quantitative techniques for managerial applications

8/11/2019 Quantitative Techniques for Managerial Applications

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1

For EOQ under planned shortages model, what relationship between

various cost components exists:

A ) Ordering Cost + Back Ordering Cost = Holding Cost

B ) Ordering Cost = Holding Cost + Back Ordering Cost

C ) Ordering Cost = Holding Cost – Back Ordering Cost

D ) None of these

2

From the following statements relating to classical EOQ mode, mark

the incorrect one:

A ) Total Ordering Cost = Total Holding Cost

B ) Total Relevant Cost = (2 DAh )

C ) If annual demand doubles with all other parameters remaining constant, the EOQ is doubled

D ) The lead-time is constant

3 Mark the wrong statement

A ) Inventory cycle is the time-period occurring between successive procurement actions

B ) Shortage cost is the penalty incurred for being unable to meet a demand as it occursC ) Lead-time is the elapsed time between the initiation of an order and the receipt of replenishme

D ) Among all models, the EOQ, with similar inputs, under classical model is the minimum


A ) In general, when back-ordering cost is small, orders are made less often but of higher quantity

B ) When back-ordering cost becomes infinite, the EOQ formula for the planned shortages model

C ) In planned shortages model, it is possible for re-order point to be a negative value.

D ) Like in classical EOQ model, the maximum stock level under back-ordering model is equal to

5 Which of the following is not an assumption underlying classical EOQ model?

A ) The annual demand is constant and uniform

B ) Shortages are not permitted at all

C ) The lead-time is zero

D ) The holding cost per unit per year is constant


A ) If ordering cost/order and holding cost/unit are both doubled, it would double the quantity un

B ) If ordering cost/order and holding cost/unit were both doubled, it would leave the order

C ) If the annual demand increases by 20%, ordering cost reduces by 20% and holding cost increa

D ) In classical model, if lead-time = 8 working days and demand = 24 units a day, the re-order le

7 Which of the following is not true?

A ) In deterministic inventory models, Re-order level = Demand during lead time (DDLT)

B ) In cases where demand is probabilistic, ROL = Expected DDLT + Safety Stock

C ) Greater the variation in demand and/or lead-time, greater the amount of safety stock needed

D ) Safety stock is the total stock kept to meet the demand during lead-time



8

If DDLT is known to be distributed normally with a variance of 6400,

then a safety stock of 160 units will yield approximately what level of

service?

A ) 48%

B ) 98%

C ) 2%

D ) 52%

9 For a 25% increase in order quantity (under classical EOQ model) the total relevant cost woul

A ) Decrease by 2.5%

B ) Decrease by 0.25%

C ) Increase by 2.5%

D ) Increase by 1.025%


A ) The division of items into A, B and C categories is accomplished by plotting the usage value

B ) FNSD analysis represents the speed classification of itemsC ) XYZ analysis is based on the classification of items according to their unit cost

D ) SOS is the classification as seasonal and off-seasonal, done with the aim of determining prope

11 Choose the incorrect statement

A ) Sequencing problems involve mainly jobs in a manufacturing plant

B ) Sequencing problems arise when we deal with situations where there is a choice of the order i

C ) In fairness, all the jobs must be done on a first-come-first served basis

D ) Maintenance scheduling problems are also solved as sequencing problems

12 Which of the following assumptions is not true about sequencing problems?

A ) The processing times on different machines are independent of the order in which jobs are pro

B ) First all the jobs are completed on the first machine and then their processing starts on t

C ) A job once started would be performed to the point of completion uninterrupted

D ) A machine cannot process more than one job at a time

13 Mark the correct statement:

A ) A sequencing problem involving 5 jobs on 2 machines can be handled in 120 ways

B ) A sequencing problem involving 5 jobs and 3 machines requires evaluation of 555 = 125 s

C ) Sequencing is no problem because the total processing time for all jobs would be equal irresp

