9 Machine B 8 10 10 6 12 1 3 Determine the sequence of these jobs to minimized total elapsed time.T. Q5) A card is drawn froma pack of cards. What is the chance of drawing a red queen given that the card drawn was a face card. OR -2004 3  In a sample of 1000 scores, the mean of a certain test is 14 and the standard deviation is 2.5. Assuming the distribution to be normal, find. a) How many students have scored between 12 and 15 ? b) How many scored above 18? (Given Z at 0.8 = 0.2881 Z at 0.4 = 0.1554 Z at 1.6 = 0.4452)  -2004 4  OCTOBER 2018 Total No. of Questions : 5] SEAT No. : P2187 -2004 [Total No. of Pages : 4 M.B.A. 204 : DECISION SCIENCE (2016 Pattern) ( Semester - II) Time : 2 ¼ Hours] [Max. Marks : 50 Instructions to the candidates: 1) Each question has an internal option. 2) Each question carries 10 marks. 3) Graph paper will not be provided. 4) Use of non-scientific calculator is allowed. Q1) Marketing manager has 5 salesmen & 5 sales districts considering the capabilities of the salesman & the nature of the district, the marketing manager estimates that sales & per month (in hundred Rs) for each salesman in each district would be as follows. Sales district Salesman A B C D E 1 32 38 40 28 40 2 40 24 28 21 36 3 41 27 33 30 37 4 22 38 41 36 36 5 29 33 40 35 39 What is a maximun sale that may be expected in an optimum assignment? OR A construction company moves material form three plants to three projects. Project X requires 50 truck loads, project Y requires 75 and project Z require 50 truck loads. Plant A can supply 45 truck load per week plant B can supply 60 & plant C can supply 60. Using cost information given below determine optimal transportation schedules for the company. Transportation cost per truck load in (Rs) To/From X Y Z A 40 80 30 B 60 70 90 C 80 20 50 Find initial solution by using VAM. OR P.T.O. Q2) Use the graphical method to solve the following LPP Maximize Z = 100x + 100y. Subject to the constraints. 6 x  4 y  24 4 x  2 y  16 3.5 x  3 y  21 x, y  0 OR A bakery keeps stock of popular brand of cake. Daily demand based on past experience is given below: Daily Demand 0 10 20 30 40 50 Probability 0.01 0.15 0.20 0.50 0.12 0.02 Using the following random numbers simulate the demand for next 10 days. i) Find stock situation (unsold cake) if the owner of the bakery decides to make 30 cakes every day. ii) Also find average demand for the cakes on basis of simulated data. Random Number : 45, 72, 56, 51, 79, 09, 61, 43, 31, and 81. Q3) A manufacturing company faced with the problem of choosing from four products to manufacture. The potential demand of each product may turn out to be good, satisfactory or poor. The probabilities of each type of demand are 0.6, 0.2 and 0.2 respectively. Profit in Rs. Product Good Satisfactroy Poor A 40,000 10,000 1,100 B 40,000 20,000 7,000 C 50,000 15,000 8,000 D 40,000 18,000 15,000 Advise the company about type of product to be manufacture using EMV criterion. Determine expected value of perfect information. Ignore probability and suggest optimum strategy using Hurwicz criteria (  = 0.7). OR -2004 2  a) Following is the pay-off matrix in terms of increase in votes to X (loss to Y) using three different starategies available to each player for advertising. Find the optimum strategies adopted by X for the campaign. Candidate Y Strategies I II III I 300 200 100 Candidate X II 600 500 400 III 600 400 600 b) Explain the characteristics of queuing system. Q4) The following are the time estimates and the precedence relationships of the activities in a project network. Activity A B C D E F G H I J K Immediate - - - A B B C E D F,G H,1 Predecessor Activity Duration in Weeks 4 7 3 6 4 7 6 10 3 4 2 Draw the project network diagram. Determine the critical path and the project completion time. OR 7 jobs are processed in three machines are given below. Jobs J1 J2 J3 J4 J5 J6 J7 Machines M1 3 8 7 4 9 8 7 M2 4 3 2 5 1 4 3 M3 6 7 5 11 5 6 12 Determine optimal sequence of jobs and idle time of all three machines. -2004 3 Q5) a) Tickets numbered