Important Questions of AOR

7/31/2019 Important Questions of AOR

1/26

Give any four definitions of OR.

Ans. Operation Research:

1. OR is an aid for the executive in making decisions by providing him with the quantitative information,based on the scientific method analysis.

2. OR is the art of giving bad answers to problems, to which, otherwise worse answers are given. 3. OR is the art of wining wars without actually fighting them.

4. OR is the application of scientific methods by interdisciplinary teams to problems involving the controlof organised (man-machine) systems so as to provide solutions which best serve the purpose of theorganisation as a whole.

Comment the following statement.

(i) OR is the art of wining war without actually fighting it.

(ii) OR is the art of finding bad answer where worse exists.

Ans. (i) An art of wining war without actually fighting it -During world war-TI, the military managementin U K and U S A engaged mterdisciplmary teams of scientists to study the strategic and tacticalproblems of military operations. The objective was to find out the most effective allocation of limitedmilitary resources to the various military operations. The OR teams were not actually engaged in militaryoperations and in fighting the war. But they were only advisors and significantly instrumental in winingthe war. Hence OR can be associated with an art of wining war without actually fighting it.

(ii) An art of finding bad answer where worst exist For the use of techniques of OR, a mathematicalmodel of the problem is to be formulated This model is actually a simplified representation of theproblems in which only the most important features are considered for reason of simplicity. Then anoptimal or most favourable solution is found. Since the model is an idealized instead of exactrepresentation of real problem, the optimal solution thus obtained may not prove to be the bestsolution to the actual problem. Although, we may not get the best answers but definitely we are able tofind the bad answer where worst exist. Thus operation research techniques are always able to save usfrom worse situation of practical life.

What is an OR Model? What are the characteristics of OR Model?

Ans. A model is defined as idealized representation of the real life situation. It represents one or fewaspects of reality.

Characteristics of OR

1. The number of simplifying assumption should be as few as possible.

2. Model should be simple but close to reality.

3. It should be adaptable to parametric type of treatment.

4. It should be easy and economical to construct.

Give the main advantage and limitation of OR model.

Ans. Advantage

1 It provides a logical and systematic approach to the problem.

2. It indicates the scope .as well as limitation of a problem.


2/26

3. It makes the overall structure of the problem more comprehensible and helps in dealing with problemin its entirety.

Limitations Models are only idealised representation Of reality and should not be regarded asabsolute in any case.The validity of a model for a particular situation can be ascertained only byconducting experiments on it.

Distinguish between:

(i) Iconic or Physical Model and Analogue or schematic model.

(ii) Deterministic and Probabilistic model.

Ans. (i) Iconic Model It represent the system by enlarging or reducing the size on some scale. In otherwords it is an image. Example-toy airplane, photographs, drawings, maps etc.

Schematic Model The models, in which one set of properties is used to represent, another set of properties are called schematic or analogue models. For example-graphs used to show differentquantities.

(ii) Deterministic model Such models assume conditions of complete certainty and perfect knowledge.Example- LPP, transportation, assignment etc.

Probabilistic (or stochastic) Model These type of models usually handle such situation in which theconsequences or payoff of managerial actions cannot be predicted with certainty. However it is possibleto forecast a pattern of events, based on which managerial decision can be made. For exampleinsurance companies are willing to insure against risk of fire, accident, sickness and so on. Here thepatterns of events have been compiled in the form of probability distribution.

What is the objective of operation Research?

Ans. The objective of OR is to provide a scientific basis to the managers of an organisation for solvingproblems involving interaction of the components of the system, by employing a system approach by ateam of scientists drawn from different disciplines, for finding a solution which is in the best interest of the organisation as a whole.

List the characteristics of operation research.

Ans. 1. System Orientation 2. Use of interdisciplinary teams 3. Application of Scientific methods

4. Uncovering of new problems 5. Improvement in the quality of decisions 6. Use of computer

7. Quantitative solutions 8. Human factors

Write a short note on Heuristic Programming?

