OPERATIONS RESEARCH Code: MB0048. Section-A

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1 Time: 2 hours OPERATIONS RESEARCH Code: MB0048 Max.Marks:140 Section-A Answer the following 1. Which of the following is an example of a mathematical model? a. Iconic model b. Replacement model c. Analogue model d. General model 1Mark x 50= 50 Marks 2. Which phase in Operations Research involves making recommendations for the decision process? a. Judgement Phase b. Research Phase c. Action Phase d. Recommendation Phase 3. A production manager of a manufacturing organisation is asked to manage and optimise the utilisation of the resources. He/she has to deal with all the aspects of buying like when to buy, how much to buy, etc. Which of the following tools or techniques of Operations Research should be used? a. Linear programming b. Inventory control methods c. Transportation model d. Goal programming 4. Models in which the input and output variables follow a defined probability distribution are a. Deterministic b. Probabilistic c. Symbolic d. Sequencing 5. has several objective functions, each having a target value. a. Queuing model b. Linear programming c. Goal programming d. Inventory control method 6. In linear programming we need to ensure that both the objective function and the constraints can be expressed as linear expressions of. a. Basic variables b. Decision variables c. Constraints d. Objective function

2 7. Optimisation refers to the maximisation or minimisation of the. a. Objective functions b. Constraints c. Co-efficients of decision variables d. Constants 8. Which of the following defines the measure of effectiveness of the system as a mathematical function of its decision variables? a. Objective function b. Optimum strategy c. Constraints d. Queuing theory 9. When a linear programming problem is represented in the canonical form, the minimisation of a function is mathematically equivalent to the of this function. a. Maximisation of the negative expression b. Minimisation of the negative expression c. Minimisation of the positive expression d. Maximisation of the positive expression 10. In Linear Programming Problems, both objective function and constraints can be expressed as. a. Linear equalities b. Non-linear equalities c. Linear inequalities d. Non-linear inequalities 11. Any inequality in one direction ( or ) may be changed to an inequality in the opposite direction ( or ) by multiplying both sides of the inequality by. a. 0 b. -1 c. 1 d According to which of the basic assumptions of linear programming problem all coefficients of decision variables in the objective and constraints expressions are known and finite? a. Linearity b. Deterministic c. Additivity d. Divisibility 13. Linear programming is a powerful tool for. a. Maximising a nonlinear objective function b. Optimising costs c. Solving a system of equalities and inequalities d. Selecting alternatives in a decision problem

3 14. In graphical analysis, the equation is replaced to form a linear equation. a. Linear Programming constraint b. Inequality constraint c. Binding constraint d. Redundant Constraint 15. In which of the following case, only one optimum solution will be obtained in a graphical solution method? a. A unique optimal solution b. Multiple optimal solution c. An unbounded solution d. Infeasible problem 16. Which of the following is a characteristic of simplex method? a. All constraints are equations b. Convexity c. Boundaries of feasible region are planes d. Objective function can be represented by a line 17. Slack and surplus variables can be incorporated in the objective function with coefficients. a. One b. Zero c. Three d. Four 18. When the primal problem is unbounded, the dual is a. Multiple optimal solutions b. Infeasible c. Degenerate d. Unbounded or infeasible 19. The objective of formulation of is to develop an integral transportation schedule that meets all demands from the inventory at a minimum total transportation cost. a. Assignment problem b. Transportation problem c. Game theory d. Simulation 20. If the number of allocation is less than then it is said to be a degenerate transportation problem. a. m - n - 1 b. m - n + 1 c. m + n + 1 d. m + n The number of rows is not equal to the number of columns and vice versa in.

4 a. Linear programming problem b. Balanced assignment problem c. Unbalanced assignment problem d. Quadratic programming problem 22. In which among the following techniques we can assign lower and upper bound for the optimum values of the variables a. Branch and bound technique b. Integer programming technique c. Non-integer programming technique d. Linear programming techniques 23. In which of the following integer programming problems all decision variables are restricted to integer values? a. Pure integer programming problems b. Mixed integer programming problems c. Zero integer programming problems d. One integer programming problems 24. Queuing theory is a collection of mathematical models of various queuing systems based on concepts. a. Probability b. Statistics c. Game d. Sequencing 25. Impatient customers who would not wait beyond a certain time and leave the queue are said to. a. Balking b. Jockeying c. Reneging d. Collusion 26. queuing disciplines are based on the individual customer s status. a. Dynamic b. Server c. Service d. Static 27. is a rule wherein customer is allowed to enter into the service immediately after entering into the system. a. FIFO b. LIFO c. Priority service d. Pre-emptive priority 28. When the customer arrivals are completely random, the is followed. a. Deterministic model b. Statistical model c. Poisson distribution