D ) Solution to a sequencing problem is found in such a manner that none of the machines is idle


A ) Sequencing problems, big or small, can be conveniently handled using Gantt charts

B ) Gantt charts have a limitation that it is not possible to find total elapsed time with them

C ) A total of 40,320 Gantt charts need to be prepared for an 8-job sequencing problem

D ) The optimal sequence is one where jobs are processed on first-come-first served basis


A ) In an n- job 2-machine sequencing problem, it is necessary that each of the jobs have to be pro



B ) In solving a sequencing problem, the objective is to determine the sequence in which the

C ) The optimal sequence in a 2-machine problem minimises the idle time on the machine on whi

D ) The optimal solution for a problem using Gantt chart and the algorithm would be the same

16 In terms of the Johnson’s Rule, optimal sequence is obtained by the following rule

A ) Job j precedes job j +1 if Min (A j , B j +1) < Min (A j +1, B j )

B ) Job j precedes job j +1 if Min ( A j , B j +1) > Min ( A j +1, B j )

C ) Job j succeeds job j +1 if Min ( A j , B j +1) < Min ( A j +1, B j )

D ) None of the above.

17 Which of the following is not correct about n -job 2-machine (A and B) sequencing problem i

A ) If minimum time of a job is on machine A, then do that job first

B ) If minimum time of a job is on machine B, then do that job in the end

C ) If there is a tie in the minimum times of two jobs: job 5 is on machine B and job 7 on ma

D ) If there is a tie in the timings of 2 or more jobs on machine B, then do them in any order in th

18 Four jobs are to be processed on two machines A and B in the order AB. The timings of the jo A ) 2, 4, 3, 1

B ) 4, 2, 1, 3

C ) 4, 1, 3, 2

D ) 2, 3, 1, 4

19 Which of the following conditions should be satisfied in order that an n- job 3-machine proble

A ) 1 only

B ) 1 and 3

C ) 1 or 3 or both

D ) 2 or 3 or both

20 Consider the following conditions for solving sequencing problems requiring processing of n

A ) Condition 1 only

B ) Condition 2 only

C ) Conditions 1 and 2 both

D ) Conditions either 1 or 2 or both

21 Choose the incorrect statement

A ) Sequencing problems involve mainly jobs in a manufacturing plant

B ) Sequencing problems arise when we deal with situations where there is a choice of the order iC ) In fairness, all the jobs must be done on a first-come-first served basis

D ) Maintenance scheduling problems are also solved as sequencing problems

22 Which of the following assumptions is not true about sequencing problems?

A ) The processing times on different machines are independent of the order in which jobs are pro

B ) First all the jobs are completed on the first machine and then their processing starts on t

C ) A job once started would be performed to the point of completion uninterrupted

D ) A machine cannot process more than one job at a time




A ) A sequencing problem involving 5 jobs on 2 machines can be handled in 120 ways

B ) A sequencing problem involving 5 jobs and 3 machines requires evaluation of 555 = 125 s

C ) Sequencing is no problem because the total processing time for all jobs would be equal irresp

D ) Solution to a sequencing problem is found in such a manner that none of the machines is idle


A ) Sequencing problems, big or small, can be conveniently handled using Gantt charts

B ) Gantt charts have a limitation that it is not possible to find total elapsed time with them

C ) A total of 40,320 Gantt charts need to be prepared for an 8-job sequencing problem

D ) The optimal sequence is one where jobs are processed on first-come-first served basis


A ) In an n- job 2-machine sequencing problem, it is necessary that each of the jobs have to be pro

B ) In solving a sequencing problem, the objective is to determine the sequence in which the

C ) The optimal sequence in a 2-machine problem minimises the idle time on the machine on whi

D ) The optimal solution for a problem using Gantt chart and the algorithm would be the same

26 In terms of the Johnson’s Rule, optimal sequence is obtained by the following rule

A ) Job j precedes job j +1 if Min (A j , B j +1) < Min (A j +1, B j )