Ans. Heuristic programming uses rules of thumb or intuitive rule to find the problem solution. Thuschecking all the alternatives so as to obtain the optimum one, is not required. They bridge the gapbetween strictly analytical formulation and operating principles which manager are habitual to use. Theyinvolve step by step search towards the optimal solution when a problem cannot be expressed inmathematical programming form. It does not provide optimum solution but very near to it.

What are the various phases of operation research problems? OR

Explain the methodology of operation research Or

Explain the steps involved in the solution of OR Problem.

Ans. Operation research is based on scientific methodology which proceeds as:


3/26

1. Formulating the problem.

2 Constructing a model to represent the system under study

3. Deriving a solution from the model.

4. Testing the model and the solution derivq4 from it.

5. Establishing controls over the solution.

6. Putting the solution to work i.e. implementation.

(i) Assignment of job to machine (ii) Product mix (iii) Advertising media selection (iv) Transportation.

2. Dynamic programming

(i) Capital budgeting (ii) Employment smoothening (iii) Cargo loading. 3. Inventory control

(i) Economic order quantity

What is the importance of OR in decision making?

Ans. 1. Better control 2. Better coordination 3. Better system 4. Better decision

Explain briefly the applications of operation research. Or

Explain the scope of operation research. Or

What are the areas of applications of OR.

Ans . Applications Operation research at present finds extensive application in industry, business,government, military and agriculture. Wide variety of. Industries namely airlines, automobile,transportation, petroleum, coal, chemical, mining, paper, communication, computer, electronics etc.have made extensive use of OR techniques.

Applications of Various OR Techniques:

1. Linear programming

(ii) Safety stocks

(iii) Reorder level,

4. Queuing theory

(i) Traffic congestion

(ii) Repair and maintenance of broken down rn/c.

(iii) Hospital operations etc.

5. Network techniques

(i) Planning, scheduling and controlling of construction of dams, bridges, roads, highways etc.

6Replacement theory

(i) Optimum replacement interval of items.

(ii) Staff replacement and recruitment. Scope and areas of applications:

1. Agriculture 2. Finance 3. Industry 4. Marketing 5. Personal Management 6. Production Management

7. L.I.C. schemes 8. Research and Development 9. Allocation and Distribution


4/26

What are the limitations of using results from a mathematical model to make decisions aboutoperations. Or

What are the limitations of operation research?

Ans. 1. Mathematical models, do not take into account qualitative factors or emotional factors whichare quite real. All influencing factors which cannot be quantified find no place in mathematical models.

2 Mathematical models are applicable to only specific categories of problems

3. Present day problems involve numerous factors; expressing them in quantity and establishingrelations among them require huge calculation

4. Management, who has to implement the advised proposals, may itself offer a lot of resistance due toconventional thinking

What are the advantages of using results from the mathematical model to make decision aboutoperations?

Ans. The mathematical models provides the management a quantitative basis for

decision making. For example it will give answer like, The cast to the company, if decision A is taken isX, if decision B is taken is Y, etc

Hence it improve the quality of decision making.

It provide a way to represent the reality in the mathematical from.

It highlights the bottlenecks in production system.

Define LPP.

Ans. A problem consists of a linear function of variable called objective function subject to set of linearequation or inequalities called constraints are known as linear programming problem.

Why LP models are called deterministic in nature.

Ans. (i) In LP model the various parameters namely the objective function coefficients, R.H.S,coefficients of the constraints and resource values are certainly known and their value do not changewith time. Thus the profit or cost per unit of product, availability of labour and material, market demandis known with certainty.

Thats why it is called deterministic in nature.

. What are the assumptions of Linear programming Models?

Ans. 1. Proportionality 2. Additivity 3. Continuity 4. Certainty.

Q. 2.4. Enumerate few application of linear programming.

Ans. Industrial Applications

1. Product Mix problem 2. Blending problem 3. Production Scheduling problem 4. Trim loss problem

5. Sub contract problem.

Management Problems

1. Media selection problem 2. Transportation problem 3. Assignment problem 4. Man power schedulingproblem

Agricultural Applications


5/26

Military Applications.

What are the advantages and limitations of linear programming methods?

Ans. Advantages

1. It helps in attaining the optimum use of productive factors.

2. It improves the quality of decisions. The individual who makes use of linear programming methodsbecomes more objective than subjective.