5 d. Probability concept 29. represents number of customers waiting in the queue. a. Service facility b. Queue length c. Waiting time d. Arrival pattern 30. Queuing theory is a collection of of various queuing systems. a. Mathematical models b. Game models c. Simulation models d. Assignment models 31. In this type of a model, a customer enters the first station and gets a portion of service and then moves on to the next station, gets some service and finally leaves the system having received the complete service. a. Single server- Single queue b. Single server- Several queues c. Several servers- Single queues d. Service facilities in a series 32. Which queuing discipline is based on the stack method? a. First Come- First Served b. Priority c. Random d. Last Come- First Served 33. is the process of defining a model of a real system. a. Simulation b. Prototyping c. CPM d. PERT 34. The technique of involves the selection of random observations within the simulation model. a. Monte Carlo b. Experimentation c. Rapid Prototyping d. PERT 35. Simulation should not be applied in all the cases because it: a. Requires considerable talent for model building and extensive computer programming efforts. b. Consumes much computer time c. Provides at best approximate solution to problem d. All of the above

6 36. may be defined as a collection of interrelated activities (or tasks) which must be completed in a specified time according to a specified sequence and require resources, such as personnel, money, materials, facilities, etc. a. Projects b. PERT c. CPM d. Simulation 37. refers to comparing the actual progress against the estimated schedule. a. Project planning b. Project scheduling c. Project controlling d. CPM 38. For the critical activities, the float is a. One b. Two c. Zero d. Negative 39. The float for activity is the difference between the maximum time available to perform the activity and its duration. a. Total b. Free c. Independent d. Zero 40. What is the abbreviation of PERT? a. Program Evaluation and Review Technique b. Probable Evaluation and Review Technique c. Path Evaluation and Reasoning Technique d. Predetermined Evaluation and Review Technique 41. If a player s strategy is to adopt a specific course of action, irrespective of the opponent s strategy, the player s strategy is called strategy. a. Pure b. Chaste c. Tainted d. Mixed 42. The critical path of a network is the a. longest time path through the network. b. path with the most activities. c. path with the fewest activities. d. shortest time path through the network 43. Which of the following is used to come up with a solution to the assignment problem? a. MODI method b. northwest corner method c. stepping-stone method

7 d. Hungarian method 44. To find an initial basic feasible solution by Matrix Minima Method, we first choose the cell with a. zero cost b. highest cost c. lowest cost d. none of these 45. Activity Duration(weeks) For the network diagram, the critical path is: a b c d The objective function for a LP model is 3X 1 + 2X 2. If X 1 = 20 and X 2 = 30, what is the value of the objective function? a. 0 b.50 c. 60 d A road transport company has one reservation clerk on duty at a time. He handles information of bus schedules and make reservations. Customers arrive at a rate of 8 per hour and the clerk can serve 12 customers on an average per hour. The average number of customer waiting for the service of the clerk is a. 2 b. 5 c. 8 d The number of customers in queue and also those being served in the queue relates to the efficiency and. a. Facility, Queue length b. Service, Capacity c. Server, Capacity d. Facility, Capacity 49. If there are 'n' number of workers and 'n' number of tasks are to be performed, but some of the tasks cannot be performed by the workers then it is a form of. a. Infeasible assignment problem b. Feasible assignment problem c. Unbalanced assignment problem d. Balanced assignment problem

8 50. Network scheduling is a technique for and of large projects. a. Scheduling, Integrating b. Planning, Scheduling c. Integrating, Implementing d. Planning, Integrating Section-B 2Marks x 25= 50 Marks Answer the following 1. i. OR techniques are used to find the best possible solution. ii. OR methods in industry can be applied in the fields of production, inventory controls and marketing, purchasing, transportation, and competitive strategies. State True or False: a. i -True, ii -False b. i -True, ii -True c. i -False, ii -False d. i -False, ii -True 2. i. include all forms of diagrams, graphs, and charts. ii. include a set of symbols to represent the decision variable of the system. a. Physical models, Probabilistic models b. General models, Mathematical models c. Physical models, Mathematical models d. General models, Specific models 3. i. phase deals with formulation of the problems relative to the objectives. ii. phase deals with formulation of hypothesis and model. a. Judgement, Research b. Research, Judgement c. Judgement, Action d. Research, Action 4. Linear programming is a mathematical technique designed to help managers in their and. a. Organising, allocation b. Planning, organising c. Planning, decision making d. Allocation, implementation 5. Which of the following options indicate the advantages of linear programming? i. It indicates how decision makers can employ productive factors most effectively by choosing and allocating resources. ii. It is used to determine the proper mix of media to use in an advertising campaign. iii. It takes into consideration the effect of time and uncertainty. iv. Parameters appearing in the model are assumed to be variables. a. Options i & iv