B ) Job j precedes job j +1 if Min ( A j , B j +1) > Min ( A j +1, B j )

C ) Job j succeeds job j +1 if Min ( A j , B j +1) < Min ( A j +1, B j )

D ) None of the above

27 Which of the following is not correct about n -job 2-machine (A and B) sequencing problem i

A )If minimum time of a job is on machine A, then do that job firstB ) If minimum time of a job is on machine B, then do that job in the end

C ) If there is a tie in the minimum times of two jobs: job 5 is on machine B and job 7 on ma

D ) If there is a tie in the timings of 2 or more jobs on machine B, then do them in any order in th


A ) If one player has 2 strategies available to him while the other has more than 2, they are sure to

B ) In mixed strategies, the value of game for both the players need not be the same

C ) If the optimal policy for A is found to be (8/13, 5/13) it implies that in long run games, h

D ) If the optimal solution to a game results in pure strategies, it implies that it has no saddle poin

29 The given payoff matrix of a game is transposed. Which of the following does not happen? A ) The game value changes

B ) The saddle point changes

C ) A has as many strategies as B had, and B has as many strategies as A had

D ) The optimal strategies of the players do not change

30 For a two-person game where A and B are, respectively, the minimising and maximising play

A ) Maximax for A and minimin for B



B ) Maximin for A and minimax for B

C ) Minimax for A and maximin for B

D ) Minimin for A and maximax for B

31 Mark the wrong statement:

A ) The solution to a game by graphic method may or may not be same as obtained by analy

B ) Any two-player game can be formulated and solved as an LPPC ) The players have to play mixed strategies when saddle point to a game does not exist

D ) If the value of the game = 0, the game is said to be favouring none of the players


A ) If each of the payoffs for a column strategy is equal to or greater than the correspondin

B ) The game has a saddle point if the payoffs associated with maximin and minimax strategies a

C ) A game can have multiple saddle points

D ) The game value can be positive, negative or zero


A ) A game is said to be fair if each of the players has equal number of strategies

B ) The value of the game can be determined only if the game has a saddle point

C ) Player A is said to dominate the other if he has more strategies to play

D ) A game favours minimising player B if it has negative value.

34 In a 2-person game having saddle point, player B is the minimising player. B has 3 strategies

A ) 21

B ) 6

C ) 8

D ) Cannot be determined from the given information

35 In a 2-player game having a saddle point, A is the maximising player with three strategies.

A ) A1

B ) A2

C ) A3

D ) Is not determinable from the given information

36 A constant K is added to each element of a pay-off matrix related to a game. What effect will

A ) The optimal strategies of the players and the value of the game remain unchanged

B ) The optimal strategies of the players do not change while the value of the game will incr

C ) The optimal strategies of the players as well as game value will all change

D ) Nothing sure can be said about it

37 Mark the wrong statement.

A ) Moving forward from the first stage to the last is the final step in dynamic programming probl

B ) In an investment problem, addition of a new investment proposal adds a new state

C ) In dynamic programming, it is possible to get second-best solution as well as the best (optima

D ) f n*( s n ) represents the optimal pay-off at stage n , for state s n .




A ) The recursive relationship establishes relationship between different states

B ) Creation of a recursive relationship is an integral part of the formulation of a dynamic progra

C ) A recursive relationship identifies the optimal policy for stage n , given that optimal policy fo

D ) In dynamic programming, it is possible to develop a recursive relationship for every problem.


A ) States of a given stage represent the possible conditions in which the system might be in that

B ) A probabilistic dynamic programming problem is so called because states of various sta

C ) Given the current state, the optimal policy for the remaining stages does not depend on the pol

D ) The optimal immediate decision depends only on the current state, and not how we got there.