3. It also helps in providing better tools for adjustment to meet changing conditions.

4. It highlights the bottlenecks in the production processes.

5. Most business problems involve constraints like raw materials availability, market demand etc. whichmust be taken into consideration. Just we can produce so many units of product does not mean thatthey can be sold. Linear programming can handle such situation also.

Limitations

1. In some problems objective functions and constraints are not linear. LPP under non linear condition

usually results in an incorrect soIution

2. LPP deals with problems that have a single objective. Real life problem may involve multipleobjectives.

3. Parameters appearing in the model are assumed to be constant. But in real life situation they areneither constant nor deterministic.

4. It is applicable to only static situations since it does not take into account the effect of time.

5. LPP can not be used efficiently for large scale problems, the computational difficulties are enormous,even when the large digital computer is available.

6. LPP may get fractional valued answers for the decision variables, whereas it may happen that only

integer values of the variable are logical. . Define:

(i) Solution to LPP (ii) Feasible solution (iii) Basic solution (iv) Basic feasible solution (v) Optimumbasic feasible solution (vi) Unbounded Solution.

Ans. (i) Solution to LPP- A set of variable *x1x2,....x,J is called a solution to LI?

if it satisfy the given constraints

(ii) Feasible solution A set of variable is called a feasible solution to LPP if it satisfy the given constraintsas well as non negativity restrictions

(iii) Basic solution-A solution obtained by setting any n variables equal to zero and solving for remainingm variables is called basic solution

(iv) Basic feasible solution-It is a basic solution that also satisfies the non negativity restrictions.

(v) Optimum basic feasible solution It is the basic feasible solution that also optimize the objectivefunction.

(vi) Unbounded solution-If the value of the objective function can be increased or decreased indefinitelythe solution is called unbounded solution


6/26

What is redundant constraint?

Ans A constraint, which does not affect the solution space, is known as redundant Constraint

Name three basic parts of simplex techniques.

Ans. 1 . Basis 2. Body matrix 3 Identity matrix

Distinguish between slack, surplus and artificial variable

Ans SlackThe positive variable, which is added to the left hand side of the constraint to convert it intoequation, is called the slack variable

Surplus-The positive variable, which is subtracted from the left hand side of the constraint to convert itinto equation, is called the surplus variable.

Artificial Variable LPP in which one or more constraints are of or = type (after en suring that all allbs are non negative)in such cases we introduce another type of variable known as artificial variables inorder to get the initial basic feasible solution.

What is the physical meaning of artificial variable?

Ans These variables are fictitious and have no physical meaning They are merely a device to get thestarting basic feasible solution so that simplex algorithm may be applied. These variables are requiredbecause in such problems the basic matrix is not obtained as identity matrix in the starting simplextable.

Define pivot element. (Or key element).

Ans. It is intersection element of key column and key row.

While finding the solution by simplex method, when does the problem have infinite optimal solution,unbounded solution and infeasible solution?

Ans. Infinite optimal solution-If a non basic variable have zero coefficient in the C-.Z row there exist aninfinite optimal solution.

Unbounded solution-An unbounded solution occurred when it is not possible to determine the basicvariable that should leave the basis This happens when there is no minimum non negative replacementratio.

Infeasible solution-When optimality condition is satisfied and artificial variable is present at somepositive level The problem does not have any feasible solution

Distinguish between the Big M and two phase method.

Ans. 1. The big M method solves the problem in one pass, whereas the two phase method solve it intwo stages.

2. The big M method is computationally inconvenient due to existence of the large number M The twophase method does not involve M during computation

3. The big M method presents a difficulty when the problem is solved on digital computer, but there isno such type of problem in two phase method.

Give outlines of a simplex method in linear programming

Ans. 1. Express the problem in standard form.

2. Find initial basic feasible solution.


7/26


8/26

Let C, represent the unit transportation cost for transporting the units from source i to destination j. Theobjective is to determine the number of units to be transported from source i to destination j. So thattotal transportation cost is minimum.

List the various methods that can be used for obtaining an initial basic solution for transportationproblem.

