Master of Business Administration Semester 2 Subject Code: MB0048 Subject: Operations Research Marks: 140 Model Question Paper Part A - 1 marks question ( Question 1 to 40)
Q. No. 1.
When a team of scientists from different disciplines work together for finding the best possible solution in the interest of the organisation as a whole then the solution thus obtained is called ______________________.
2.
a. Feasible solution b. Optimum strategy c. Optimal decision d. Quantitative solution ______________________ has several objective functions, each having a target value. a. Queuing model b. Linear programming c. Goal programming d. Inventory control method
3.
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5.
In linear programming we need to ensure that both the objective function and the constraints can be expressed as linear expressions of _________________. a. Objective function b. Decision variables c. Constraints d. Basic variables Both objective functions and constraints can be expressed as ____________________. a. Linear equalities b. Non-linear equalities c. Linear inequalities d. Non-linear inequalities 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
6.
When a linear programming problem is represented in the canonical form, all constraints are of ________ ________ type. a. = b. ≥ c. ≠ d. ≤
7.
The feasible region has an important property which is called the _________________ of geometry, provided the feasible solution of for the problem exists. a. Non-convexity property b. Convexity property c. Edge-transitive d. Vertex-transitive
8.
The objective function is maximised or minimised at one of the _________________ referred to as optimum solution. a. Vertex b. Extreme points c. Boundary d. Interior point
9.
At least one corner of the region of _______________ will be an optimal solution whenever the maximum or minimum value of z is finite. a. Infeasible solution b. Alternative solution c. Feasible solution d. Unbounded solution
10.
To obtain inequality constraints introduce _________ variables (Si’s) for <= type of constraint. a. Stack b. Surplus c. Slack d. artificial
11.
The new system after adding artificial variable is equivalent to the old system of constraints only if the artificial variables are valued at ________. a. One b. Three c. Two d. Zero
12.
The variables assigned the value zero are called ________________. a. Non-basic variables b. Basic variables c. Surplus variables d. Slack variables
13.
When the primal problem has a degenerate optimal solution, the dual has ________________ solutions. a. Degenerate b. Infeasible c. Unbounded d. Multiple optimal
14.
For long term planning, it is important to know the bounds within which each available resource can vary, without causing drastic changes in the current ______________ solution. a. Non optimal b. Degenerate c. Optimal d. Unbounded
15.
Identify which among the following in the objective function of the primal become constants in the objective function of the dual. a. Constants b. Coefficients c. (≤) type of constraints d. (≥) type of constraints
16.
The unit cost to ship from each source to each destination is written in the ____________________ corner of the cell in the matrix. a. Lower-right-hand b. Lower-left-hand c. Upper-right-hand d. Upper-left-hand
17.
A ___________ is the sequence of cells in the transportation table such that no cell appears more than once in the sequence. a. Loop b. Rim c. Degeneracy d. Transportation problem
18.
Identify in which among the following methods does a row or column difference indicate the minimum unit penalty incurred by failing to make an allocation to the least cost cell in that row or column. a. Matrix minima method b. MODI method c. Vogel’s approximation method d. North-west corner rule
19.
__________________ applies the concept of opportunity costs.
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a. Path-following algorithm b. Criss-cross algorithm c. Assignment algorithm d. Ellipsoid algorithm In infeasible assignment problem _______ value is assigned to the cells.
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a. ∞ b. 1 c. 0 d. -1 If there are three workers in a construction field all with different ability and three tasks are to be completed, then it is an example of _________________. a. Linear programming problem b. Transportation problem c. Balanced assignment problem d. Unbalanced assignment problem
22.
_____________ means that only one person would join the queue, but demand service on behalf of several customers. a. Balking b. Reneging c. Collusion d. Jockeying
23.
____________ 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. Preemptive priority
24.
When the customer arrivals are completely random, the ____________ is followed. a. Deterministic model b. Statistical model c. Poisson distribution d. Probability concept
25.