A ) Dynamic programming may be deterministic or probabilistic

B ) In a dynamic programming problem, the state at the next stage is determined by the state and

C ) In a probabilistic dynamic programming problem, the next stage is not sure and there is

D ) In probabilistic dynamic programming problems, the optimal policy at a given stage is based


A ) The effect of a policy decision at each stage is to transform the current state to a state as

B ) Determination of optimal policy at a given state requires calculation of immediate and total pa

C ) The best of all the (total) pay-offs in respect of different states of a stage is known as the opti

D ) Optimal policy for the entire problem consists of determining optimal policy at each stage for


A ) Dynamic programming problems require making a sequence of interrelated decisions

B ) A state represents a decision pointC ) Depending upon the variable of interest, the solution to a dynamic programming problem call

D ) Pay-off is also called the reward

43 Mark the incorrect statement

A ) Dynamic programming cannot be used for solving problems that call for distributing sc

B ) Dynamic programming calls for dissecting a problem into a sequence of sub-problems

C ) Dynamic programming provides a generalised approach to problem solving

D ) Dynamic programming provides a multi-stage approach to solving problems.

44Mark the correct statement

A ) Sub-problems of a given problem are called variables

B ) In dynamic programming, solution to each sub-problem is obtained independently

C ) Dynamic programming calls for standard mathematical formulation of a problem

D ) Dynamic programming provides for a systematic procedure for determining optimal co


A ) Dynamic programming is a technique that can be used to solve any complex problem

B ) Dynamic programming uses a set of well-defined rules for solving all problems



C ) Dynamic programming divides a problem into a number of decision stages

D ) Dynamic programming deals only with deterministic decision-making problems.

46 Choose the correct alternative - The first step in dynamic programming is to

A ) Define the nodes.

B ) Determine the optimal policy

C ) Define the recursive relationship.D ) Divide the given problem in to stages.

47 One can increase the chance that results of simulation are not erroneous by

A ) changing the input parameters

B ) using discrete probability distributions and not continuous

C ) validating the simulation

D ) all of the above


A ) Simulation cannot be used where mathematical methods can be used

B ) Solutions to decision problems by using simulation would be identical to those using mathem

C ) Simulation is descriptive in nature

D ) One drawback of using simulation is that it is only applicable where all quantities are determi

49 Which of the following statements is not true?

A ) In Monte Carlo simulation, a problem is solved by simulating the original data with random n

B ) A random number generator is a procedure or device to obtain random numbers

C ) In a series of random numbers, different digits appear in a definite, ordered fashion

D ) Random numbers generated by mid-square method are called pseudo-random numbers

50 Mark the wrong statement: A ) For a deterministic model, a single simulation run is sufficient

B ) Probabilistic simulation is like random sampling whose output is subject to statistical error.

C ) Monte Carlo simulation involves modelling a deterministic system

D ) Randomness is a key requirement of Monte Carlo simulation


A ) During the course of a simulation, the model mimics the important elements of what is being

B ) A simulation model can never be physical.

C ) The model for simulation must be so designed that it would enable evaluation of the key decis

D ) In a mathematical model, mathematical symbols or equations are used to represent system rel


A ) A clear statement of the problem facilitates the development of an appropriate model

B ) Simulation aims to determine how the system under consideration would behave under certai

C ) The scope and level of detail of simulation should be decided upon carefully

D ) The output of a simulation model is independent of the size of simulation run

53 Which of the following is not true about simulation?



A ) It is a very effective substitute for hunch and intuition in decision-making

B ) It is an optimising technique

C ) It seeks to determine how the system under consideration would behave in certain conditions

D ) It is effectively used in decision-making situations that cannot be handled with mathematical

54 Which of the following is not a phase of simulation process?

A ) Definition of the problem and statement of objectivesB ) Construction of an appropriate model

C ) Experimentation in real life situations

D ) Performing experiments on the model evolved


A ) To simulate means to imitate a system

B ) Simulation involves developing a model of some real phenomenon and then experimenting o

C ) Simulation is a powerful mathematical modelling tool.