Ans. 1. North West corner method 2. Row minimum method 3. Column minimum method

4. Least cost method 5. Vogel approximation method.

What is degeneracy in transportation problem?

Ans. In a transportation problem with m origins and n destinations if a basic feasible solution has lessthan ( m + n i) allocations, the problem is said to be a degenerate transportation problem.

What do you understand by a balanced and an unbalanced transportation problem? How anunbalanced problem is tackled?

Ans In a transportation problem if the total availability from all the origins is equal to the total demand

at all the destinations z Such transportation problems are known as balancedtansportation problems. (Total supply = Total demand) In many situations, the total availability may not

be equal to the total demand i.e. Such problems are known as unbalancedtranportation problem.

The unbalanced problem could be tackled by adding a dummy destination or source depending uponthe requirement and the costs of shipping to this destination (or from source) are set equal to zero. Thezero cost cells are treated the same way as real cost cell and the problem is solved as a balancedproblem. (Total supply Total demand)


9/26

Describe the steps involved in vogal approximation method (VAM).

Ans Step. 1. For each row of the transportation table identify the smallest and next to smallest cost.Determine the difference b etween them for each row. These are called penalities. Similarly computethese penalties for each column.

Setp. 2. Identify the row or column with the largest penalty and allocate as much as possible within therestrictions of the rim conditions to the lowest cost cell in the row or column selected.

Setp. 3. Cross out of the row or column completely satisfied by the allocation.

Setp. 4. Repeat steps 1 to 3 untill all assignment have been made.

Define the following terms in transportation Problem.

(i) feasible solution (ii) Optimal solution.

Ans. 1. Feasible Solution. A feasible solution to a transportation problem is a set of non negativeallocations, x that satisfy the rim conditions.

2. Optimal Solution. A feasible solution that minimize the transportation cost is called the optimal

Solution. Explain North west corner rule for finding initial solution for a transportation problem.

Ans. 1. Start in the north west corner of the requirement table:

(a) If D1< S1, set x11 equal to find the balance supply and demand and proceed horizontally (cell 1, 2).

(b) If = S1 set x11 equal to D1, find the balance supply and demand and proceed diagonally (cell 2, 2).

(c) If D1>S1, set x11equal to compute the baiance supply and demand and proceed vertically (cell 2, 1).

2. Continue in this manner, step by step away from the north west corner until, finally a value is reachedin the south east corner.

Give an algorithm to solve transportation problem. Or

Describe the steps involved in solving transportation problem.

Ans. 1. Make a transportation Model. For this enter the supply a., from the origin demand b1 at thedestinations and unit cost C,, m the varous cells

2 Find initial basic feasible solution

3. Perform optimality test:

(a) Find dual variable

(b) Make opportunity cost matrix

(c) Compute the cell evaluation matrix If all cell evaluation are positive or zero thecurrent basic feasible solution is optimal.

(d) In case any cell evaluation is negative, select the vacant cell with the most negative evaluation. Thisisalled identified cell.

4. Iterate towards optimal solution. For this make as much allocation in the identified cell as possible sothat it become basic.


10/26

5. Repeat step 3 and 4 till optimal solution is obtained.

State the Assignment model. Is assignment problem a special case of transportation?

Ans Assignment Model Suppose there are n jobs to be performed and n person are available for doingthese jobs. Assume that each person can do each job at a time, though with varying degree of efficiency.The problem is to find an assignment so that the total cost for performing all jobs is minimum Yes, theassignment problem is a special case of transportation problem when each origin is associated with oneand only one destination.

Give the mathematical formulation of an assignment problem

Ans Let = 0, if the facility is not assigned to 1th job

1, if the th facility is assigned to th job.

The model is given by

What do you mean by restrictions an assignments? Or

How a restriction problem tackled? Or

How will you solve an assignment where a particular assignment is prohibited?

Ans. Sometime technical, space, legal or other problems do not permit the assignment of a particularfacility to a particular job. Such problem are known restrictions an assignment problem. Such problemcan be solved by assigning a very heavy cost to the corresponding cell. It will automatically excludedfrom further consideration.