Because of the random nature of the processes involved, the queuing theory is rather demanding and all models are based on very strong _____________. a. Facts b. Theory c. Assumptions d. Simulation
26.
Average number of customers in the system is represented in queuing system as ______________. a. E(m) b. E(w) c. E(v) d. E(n)
27.
With respect to the notations used in Queuing theory "V" refers to ______________________. a. Service time b. Waiting time in the queue c. Waiting time in the queue + service time d. Waiting time of customers
28.
A _____________ is characterised by the minimum permissible number of customers that it can contain. a. Queue discipline b. Service rate c. Service time d. Queue
29.
The _______________ assumes that arrivals join a queue that is of unlimited size, waiting in line until their turn for service comes on a first-cum-first-serve basis and then enter a service facility consisting of a single channel. a. Waiting line b. LCLS c. Simplest waiting line model d. FSFC
30.
Lending system in a library is an example of ____________________ waiting line. a. Simplest waiting line b. Single facility waiting channel c. Multiple channel d. Parallel facility
31.
A ____________ involves several variables making it impossible to determine the number of trials required to obtain the desired accuracy at a specified confidence level. a. Analytical model b. Quantitative model c. Mathematical model d. Simulation model
32.
Operation starts with an arbitrary ___________ integer called the seed. a. Two digit b. Four digit c. Five digit d. Three digit
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The accuracy associated with simulation improves as the ___________ of the number of trials. a. Thrice b. Twice c. Cube root d. Square root
34.
The technique of Monte Carlo involves the selection of _____________ observations within the simulation model. a. Random b. Discrete c. Sequential d. Indiscrete
35.
The study of complicated systems or sub-systems can be done with the help of _____________. a. Queuing method b. Game theory c. Linear programming method d. Simulation
36.
Simulation has been described as _______________. a. What to do b. Why to do c. What to do when all else fails d. How to do
37.
PERT is basically ____________ method. a. Size-oriented b. Scale-oriented c. Time-oriented d. Time and size oriented
38.
PERT is used for projects involving activities of _____________ nature. a. Continuous b. Non-repetitive c. Repetitive d. Scant
39.
John Von Neuman developed the ___________ in the year 1928. a. Game theory b. Simulation theory c. Queuing theory d. Monte Carlo analysis
40.
In a two-person zero-sum game, if the maximin and the minimax are equal, the game has a _______________ point. a. Equal b. Tip c. Belt d. Saddle
Part B - 2 marks question ( Question 41 to 60) 41.
42.
43.
Consider the below mentioned statements: 1. OR scrutinises the problem from an organisation’s perspective. 2. OR techniques can be used in agriculture to increase agricultural output. State True or False: a. 1-True, 2-true b. 1-False, 2-True c. 1-False, 2-False d. 1-True, 2-False ________________ phase deals with formulation of the problems relative to the objectives. _________________ phase deals with formulation of hypothesis and model. a. Judgement, Research b. Research, Judgement c. Judgement, Action d. Research, Action Consider the below mentioned statements: 1. Parameters appearing in the linear programming model are assumed to be deterministic. 2. To solve large-scale problems using linear programming, break the main problem into several small problems and then solve them separately. State True or False: a. 1-True, 2-True b. 1-False, 2-True c. 1-False, 2-False d. 1-True, 2-False
44.
In 1. 2. 3. 4.
which of the following examples the linear programming technique can be used? In problems where objective functions are linear In distribution problems In getting integer valued solutions In problems where objective functions are non-linear
a. Options 1 & 2 b. Options 1 & 3 c. Options 2 & 3 d. Options 2 & 4 45.
In three-dimensional space and higher, the circles become ____________ and __________________. a. Hyper-spheres, semi-circles b. Spheres, semi-spheres c. Spheres, hyper-spheres d. Hyper-spheres, semi-spheres
46.
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48.