from 1 to 20 are mixed up and a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 7? b) A card is drawn at random from a well shuffled pack. Find the probability that card is i) An ace ii) Not diamond OR The Indian IT employees spent on an average 77 hours logged on to the Internet while at work. Assume the times are normally distributed and that of standard deviation is 20 hours. a) What is the probability a randomly selected employee spent fewer than 50 hours logged on to the Internet? b) What precentage of employees spent more than 100 hours logged on to the Internet? c) What precentage of employee logged on to the internet between 50 to 100 hours? Given that Z 1.15 1.35 Area 0 to Z 0.3749 0.4115  -2004 4  APRIL 2022 Total No. of Questions : 5] SEAT No. : P8034 [Total No. of Pages : 3 -302 M.B.A. - II 302-GC-12 : DECISION SCIENCE (2019 Pattern) (Semester - III) Time : 2½ Hours] [Max. Marks : 50 Instructions to the candidates: 1) Each question carries 10 marks. 2) Graph paper will not be provided. 3) Use of non-scientific calculator is allowed. Q1) Solve any five: [5×2=10] a) Define Probability. b) List techniques of initial solution for Transportation problem. c) Enlist various methods of decision making under uncertainity. d) What is 2×2 zero sum game? e) Enumerate any two quantitative techniques for optimal decision in business. f) List the drawbacks of graphical solution in LPP. g) Define total float in Network diagram. h) Define (M/M/I, Infinite, FIFO) in Queuing theory. Q2) Solve any two of the following: [2×5=10] a) Discuss the use of CPM & PERT in Project Management. b) Explain the role of quantitative techniques in decision making. c) Describe the steps in Solving Assignment Problem. P.T.O. Q3) Solve any one of the following: [1×10=10] a) A small bank is allocating maximum 0%. Rs. 21,00,000/- for personal & car loans. The interest rates per annum are 11% for car loan & 13% for personal loans. The loans are repaid at the end of one year period. The amount of personal car cannot exceed 40% of the car loans. Past experience has shown that bad debts to 1.2% of all personal loans. Formulate & solve the above problem to find the optimum loan allocations. b) Following is the distribution of defective pieces in a manufacturing process of a MNC in Pune. No. of defective items 0 10 20 30 40 50 Probability 0.01 0.20 0.15 0.50 0.12 0.02 Consider the following sequence of random numbers. 38, 58, 19, 51, 66, 15, 24, 78, 42, 08 Using this sequence, simulate the number of defective items for next 10 days. Q4) Solve any one of the following: [1×10=10] a) In a group of 1000 customers, there are 650 who uses Jio connection, 400 uses Airtel connection and 150 uses both connections, Jio & Airtel. If a customer is selected at random, what is the probability that he uses : i) Jio only ii) Airtel only iii) Only one of the two connection and iv) At least one of the two connections. b) A repairman is to be hired to repair machines which breakdown at an average rate of 6 per hour. The breakdown follow poisson distribution. The productive time of a machine is considered to cost Rs. 20 per hour. Two repairman Mr. X & Mr. Y have been interviewed for this purpose Mr. X charged Rs. 100 per hour. and he services breakdown machines at rate of 8 per hour. Mr. Y demand Rs. 140 per hour and he services at an average rate of 12 per hour. Which repairmen should be hired? (Assumes 8 hours shift per day). -302 2 Q5) Solve any one of the following: [1×10=10] a) Given the following: Activity 1-2 2-3 2-4 2-5 3-7 4-5 4-7 5-6 6-7 Duration 3 4 4 5 4 2 2 3 2 (in days) Construct the project network. Calculate project duration & determine critical path. b) Determine the optimal strategies for A & B in the following game. Obtain value of game. B’s Strategy B1 B2 B3 A1 9 8 –7 A’s A2 3 –6 4 Strategy A3 6 7 7  -302 3  OCTOBER 2022 (2019 Pattern) Total No. of Questions : 5] SEAT No. : PA-3623 - 302 [Total No. of Pages : 3 M.B.A.- II 302 -GC-12 : DECISION SCIENCE (2019 Pattern) (Semester - III) Time : 2½ Hours] [Max. Marks : 50 Instructions to the candidates: 1) Each question carries 10 marks. 