What is the unbalanced assignment problem? How is it solved by the Hungarian method?

Ans When the number of facilities is not equal to the number of jobs, such problems are known asunbalanced assignment problem. Since the Hungarian method of solution require a square matrix,fictitious facilities or jobs. Jobs may be added and zero costs be assigned to the corresponding cells of the matrix. These cells are then treated the same way as the real cost cells during the solutionprocedure.

How do you come to know that Assignment problem has alternate optimal solution?

Ans. Sometimes it is possible to have two or more ways to strike off all zero elements in the reducedmatrix for a given problem. In such cases there will be an alternate optimal solution with same cost.

Describe the steps involved in solving assignment problem by Hungarian method.


11/26

Ans. 1. Prepare a square matrix.

2. Reduce the matrix.

3. Check whether an optimal assignment can be made in the reduced matrix or not.

4. Find the minimum number of lines crossing all zeros. If this number of lines is equal to the order of

matrix then it is an optimal solution. Otherwise gp to step 5. 5. Iterate towards the optimal solution.

6. Repeat step 3 through 5 until an optimal solution is obtained.

Compare assignment problem with transportation problem.

Ans. An assignment model may be regarded as special case of the transportation model. Here facilitiesrepresent the sources and jobs represent the destination. Number of sources is equal to the number of destinations, supply at each source is unity and demand at each distination is unit. In assignment thenumber of units allocated to a cell be either one or zero. The assignment problem is a completelydegenerate form of transportation problem.

Distinguish between transportation, assignment and sequencing model what is sequencing model). Ans. Transportation and assignment are allocation model (as explained above) Sequencing model. areapplicable in situation in which the effectiveness measure a function of order as sequence of performinga series of jobs. The selection of the apropriate order in which waiting customer/Job may be served iscalled sequencing.

State the assumption made in sequencing model.

Ans 1 Only one operation is carried out on a m/c

2. Each operation once started, must be completed.

3. Only one rn/c of each type is available.

4. A job is processed as soon as possible but only in the order specified. 5. Processing time are independent of order f performing the operation.

6. Transportation time is negligible.

7. Cost of in process inventory is negligible.

Duality Theory, Sensitivity analysis and Goal Programming

Q. 4.1 Explain the meaning of duality in LP

Ans For every LP problem there is related unique L P problem mvolvmg the same data which alsodescribes the original problem. The given original problem is known as primal programme. Theprogramme can be rewritten by transposing the rows and columns of the statement of the problem.Inverting the programme in this way results in dual programme. The two programmes have very closelyrelated properties so that optimal solution of the dual problem gives complete information about theoptimal solution of primal problem. Solving the problem by writing dual programme is known as dualityin LP


12/26

Q. 4.2. In a primal problem 1. jr variable unrestricted 2. il constraint occur with equality sign. Whatcan you say about its dual problem of the above two problems.

Ans. 1. If in primal th variable is unrestricted then one of the constraint will be of equality sign in dualproblem.

2. If in primal th constraint with equality sign then one of the variable will be unrestricted in the dualproblem.

Q. 4.3. If the dual of an LPP is solved, where will we get the value of decision variables of the primalLPP.

Ans. The value of decision variables of primal are given by the base row of the dual solution under theslack variable, neglecting the -ye sign if any, and under the artificial variables neglecting the ye sign if any, after deleting the constant M.

Q. 4.4. What is the importance of duality?

Ans.

1.If. the primal problem contains a large number of rows and a smaller number of columns, thecomputational procedure can be considerably reduced by converting it into dual and then solving it.

2. This can help managers in answer questions about alternative course of actions and their relativevalues.

3. Economic interpretation of the dual helps the management in making future decisions.

4. Calculation of the dual checks the accuracy of the primal solution.

Q. 4.5. Write short note on sensitivity analysis.

Ans. During the formulation it is assumed that the parameters such as market demand, capacityresources, consumption, availability, cost or profit are all known with certainty and do not change overtime. In actual practice the market fluctuate and all these variables kept on changing. It is therefore

desirable to study how the current optimal solution changes when the parameter of the problem getchanged. In thei problems this information may be more important than the single result provided byoptimal solution. The study of the effect of discrete changes in parameters on the optimal solution iscalled the sensitivity analysis. Such an analysis converts the static linear programming. solution intodynamic tool to study the effect of changing conditions such as in business and industry. In other wordsthe objective of analysis is to determine how sensitive the optimal solution is to the changes in thoseparameters. Such an analysis is known as sensitivity analysis.