Which of the following statements of theorems are used while solving the linear programming problems graphically? 1. The collection of all feasible solutions to an LPP problem constitutes a convex set whose extreme points correspond to the basic feasible solutions. 2. If the convex set of the feasible solutions of the system of simultaneous equation is a convex polyhedron, then at least one of the extreme points gives an optimal solution. 3. A curve in a two dimensional space is best represented by the parametric equations like x(t) and y(t). 4. Optima of unconstrained problems are found at stationary points, where the first derivative or the gradient of the objective function is zero a. Options 1 & 2 b. Options 2 & 3 c. Options 3 & 4 d. Options 1 & 4 Artificial variables are incor porated into the objective function with ____________________ coefficient M in the minimisation program and __________________ coefficient –M in the maximisation program guaranteeing that the artificial variable takes the zero value in optimal solutions. a. Very small positive, very large negative b. Very large positive, very small negative c. Very large negative, very large positive d. Very large positive, very large negative Consider the below mentioned statements: 1. The Simplex method optimises the objective of maximisation or minimisation with the constraints of the new problem. 2. If a feasible solution is arrived, the optimal value of the new objective function is more than zero. State True or False: a. 1-True, 2-True b. 1-False, 2-True c. 1-False, 2-False d. 1-True, 2-False
49.
State whether the following statements are true or false. 1. For any pair of feasible primal and dual solutions, (objective value in the maximisation problem) ≤ (objective value in the minimisation problem). 2. The dual variables 'yi' that represent the worth per unit of resource 'i' are also called as dual prices, shadow prices and simplex multipliers. a. 1-True, 2-True b. 1-False, 2-True c. 1-False, 2-False d. 1-True, 2-False
50.
51.
Which among the following linear programming’s parameters when changed causes changes in the optimal solution? 1. Objective function coefficient of a non-basic variable 2. Coefficients in the objective function of the primal 3. Objective function coefficient of a non-basic variable 4. Constants in the constraints of the primal a. Statements 1 & 3 b. Statements 2 & 4 c. Statements 1 & 2 d. Statements 3 & 4 The capacity of each source is shown at the __________ of each row, and each destination is written under its corresponding column. These capacities and demands are known as ___________ conditions. a. End, Rim b. End, Loop c. Top, Rim d. Top, Loop
52.
All the values of Δij = Cij - ui - vj should be ___________ or ___________ for the solution to be optimum. a. Non-zero, Negative b. Positive, Negative c. Zero, Positive d. Zero, Negative
53.
The travelling salesman problem is defined as _________________________________. th
a. xijk=∞ if k is directed from city i to city k th b. xijk=0 if k is directed from city i to city j th c. xijk=-1 if k is directed from city j to city k th d. xijk=1 if k is directed from city i to city j 54.
Network scheduling is a technique for ____________ and __________________ of large projects. a. Scheduling, Integrating b. Planning, Scheduling c. Integrating, Implementing d. Planning, Integrating
55.
The number of customers in queue and also those being served in the queue relate to the ____________ efficiency and ______________. a. Facility, Queue length b. Service, Capacity c. Server, Capacity d. Facility, Capacity
56.
A queuing model has which of t he following operating characteristics which enables us to understand and efficiently manage a queue? 1. Queue length 2. Number of customers in system 3. Service facility 4. Capacity a. Option 1 & 4 b. Option 2 & 4 c. Option 2 & 3 d. Option 1 & 2
57.
Service systems are usually classified in terms of their number of _________, or numbers of _____________. a. Queue, Customers b. Channels, Servers c. Servers, Customers d. Channels, Queue
58.
Consider the following statements: 1. H = Average number of units being serviced. 2. L = Average number of units waiting for services. State true or false. a. 1-True, 2-True b. 1-False, 2-True c. 1-False, 2-False d. 1-True, 2-False
59.
The overall efficiency ____________ of the system will increase with the number of service channels_________ provided. a. M , F b. F, M c. H, U d. F, T
60.