9 b. Options i & ii c. Options i & iii d. Options ii & iii 6. Identify which among the following are the reasons why sensitivity analysis is important. i. Values of linear programming parameters might change. ii. The labour of computation can be considerably reduced. iii. Useful in planning future decisions. iv. Linear programming parameters have an uncertainty factor attached to them. a. Options i & iv b. Options i & ii c. Options i & iii d. Options ii & iv 7. Write the dual of Max Z = 5x 1 + 6x 2 Subject to 4x 1 + 2x 2 16 x 1 + 2x x 1 + 2x 2 20 x 1, x 2 0 a. Min W = 16y y y 3 Subject to 4y 1 + y 2 + 5y 3 5 2y 1 + 2y 2 + 2y 3 6 y 1, y 2, y 3 0 b. Min W = 16y y y 3 Subject to 4y 1 + y 2 + 5y 3 5 2y 1 + 2y 2 + 2y 3 6 y 1, y 2, y 3 0 c. Min W = 16y y y 3 Subject to 4y 1 + y 2 + 5y 3 5 2y 1 + 2y 2 + 2y 3 6 y 1, y 2, y 3 0 d. Min W = 16y y y 3 Subject to 4y 1 + y 2 + 5y 3 5 2y 1 + 2y 2 + 2y 3 6 y 1, y 2, y Consider the below mentioned statements: i. Hungarian method can be applied to maximisation problem. ii. All assignment problems are maximisation problems. State True or False: a. i-true, ii-true b. i-false, ii-false c. i-false, ii-true d. i-true, ii-false

10 9. Match the following sets: Part A 1. Service facility 2. Queuing system 3. Multiple service channels 4. Static queuing discipline Part B A. Arrival pattern, service facility and queue discipline B. Availability of service, number of service centres and duration of service C. Based on Individual Customer status in the queue D. Series or parallel arrangement a. 1D, 2A, 3B, 4C b. 1A, 2D, 3B, 4C c. 1B, 2A, 3D, 4C d. 1B, 2C, 3A, 4D 10. Which of the below aspects form a part of a service system? i. Configuration of service system ii. Speed of the service iii. Cost of the service system iv. Size of the service system a. Options i & ii b. Options i & iv c. Options i & iii d. Options ii & iii 11. Consider the following statements: i. Single server - Single queue model involves one queue one service station facility called single server models where customer waits till the service point is ready to take him for servicing. ii. Different cash counters in an electricity office where the customers can make payment in respect of their electricity bills provide an example of several servers -several queues model. State true or false a. i -False, ii -False b. i -True, ii -True c. i -False, ii -True d. i -True, ii -False 12. A factory produces 150 scooters. But the production rate varies with the distribution depicted in table below. Production rate Probability At present the truck will hold 150 scooters. Random Numbers 82, 54, 50, 96, 85, 34, 30, 02, 64, 47. Using the random numbers, the average number of scooters waiting for shipment in the factory is a. 0.4/day b. 0.5/day c. 0.6/day d. 0.7/day

11 13. The Monte Carlo technique is restricted for application involving random numbers to solve and problems. a. Deterministic, Speculative b. Probabilistic, Speculative c. Indeterministic, Stochastic d. Deterministic, Stochastic 14. Match the following sets: Part A 1. PERT 2. CPM 3. Events 4. Activities Part B A. Used for projects involving activities of repetitive nature B. Used for projects involving activities of non repetitive in nature in which time estimates are uncertain C. Represent point in time that signifies the completion of some activities and the beginning of new ones D. Represented by arrows and consume time and resources. a. 1A, 2B, 3C, 4D b. 1A, 2D, 3B, 4C c. 1D, 2A, 3B, 4C d. 1B, 2A, 3C, 4D 15. Match the following sets related to the applications of linear programming problems: Part A Part B 1. Finance A. The problem is to determine the quantities of each 2. Production and operations product that should be produced. management B. The problem of the investor could be a portfolio-mix 3. Distribution selection problem. 4. Marketing C. The problem is to determine how many advertisements to place in each medium. D. The problem is to determine the shipping pattern. a. 1D, 2A, 3B, 4C b. 1A, 2D, 3B, 4C c. 1B, 2A, 3D, 4C d. 1B, 2C, 3A, 4D 16. Match the following sets: Part A 1. Saddle point 2. Competitive situations 3. Two person zero sum game 4. Theory of Games and economic behaviour Part B A. Position where Maximin - minimax coincide B. Arise when two or more parties with Conflicting interests operate C. Rectangular game D. Developed by John Von Neuman and