D ) Simulation is very beneficial since results of taking a particular course of action can be estima

56 A company has sold 5000 and 7000 units in two consecutive years and incurred a loss of Rs 1

A ) 9000 units

B ) 8000 units.

C ) 9500 units

D ) 10,000 units.

57 BEP is that level of production at which

A ) total revenue is equal to total cost

B ) there is no profit, no loss

C ) total contribution is just sufficient to recover the total fixed cost

D ) tll of the above

58 Margin of safety is

A ) the excess of actual sales over break-even sales.

B ) the excess of sales over total cost

C ) the excess of selling price per unit over fixed cost per unit

D ) the excess of total sales over total variable cost

59 P/V ratio is the ratio of

A ) profit to value of goods sold.

B ) profit to number of units soldC ) contribution margin to sales.

D ) sales to contribution margin

60 Contribution margin refers to

A ) The excess of selling price over unit total cost.

B ) The excess of selling price over unit fixed cost.

C ) The excess of selling price over unit variable cost.

D ) None of the above.



61 IRR method is considered to be inferior to the NPV method because

A ) it is relatively more difficult to compute.

B ) it may give multiple rates of return.

C ) the underlying assumption of varying reinvestment rates is unrealistic.

D ) all of above.

62 Simulation approach to evaluate risky investments

A ) tests the impact of changes in factors affecting investments on investment decisions.

B ) identifies various factors affecting cash flows and their probability distributions to com

C ) increases the required rate of return to be used for discounting so as to compensate for risk in

D ) computes the period within which entire investment cost would be recovered.

63 The present value of an annuity of Rs 1356 to be received for 11 years is Rs 9227.85. The dis

A ) 9%

B ) 10%

C ) 11%

D ) 7%

64 Following is not a method of evaluating an investment proposal under uncertainty.

A ) Discounted cash flow technique.

B ) Certainty equivalent approach.

C ) Simulation.

D ) Statistical distribution approach.

65 Discounting of cash flows is a technique to

A ) find discount offered in a deal.

B ) compute present value of a (series of) future payment(s).C ) compute compounded value of a stream of cash flows.

D ) none of the above.


A ) In time-series data, fitting trend line to the given data makes future projections.

B ) Regression analysis deals with making forecasts about one or more dependent variables

C ) Explained variation is that component of total variation which is explained by the line of relat

D ) The ratio of explained variation to total variation is called co-efficient of determination.

67Mark the wrong statement.

A ) MAD is equal to summation of forecast errors divided by n , where forecast error is the

B ) If choice between two values of smoothing constant (a) is to be made, the one with lower MA

C ) Mean squared error is the average of the squared differences between the actual and forecaste

D ) MAPE is the mean of absolute differences between actual and forecasted values, expressed as

68 Which of these is not correct?

A ) In exponential smoothing, current forecast is obtained by adjusting the previous forecast by a

B ) Forecast error = Forecasted value – Actual value



C ) A high value of a gives relatively large weightage to recent value while a low value gives rela

D ) The weights used in exponential smoothing are a + a(1 - a) + a(1 - a)2 + …

69 Which of these is not correct about exponential smoothing?

A ) In this technique of forecasting, the forecasted value for a period is calculated as the weighted

B ) Successive weightage of preceding time periods are declining.

C ) a is called the smoothing constant.D ) Summation of weights is equal to 1 if is low (less than 0.5) and more than 1 if is high

70 Mark the correct statement

A ) An n -period simple moving average gives a weightage of 1/n to each value included in t

B ) Weighted moving average gives equal weightage to the various values under consideration

C ) For a given time-series set of data, the weighted average values would be consistently higher t

D ) In the 3-month moving average, the first forecast would be for the month 2 and calculated as s

71 Which of the following is not true about time-series?

A ) It refers to time-based data.B ) It consists of four components: secular trend, seasonal variations, cyclical variations and rand

C ) Forecasting with it implies that predictions about the future values are made only from past da

D ) It can be broken down into explained and unexplained variations


A ) Delphi method is an iterative group process that employs a group of experts

B ) In Delphi method of forecasting, the experts are usually not known to each other

C ) Exponential smoothing is a time-series model of forecasting.