Q. 4.6. Write a short note on Goal programming.

Ans. Goal programming is quite similar to linear programming but is applied for situation which havemultiple goal as objective. For a company manufacturing lathes and milling machines there can be

following objectives 1. Maximize profit in rupees

2. Maximize number of lathes to be manufactured.

3. Maximize number of milling machines to be manufactured.

It is obvious that the three goals cannot be added, since their units are different. Goal programming asksthe management to set some targets for each of the goal and rank them in order of importance. Having


13/26

received this information, goal programming tries to mimmize the deviations from the targets It startswith the most important goal and continues till the achievement of a less important goal.

Probabilistic Models (Decision Theory and Game Theory)

Q. 5.1. What do you mean by zero sum game and two person zero sum games in game theory?

Ans. Zero sum game: It is the game in which the sumof payments to all the players after the play of thegame is zero. Two person zero sum game : It is a game involving two players, in which the gain of oneplayer equals the loss of other.

Q. 5.2. What is saddle point and game value in game theory?

Ans. Saddle point : Saddle point is the number, which is lowest in its row and highest in its column.

- Game value : It is the average wining per play over a long no. of plays.

Q. 5.3. Write short note on pure strategy. How it differ from mixed strategy?

Ans Pure strategy If a player knows exactly what the other player is going to do, a deterministicsituation is obtained and objective function is to minimize the gain Therefore the pure strategy is adecision rule always to select a particular course of action.

Mixed strategy If a player is guessmg as to which activity is to be selected by the other on any particularoccasion, a probabilistic situation is obtained and objective function is to maximize the expected gain.Thus, the mixed strategy is a selection among pure strategies withfixed probabilities.

Q. 5.4. Indicate the difference between decision making under risk and uncertainty in statisticaldecision theory.

Ans Decision making under risk In this case more than one states of nature exist and there is enoughinformation available to assign probability to each of the possible state.

Decision making under uncertainty : Here more than one state of nature exists but there is noinformation about the various states, not even sufficient knowledge to assign probabilities to them.

Q 5.5 Enumerate the vanous quantitative methods which are used for decision making underuncertainty and decision making under risk

Ans Decision making under uncertainty

1 Criterian of optimism

2. Criterian of pessimism. 3. Minimax regret criterion.

4. Criterion of realism.

5. Laplace criterion.

Decision making under risk:

1. Expected value criterion


14/26

2 Expected opportunity loss criterian

3 Expected value of perfect mformation

4. Use of incremental analysis.

Q. 5.6. List the steps in decision, making approach.

Ans. 1. List all the alternatives.

2. Identify the expected future events.

3 Construct a payoff table

4. Select optimum criterion.

Q 5.7 Distinguish between game of strategy and game of chance

Ans Game of strategy If in the game the actions are determined by skills, at is called a game of strategy

Game of change If m the game the actions are determmed by chance, it is termed as game of chance.

Q 5.8 What do you mean by optimal strategy?

Ans Optimal strategy The strategy that puts the player in the most preferred position irrespective of thestrategy of his opponents is called an optimal strategy Any deviation from this strategy would reduce hispayoff

Dynamic Programming

Q. 7.1 State the Principle of optimality in dynamic programming.

Ans. This principle implies that a wrong decision taken at one stage does not prevent from taking theoptimum decision for the remaining stages. An optimal policy has the property that whatever the initialstate and decision are, the remaining decisions must constitute an optimal policy with regard to thestate resulting from the first decision.

Q. 7.2. Explain concepts of state and stage in dynamic programming.

Ans. Stage : Stage is a certain time interval or certain sub division of the problem for which independentfeasible decision are possible.

State: is the description of the system, which tells the necessary parameters of the system for makingdecisions.