A simulation model involves several vari ables making it ____________ to determine th e _____________ required to obtain the desired accuracy at a specified confidence level. a. Impossible, Number of errors b. Impossible, Number of trails c. Possible, Number of trails d. Possible, Number of errors
Part C - 4 marks question ( Question 61 to 75) 61.
A production manager of a m anufacturing organisation is asked to manage and optim ise 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 OR should be used? a. Linear programming b. Inventory control methods c. Transportation model d. Goal programming
62.
63.
Consider the below mentioned statements: 1. The telephone industry is an example where linear programming model can be applied. 2. The user of linear programming technique becomes more subjective and less objective. 3. Linear programming can be used to determine the quantities of each product that should be produced, given the present profit margin on each product. 4. Linear programming can be used to determine the proper mix of media to use in an advertising campaign. State True or False: a. Statements 1, 2 and 4 are true b. Statements 1, 2 and 3 are true c. Statements 2, 3 and 4 are true d. Statements 1, 3 and 4 are true Assume that you are working in a com pany consisting of four departments. T he four departments produce four different but inter-related type of products. The manager feels that all the resources are not utilised properly. Given that the objective is single, you are asked to give a suggestion for maximum utilisation of the resources and overcome all the bottlenecks in an efficient way. Which of the following programming technique will you use to solve the problem? a. Goal programming b. Quadratic programming c. Linear programming d. Non-linear programming
64.
Match the following sets: Part A 1. Multiple optimal solutions 2. Unbounded solution 3. The objective function 4. Well-behaved problems Part B A. When the values of the decision vari ables may be increased indefinitel y without violating any of the constraints B. Represented by a line or a plane C. Have a solution D. When the objective function is parallel to a binding constraint a. 1D, 2A, 3B, 4C b. 1A, 2D, 3B, 4C c. 1B, 2A, 3D, 4C d. 1B, 2C, 3A, 4D
65.
Consider the following statements: 1. In penalty cost method M is eliminated. 2. Whenever artificial variables are part of the initial solution X0, the last row of simplex table will contain the penalty cost M 3. Simplex method is also known as penalty cost method. 4. If the optimal value of the new objective function is zero, it means there is no solution to the problem and the method terminates. State True or False: a. Statements 1, 2 & 3 are true b. Statements 1, 3 & 4 are true c. Statements 1, 3 & 4 are false d. Statements 1, 2 & 3 are false
66.
Write the dual of Min Z = 13x1 + 14x2 Subject to 6x1 + 4x2 ≥ 20 x1 + x2 ≤ 5 x1 ≥ 0 x2 is unrestricted in sign a. Max W = 20y1 + 5y2 Subject to 6y1 - y2 ≤ 13 4y1 - y2 = 14 y1 ≥ 0 y2 is unrestricted in sign b. Max W = 20y1 - 5y2 Subject to 6y1 - y2 ≤ 13 4y1 - y2 = 14 y1 ≥ 0 y2 is unrestricted in sign c. Max W = 20y1 - 5y2 Subject to 6y1 - y2 ≥ 13 4y1 - y2 = 14 y1 ≥ 0 y2 is unrestricted in sign d. Max W = 20y1 - 5y2 Subject to 6y1 - y2 ≤ 13 4y1 - y2 ≥ 14 y1 ≥ 0 y2 is unrestricted in sign
67.
Consider the below mentioned statements: 1. The negative variables are augmented by as many zero-valued variables as it is necessary to complete m+n-1 basic variables. 2. The extremely small value ε is infinitely small and it never affects the value it is added to or subtracted from. 3. The selected zero valued variables are designated by allocating an extremely small positive value ε to each one of them. 4. Introduce 'ε' in unallocated minimum cost cell to avoid forming a loop. State True or False: a. Statements 1, 2 and 4 are true, 3 is false b. Statements 1, 2 and 3 are true, 4 is false c. Statements 2, 3 and 4 are true, 1 is false d. Statement 1, 3 and 4 are true, 2 is false
68.