D ) Time-series models are so called since they make possible forecasting at regular interval


A ) Qualitative forecasting is always better than quantitative forecasting.

B ) Delphi method is a method of qualitative forecasting.

C ) Quantitative forecasting methods are objective in nature.

D ) Consumer panels are used by marketing research methods

74 Which of these is not true about time series models of forecasting?

A ) They attempt to predict the future on the basis of historical data.

B ) They hold the future to be a continuum of the past.

C ) They are based on the premise that what would happen in future is a function of what has hap

D ) They are based on the past, present, and future conditions.

75 Mark the correct statement.

A ) Since future is uncertain, forecasting has absolutely no useful role.

B ) Qualitative models of forecasting make no use of numbers at any stage.

C ) Qualitative models employ personal judgement and involve qualities like intuition and j

D ) Delphi method is illustrative of quantitative models.

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nt stock

becomes the same as that of the classical model

the order quantity

er classical EOQ model

quantity under classical EOQ model unchanged

ses by 50%, it would reduce the order quantity by 20%.

el = 192 units



d

f items to obtain Pareto curve

r procurement strategies

which given tasks can be done

cessed on them

he second machine

quences

ctive of the order in which they are processed due to given processing times that do not change

at any time

cessed on the two-machines in the same order



jobs may be performed so that the total elapsed time is maximised

ch the jobs are performed later

which the order of processing is A-B?

chine A, then the jobs can be scheduled as (5, 7) in the beginning, or (7, 5) in the end

last

bs are known to be: (11, 9), (7, 18), (12, 16), and (3, 10). The optimal sequence would be:

m may be solved using algorithm?(1) Min A i Max B i (2) Min A i Max B i (3) Min C i

jobs on k machines in the order A, B, C,…K.(1)Min A i Max B i , Max C i …and Max J i (2)

which given tasks can be done

cessed on them

he second machine



quences

ctive of the order in which they are processed due to given processing times that do not change

at any time

cessed on the two-machines in the same order

jobs may be performed so that the total elapsed time is maximised

ch the jobs are performed later

which the order of processing is A-B?

chine A, then the jobs can be scheduled as (5, 7) in the beginning, or (7, 5) in the end

last

play mixed strategies

e would play the first strategy and the second strategy at random in the ratio 8:5

.

ers, the optimal strategies are



tic method

payoff of another column strategy, the former is said to dominate the latter

e the same

vailable to him: b1, b2 and b3. For each of these it is known that: b1 : lowest payoff – 2 highest

The three A1: -8 to 12strategies have payoffs ranging as follows: A2: 6 to 18 A3: 2 to 21 The op

it have on the solution?

ase by K.

em solution

) solution



tical models

istic

mber generators

imulated

ion alternatives

tionships

conditions



ethods

it

ted prior to its implementation in real world.

0,000 in the first year and Rs 5000 in the second year. The selling price per unit is Rs 100. What



ute estimated returns

olved.

ount factor used is:

on the basis of one or more independent variables

onship.

xcess of actual value over forecast value

D should be preferred

values

a percentage of the actual values

raction of the forecast error



tively low weightage.

average of all the previous values

(more than 0.5)

e average.

han simple moving average values

imple average of months 1, 2 and 3

m variations.

ta

of time

ened in the past.

dgement



ax B i

in K i Max B i , Max C i …and Max J i What is the requirement for applying the algorithm?



ayoff – 21 b2 : lowest payoff – -7 highest payoff – 14 b3 : lowest payoff – 6 highest payoff – 8

imal strategy for A is



s the BEP?



hat is the payoff associated with the optimal strategy of B?

quantitative techniques for managerial applications

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