Q. 7.3. What are the essential characteristics of dynamic programming?

Ans.

1. The problem can be divided into stages, with a policy decision required at eacfi stage.

2. Each stage has a number of states associated with it.

3. The effect of the policy decision at each stage is to transform the current state into a state associatedwith next stage.

4. Given the current stage, an optimal policy for remaining stages is independent of the policy adoptedin the pervious stages.


15/26

5. The solution procedure begins by finding an optimum policy for each state of the last stage.

6. A functional equation is available which identifies the optimal policy for each state with (n 1) stagesleft.

7. Using this function4l equation, the solution procedure moves backward stage by stage, each timefinding the policy when starting at initial stage.

Q. 7.4. Distinguish between linear programming and dynamic programming. What sort of problemscan be solved by dynamic programming?

Ans Linear programming models assume that data do not change w r t time It is one time decisionprocess and assumes average values of the decision variables Other important limitation of linearprogramming is that it assumes that data to be known with certainty.

Dynamic programming can be used to determine optimal strategies, by taking into account theuncertainties and can analyze multiperiod and multistage problems. In other words the technique is freefrom the limitation of linear programming. But it can be used to tackle very simple situations involving afew variables. If the no. of variable is larger the computation took becomes quite complex and involved.Moreover linear programming has standard ways to formulate the problems and solve them; there is nostandard approach in dynamic programming. It is on the other hand a general way of solving large,co;mplex problem by splitting them into smaller problems, which are more easily solved.

Q. 7.5. What is dynamic programming ? Write some application of dynamic programming.

Ans. Dynamic programming: It is a mathematical technique dealing with the optimization of multistagedecision process. The word programming has been used in the mathematical sense of selecting anoptimum allocation of resources and dynamic is particular useful for problems where dec isions aretaken at several distinct stages such as everyday or every weak. Dynamic programming is a techniquefor solving large complex problem (time varying variables) by splitting them into smaller problems,which are more easily solved.

Applications The following are a few of the large no of fields in which dynamics programming has beensuccessfully applied:.

1. Production

2. Inventory control

3. Allocation of resources

4. Selection of advertising media

5. Spare part level determination

6. Equipment replacement policy.

Queuing Theory

Q. 8.1. What is a queueing problem ? What is to be determined system?


16/26

Ans A queuemg problem is to determine the optimum level or service which minimize the total cost of providing service and waiting for the service. In a specified queuing system, the problem is to determinethe following:

(a) Probability distribution of queue length.

(b) Probability distribution of waiting time of customer in the queueing

(c) The busy, period distribution.

There are two costs involved in queueing problems:

1. Waiting time cost.

2. Service cost.

Q. 8.2. Differentiate between transient and steady state.

Ans Transient state It the operating characteristics vary with time, it is said to be transient state. Usuallya system is transient during the early stages of its operation.

Steady State : If the operating characteristics are independent of time, it is said to be steady state.

Q. 8.3. Define Traffic intensity or utilization factor.

Ans Utilization factor/Traffic Intensity It is the proportion of time a server actually spends with thecustomers.

Q. .8.4. State some of the important distributions of arrival and

Ans . Important distributions of arrival and service time

1. M - Markovian arrival and departure distribution.

2. Ek Erlangian with parameter k service times.

3. CI General independent arrival distribution.

4. G - General departure distribution

5. D Deterministic interarrival and service time.

Q. 8.5. Write a note on Ken lal and Lees notation for the identification of queues.

Ans. The complete notation can be expressed as (a/b/c) : (a/ elf)

a = arrival distribution

b = departure distribution

c = no of parallel service channel in the system

d = Service discipline

e = maximum number of customer allowed in the system.

f = calling source or population.


17/26

Q. 8.6. Explain the notation (MIM/1) (FCFS/oc/).

Ans. Compare with standard notation

M Markovian (possion) arrival distribution.

M Markovian (exponential) service distribution.