Consider the following statements and state true or false according to a typical network problem. 1. It involves finding route from one node to another between which alternative paths are available at various stages of the journey. 2. It should select the route that yields minimum cost. 3. A number of different constraints may be placed on acceptable routes for instance, not returning to the node passed or passing through each node just once. 4. A sales person can travel to only one city. State True or False: a. Statements 1, 2 & 3 are true b. Statements 1, 3 & 4 are true c. Statements 1, 3 & 4 are false d. Statements 1, 2 & 3 are false
69.
Match the following sets: Part A 1. Service facility 2. Queuing system 3. Multiple 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. Customer status D. Series or parallel a. 1D, 2A, 3B, 4C b. 1A, 2D, 3B, 4C c. 1B, 2A, 3D, 4C d. 1B, 2C, 3A, 4D
70.
The Airline ticket counter is manned by a single clerk, who takes an average of 5 minutes to issue ticket. The customers arrive once in every 8 minutes on an average. One hour of customer is valued at Rs. 15 and the c lerk’s time is valued at Rs. 4 per hour. What is the average hourly queuing system costs associated with the ticket counter? a. Rs 30 b. Rs 25 c. Rs 28 d. Rs 29
71.
An electrical repairman finds that the time spent on his jobs has an exponentia l distribution with a m ean of 30 minutes. If he repairs electrical items in the order in which they came in and if the arrival of items follow a Poisson distribution with an average rate of 10 per 8 hour day, what is the repairman’s expected idle time each day? How many jobs are ahead of the average set just brought in? a. 3 hours, 3 electrical items b. 2 hours, 3 electrical items c. 1 hours, 2 electrical items d. 3 hours, 2 electrical items
72.
Match the following sets: Part A 1. W 2. U 3. H 4. L Part B A. Average number of units being ser viced B. Average waiting time C. Average running time D. Average number of units waiting for services a. 1D, 2A, 3B, 4C b. 1A, 2D, 3B, 4C c. 1A, 2B, 3C, 4D d. 1B, 2C, 3A, 4D
73.
Mr Raghu is a Mechanic and owns a garage "Bike Junction". He gives appointments to customers every half an hour. However, he does not know the nature of problems of automobiles arriving at his Garage. From past records, he has the following probability distribution and also knows the exact repair timings. He starts his garage at 8.00 A.M. Using the following inf ormation determine the aver age waiting time of the custom ers and idle time of the Mechanic. Random Numbers 56, 40, 26, 66, 87, 48, 17, 22, 04, 15. Table shows probability distribution in past record. Nature of repair Wash Oil change Boring Puncture Service
Probability 0.10 0.30 0.15 0.30 0.15
Time taken for treatment (min) 50 15 40 15 30
a. 1 minutes, 15 minutes b. 2 minutes, 25 minutes c. 3 minutes, 35 minutes d. 4 minutes, 45 minutes 74.
Consider the below mentioned statements: a) Randomness is a key requirement of Monte-Carlo simulation. b) Monte-Carlo simulation involves modelling a deterministic system. c) Simulation is a statistical experiment as such its results are subject to statistical error. d) In Monte-Carlo simulation, a problem is solved by simulating the original data with random number generators. State True or False: a. Statements 1, 2, 3 and 4 are false
75.
b. Statements 1, 2, 3 and 4 are true c. Statements 2, 3 and 4 are true, Statement 1 is false d. Only statement 2 is true Match the following sets: Part A 1. PERT 2. CPM 3. Events 4. Activities Part B A. Construction project B. R & D work. C. Point in time D. Represented by arrows a. b. c. d.
1A, 2B, 3C, 4D 1B, 2A, 3B, 4C 1D, 2A, 3B, 4C 1B, 2C, 3A, 4D