2) Graph paper will not be provided. 3) Use of non-scientific calculator is allowed. Q1) Solve any five of the following. [2×5=10] a) Define transition probability in Markov Chain. b) Mention condition for balanced transportation problem. c) Define independent events in probability. d) Write condition for saddle point in game theory. e) Define EVPI (Expected value of perfect Information). f) Write format of LPP (Linear Programming Problem). g) Define critical pathin network diagram. h) List elements of queuing system. Q2) Solve any two of the following. [2×5=10] a) Discuss different decision enviornment in Decision Theory. b) Describe role of linear programming problem (LPP) in managerial decision making. c) Determine the initial solution of following transportation problem using North West Corner Method. Destinations Sources D1 D2 D3 D4 Supply S1 19 30 50 10 7 S2 40 8 15 18 9 S3 30 20 20 25 18 Demand 05 08 07 14 -302 1 P.T.O. Q3) Solve any One of the following. [1×10=10] a) Solve the following game by using principle of dominance. Player B B1 B2 B3 B4 A1 14 4 8 12 Player A A2 8 3 2 12 A3 8 7 –6 16 A4 6 5 12 10 b) Following data is related to frequency of student absenteeism in a class No. of students Absent 0 5 10 15 20 25 Frequency 4 22 16 42 10 06 Simulate the students absenteeism for next 10 weeks. Also find out average absenteeism. Use the following random numbers. 87, 05, 30, 53, 89, 61, 19, 55, 23, 58 Q4) Solve any one of following. [1×10=10] a) A computer centre has got four expert programmes The centre needs four application programmes to be develop. The head of computer centre after studying carefully programmes to be developed estimes computer time (in hrs) required by the respective experts to develop the application programmes as follow. Programmes A B C D Programmers 1 120 100 80 90 2 80 90 100 70 3 120 140 120 100 4 90 90 80 90 Assign programmers to the programmes in such a way that total computer time is minimize. -302 2  b) The profit of organized retail outlet is approximately normally distributed with mean Rs. 4400 & standard deviation Rs. 620 Find associated probability of profit i) More than 3300 ii) less than 5400 iii) between 3500 & 4400 Given P[0 < Z < 1.77] = 0.4616 P[0 < Z < 1.61] = 0.4463 P[0 < Z < 1.45] = 0.4263 Q5) Solve any One of following. [1×10=10] a) A project has been defined to contain the following list of activities along with their required time of completion. Activity A B C D E F G H I Time in Dasy 1 4 3 7 6 2 7 9 4 Immediate – A A A B C E,F D G,H predecessor Draw network diagram. Identify Critical Path. b) In a bank on an average every 15 minutes one customer arrives for cashing the cheque. The staff at the only payment counter takes 10 minutes for serving a customer on an average. Find i) average queue length. ii) Increase in arrival rate for justifying a second counter.    -302 3  OCTOBER 2022 (2021 Pattern) Total No. of Questions : 5] SEAT No. : PA-4364 [Total No. of Pages : 3 -3002 M.B.A. (GC-12)-302: DECISION SCIENCE (2021 Pattern) (Semester - III) Time : 2½ Hours] [Max. Marks : 50 Instructions to the candidates : 1) All questions are compulsory. 2) Each question carries 10 marks. 3) Each question has an internal option. 4) Use of simple calculator is allowed. Q1) Solve any Five out of eight questions : a) Define dependent event. b) Define critical path. c) State mined strategy. d) State unbalanced transportation problem. e) Define saddle point. f) Memorize mean service rate. g) State full form of CPM. h) Define Monte Carlo simulation. Q2) Solve any two out of three questions : a) Explain the applications of Markov chain. b) Compare CPM and PERT. c) Describe the importance of decision science in decision making. P.T.O. Q3) a) Use the graphical method to solve the following LPP. Maximize Z = 100x + 100y Subject to constraints 6x + 4y  24 4x + 2y  16 3.5x + 3y  21 x, y  0 OR b) Obtain the initial feasible solution of the following transportation problem using