12 a. 1A, 2B, 3C, 4D b. 1A, 2D, 3B, 4C c. 1D, 2A, 3B, 4C d. 1B, 2C, 3A, 4D Morgenstern 17. In a two person zero sum game, the pay-off matrix of A is: Player B B 1 B 2 B 3 Player A A A The pay-off matrix of B is: a. Player B B 1 B 2 B 3 Player A A A b. Player A Player B B 1 B 2 B 3 A A c. Player B Player A A 1 A 2 B B B d. Player B Player A A 1 A 2 B B B Arrival at a telephone booth are considered to be Poisson with an average time of 10 minutes between one arrival and the next. The length of the phone call is assumed to be distributed exponentially with mean 3 minutes. The probability that a person arriving at the booth will have to wait is a. 0.3 b. 0.6 c. 0.9 d Consider the following assignment problem

13 P 1 P 2 P 3 P 4 T T T T Optimum assignment schedule is a. T 1 to P 1, T 2 to P 4, T 3 to P 2, and T 4 to P 3 b. T 1 to P 3, T 2 to P 4, T 3 to P 2, and T 4 to P 1 c. T 1 to P 3, T 2 to P 2, T 3 to P 4, and T 4 to P 1 d. T 1 to P 3, T 2 to P 2, T 3 to P 4, and T 4 to P An activity has an optimistic time of 15 days, a most likely time of 18 days, and a pessimistic time of 27 days. What is its expected time? a. 20 days b. 60 days c. 18 days d. 19 days W 1 W 2 W 3 W 4 F F F For the above Transportation problem, the total cost using Vogel approximation Method is: a. 779/- b. 660/- c. 550/- d. 440/- 22. A branch of city bank has one cashier at its counter. On an average nine customers arrive for every five minutes and the cashier can serve 10 customers in five minutes. Assuming Poisson distribution for arrival rate and exponential distribution for service rate, find i. Average number of customer in the system: a. 1 b. 5 c. 0 d. 9 ii. Average number customer in the queue: i. 1 b. 15 c. 8 d B 1 B 2 B 3 B 4 B 5 A A A A

14 i. The saddle point for the game is a. (2,3) b. (1,5) c. (5,6) d. (4,5) ii. The value of the game is a. 8 b. 1 c. 0 d Match the following sets: Part A 1. Balking 2. Collusion 3. Reneging 4. Jokeying Part B A. Customers Keep on switching over from one queue to another in a multiple service centres. B. Impatient customers who would not wait beyond a certain time and leave the queue. C. Only one person would join the queue, but demand service on behalf of several customers. D. Customers do not join a queue because of their reluctance to wait. a. 1D, 2C, 3B, 4A b. 1D, 2C, 3A, 4B c. 1C, 2D, 3B, 4A d. 1C, 2D, 3A, 4B 25. The ABC manufacturing company can make two products P1 and P2. Each of the products requires time on a cutting machine and a finishing machine. Relevant data are: Product P 1 P 2 Cutting hrs (per unit) 2 1 Finishing hrs (per unit) 3 3 Profit (per unit) Rs.6 Rs.4 Maximum Sales (Unit per 200 week) The number of cutting hours available per week is 390 and number of finishing hours available per week is 810. a. The company should produce i. 120 units of P 1 ii. 150 units of P 1 iii. 160 units of P 1 iv. 180 units of P 1 b. The company should produce i. 150 units of P 2 ii. 180 units of P 2 iii. 190 units of P 2

15 iv. 200 units of P 2 Section-C 10Marks x 2 = 20Marks Answer the following questions. 1. Explain the following a. Monte Carlo simulation Method b. Degeneracy in Transportation problems c. Operating Characteristics and constituents of a Queuing system 2. Solve the following assignment problems. Machine Operators I II III IV V A B C D E Read the following case study and answer the following questions: 20 Marks A project is composed of seven activities whose time estimates are listed. Activity Estimated duration Optimistic Most likely Pessimistic (a) Draw the network (b) Compute the expected project length and variance of the project length 5 Marks x 2 = 10Marks 4. (c) Compute the probability that the project will be completedi. 4 weeks earlier than expected ii. Not more than 4 weeks later than expected (d) If the project due is 19 weeks, what is the probability of meeting the due date. 5 Marks x 2 = 10Marks

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