i) NWCM and ii) LCM. D1 D2 D3 D4 Supply S1 19 30 50 10 7 S2 70 30 40 60 9 S3 40 8 70 20 18 Demand 5 8 7 14 34 Q4) a) A bakery keeps a stock of popular brand of cake. Daily demand based on past experience is given below. Daily Demand 0 10 20 30 40 50 Probability 0.01 0.15 0.20 0.50 0.12 0.02 Using the following random numbers simulate the demand for next 10 days and also calculate the average demand for the cake basis of simulated data. Random numbers : 45, 72, 56, 51, 79, 9, 61, 43, 31 and 81 OR b) Draw network diagram from the following activities and find critical path and total slack of activities. Job A B C D E F G H I J K Job time 13 8 10 9 11 10 8 6 7 14 18 days Immediate - A B C B E D,F E H G,I J predecessor. -3002 2 Q5) a) Given the following pay off matrix use i) Laplace criterion ii) Minimax Regret criterion iii) Hurwicz criterion ( = 0.6) to find optimal strategy. Action A1 A2 A3 A4 S1 10 5 8 6 States of Nature S2 3 9 15 2 S3 –3 4 6 10 OR b) Solve the following assignment problem for minimization. 1 2 3 4 5 A 8 8 8 11 12 B 4 5 6 3 4 C 12 11 10 9 8 D 18 21 18 17 15 E 10 11 10 8 12  -3002 3  APRIL 2023 (2019 Pattern) Total No. of Questions : 5] SEAT No. : P-3765 [Total No. of Pages : 4 -42 M.B.A. 302 : GC-12 : DECISION SCIENCE (2019 Pattern) (Semester - III) Time : 2½ Hours] [Max. Marks : 50 Instructions to the candidates: 1) Each question carries 10 marks. 2) Graph paper will lnot be provided. 3) Use of non-scientific calculator is allowed. Q1) Solve any five of the following : [5 × 2 = 10] a) Define optimistic time estimate in PERT. b) Enlist different queue discipline in queuing theory. c) What is saddle point in Game theory? d) Define Markov Chain. e) Mention assumptions underlying Linear Programming Problem (LPP). f) Write different methods of initial solution to transportation problem. g) Write condition for balanced assignment problem. h) What do you mean by optimal solution in solving transportation problem? Q2) Solve any two of the following : [2 × 5 = 10] a) Solve the following LPP by graphical solution Max Z= 9x1 + 3x2 Subject to 2x1 + 3x2  13 2x1 + x2  5 x1 +x2  0 P.T.O.  b) Explain the steps in solving transportation problem. c) Explain the use of various tools of decision theory in today’s business environment. Q3) Solve any one of the following : [1 × 10 = 10] a) Three brands of product P, Q and R having market share as 30%, 30% and 40% respectively. Customers shift their brands. Brand switching matrix every quarter is given below. To From P Q R P 50% 30% 20% Q 20% 70% 10% R 20% 20% 60% Apply concept of Markov Chain to find market share at the end of First & Second quarter. b) Using the following cost matrix determine i) Optimal job assignment ii) Optimal cost assignment. Cost ('000 Rs.) Job Machinist 1 2 3 4 5 A 10 3 3 2 8 B 9 7 8 2 7 C 7 5 6 2 4 D 3 5 8 2 4 E 9 10 9 6 10 -42 2 Q4) Solve any one of the following : [1 × 10 = 10] a) XYZ company is considering three options for managing its data processing operations: continue with own staff, outsourcing or the use of combination. The annual profit of each option depends on demand as follows : Profit Staffing Demand ('000 Rs.) option High Medium Low Own staff 650 650 600 Outsourcing 900 600 300 Combination 800 650 500 Determine Optimal strategy for i) Maxi-min ii) Laplace iii) Hurwicz ( = 0.6) & iv) Regret criterion. b) The machine operator has to perform two operations, turning and threading on a number of different jobs. The time required to perform these operation on these machines is given below. Determine sequencing of jobs to minimize the total time. Also find idle time of operations on both machines. Jobs 1 2 3 4 5 6 Turning time 03 12 05 02 09 11 (in min) Threading time 08 10 10 06 03 01 (in min) Q5) Solve any one of the following : [1 × 10 = 10] a) Vijay has started new retail outlet in the mid of the market. In market there is business & competition, therefore survival of new outlet is very rare chance of survival is almost 5%. Vijay has started such 7 new retail outlet. Find out the probability i) no shop will survive and ii) exactly 5 shops will survive. -42 3  b) The three estimates for activities of a project are given below : Activity 1-2 1-3 1-4 2-5 3-5 4-6 5-6 Pessimistic 7 7 12 15 1 8 7 duration Most likely 6 1 4 6 1 2 4 duration Optimistic 5 1 2 3 1 2 1 duration Draw network diagram. Find out Critical path & Project duration. Estimate expected Standard deviation of critical path.  -42 4  APRIL 2023 (2021 Pattern) Total No. of Questions : 5] SEAT No. : P3854 -3002 [Total No. of Pages : 3 S.Y.M.B.A. (Project Management) 302 - GC - 12 : DECISION SCIENCE (2021 Pattern) (Semester - III) Time: 2½ Hours] [Max. Marks : 50 Instructions to the candidates: 1) Each question carries 10 marks. 2) Graph paper will not be provided. 3) Use of non-scientific calculator is allowed. 4) All questions are compulsory. Q1) Solve any five. [5×2=10] a) Define balanced transportation problem. b) State linear programming. c) Define conditional probability. d) Define saddle point. e) State what is critical path. f) Define mean arrival rate. g) Define probability. Q2) Solve any two of the following. [2×5=10] a) Discuss dependent Event and Independent Event. b) Describe the role of quantitative techiniques in decision making. c) Solve the following problem graphically. Maximize Z = 3x + 4y Subject to x + y  6 2x + y  8 x,y  0 -3002 1 P.T.O. Q3) Solve any on of the following. a) How should the activities be assigned to the workers so that the job is completed in minimum time? Workers Activities 1 2 3 4 A 14 12 15 15 B 21 18 18 22 C 14 17 12 14 D 6 5 3 6 OR b) Find initial solution by using North - West corner method and Least Cost Method (LCM) D1 D2 D3 D4 supply S1 19 30 50 10 7 S2 70 30 40 60 9 S3 40 8 70 20 18 Demand 5 8 7 14 34 Q4) Solve any one of the following. a) The following table gives the activities in a construction project and other relevant information Activity 1-2 1-3 2-3 2-4 3-4 4-5 Duration 20 25 10 12 6 10 (Days) i) Draw the network diagram for the project. ii) Find critical path. iii) Determine the expected project completion time. OR -3002 2  b) A departmental store has a single cashier. During the rush hours, customers arrive at a rate of 20 customers per hour. The cashier takes on an average 2.5 minutes per customer for processing. i) What is the probability the cashier is idle? ii) What is the average number of customers in the queuing system? iii) What is average queue length? iv) What is the average time spent by a customer in the system? Q5) Solve any one of the following. a) From the pay off matrix (Profit). Determine optimal strategy by using. i) Maximin criterion ii) Maximax criterion iii) Minimax Regret criterion iv) Laplace criterion States is Nature Strategies N1 N2 N3 S1 7,00,000 3,00,000 1,50,000 S2 5,00,000 4,50,000 0 S3 3,00,000 3,00,000 3,00,000 OR b) Solve the following game. Player (B) B1 B2 Player A1 3 5 (A) A2 4 1 i) Find the value of game. ii) Find the optimal strategies of player A and player B.  -3002 3  302 - DECISION SCIENCE MBA II SEMESTER III – OCTOBER 2023 (2019 PATTERN)  DECISION SCIENCE MBA II SEMESTER III – OCTOBER 2023 (2019 PATTERN Revised) I Tot.al No. of Qurstions-: 51 (\ ~I SEAT No. :[.___ _ _ ---J PB2129 ~ ~I [Toul No. of Pages : 3 -..._'-' (6201~002 S.);M. B.A. 302 : q.e....12 ~ECISION SCIENCE ~9 P~ern)(Semester - ID) Ti.me: 2½ Ho11rs) ~ ~ [Max. Marks: 50 Instructions to the c ate~~ I) All que~1·, e ~,~ulsory. 2) E11ch q 11 ca~es 10 marks. J) Fig~~ ti,~),, indicate ji,I/ ,narks. ,.., 4) GNQ/!~ ap~(:Vtll be pro ided. ~ I 5) Use "of" non~ientific calculator is allowed. ~ ,~ '-~· ~ ~ ~ ~ QJ) Solve ~-Five of the following. ('\~ - ~ '- ~.v a) ~rite a short note on Hungariarfinetho(fff]ood 's Technique to solve assignment problem. ~ 7 ~ b) Explain in brief Vogel's Ap~ Method. c) What do you understand ~ e ~~le Solution and Optimum Solution in case of an LPP?t~~ ~ "./ ~/ d) Define Transition P sbil~,-in Markov chain. I"'\~ " ✓ /I e) State the condition for ~).]anced Transportation Problem. ~ ~ '¥ f) Define Independen~"ents in Probability. 4~2x