I = Single channel

FCFS Service discipline - First come first served

cc = Max. no. of customer allowed in the system

(Infinite).

cc = Calling source or population (infinite)

Q. 8.7. Distinguish between Balking, Jockeying and Reneging.

Ans. If a customer decides not be enter the queue since it is too long, he is said to have balked. If thecustomer enter the queue, but after sometimes looses patience and leave it, he is said tohave reneged.

When there are two or more parallel queue and customer moves from one queue to other is known asJockeying.

Q.8.8. What do you mean by calling source or population.

Ans. The arrival pattern of the customer depends upon the source, which generate them is called callingsource or population. A finite source exist when the arrival affects the probability of future customer.

Q. 8.9. Name the different queuing discipline.

Ans.

FIFO : First In First Out

FCFS : First Come,. First Served

LIFO :Last In First Out

SIRO : Service In Random Order.

Q. 8.10. List down the assumptions made in single channel queuing model with poission arrival andexponential service rate.

Ans. Assumption-

1. The customer arrive for service at a single facility at random according to poission distribution withmean arrival rate 2.

2. The service time has exponential distribution with mean service rate . 3. The service discipline followed is first come first served.

4. Customer behaviour is normal.

5. Service facility behaviour is normal.

6. The waiting space far queue is finite.

7. The calling source has infinite size.


18/26

8. The system is in stable state.

Q. 8.11. Give some applications of queuing theory.

Ans. Queuing theory has been applied to wide variety of business situations. All situation where

customers are involved such as restaurants, cafeterias, departmental stores, cinema halls, banks, postoffices, petrol pump, airline counter, patient in clinic etc. are likely to have waiting lines. The customerexpects a certain level of service, whereas the firm providing service facility tries to keep the costminimum while providing service.

Q. 8.12. How do you classify Queuing Model?

Ans. The various types of queuing models can be classified as follows:

1. Probabilistic models

2. Deterministic models

3. Mixed Queuing models.

Replacement Models

Q. 9.1. What is replacement problem?

Ans The replacement problems are concerned with the situations that arise when some time such asmachmes, equipments and electric bulbs etc need replacement due to decreased efficiency, failure orbreakdown.

The problem of replacement is to decide best policy to determine an age at which

the replacement is more economical instead of continuing at increased cost.

Q. 9.2. What are the situations, which makes the replacement of items necessary?

Ans. 1. The old item has become in worse condition and work badly.

2. The old item has failed due to accident.

3. A better or efficient design of machine has come in market.

Q. 9.3. Explain money value, present value and discount rate.

Ans. Money Value : Money has a value over time. We often speak; Money is worth 10% per yearspending Rs. 100 today would be equivalent to spending Rs. 110 at the end of one year. In, other words

if we spend Rs. 110 after a year from now, we could equivalently spend Rs. 100 today which would be of worth Rs. 110 next year.

Present Worth Factor If i is the interest rate then (1 +i) is called the present

worth factor. In other wards Present value of one rupee spends in n years time ftom now onwards.

Discount rate The present worth factor of unit amount to be spent after one year is given by V = (1 + r)where i is interest rate and V is called discount rate or depreciation value.


19/26

Q. 9.4. Discuss the brief replacement procedure for the items that deteriorate with time.

Ans. When ignoring the changes in the value of money-The item should be replaced when the averageannual cost to date becomes equal to the current maintenance cost.

When considering the changes in the value of money-

(a) The machine should be replaced if the next periods cost is greater than the weighted average of previous cost.

(b) The machine should not be replaced if the next periods cost is less than the weighted average of previous costs.

Q. 9.5. Briefly explain Individual and Group replacement.

Ans. Group replacement is concerned with those items that either work or fail completely. It oftenhappens that a system contains a large no. of identical low cost items that are increasingly liable tofailure with age When the value of individual items is so small that cost of keeping records of individualages cannot be justified. It may be advantageous to replace all items at fixed intervals. Such a policy iscalled Group replacement.

Individual replacement: Under this policy an item is replaced immediately after

its failure

Group replacement: Under this policy, decision is taken as to when all the items

must be replaced irrespective of the fact that the item has failed or have not failed,

with the provision of that an item fails before optimal time, it may be replaced individually

Q. 9.6. What is the advantages of preventive replacement over routine replacement?

Ans. Advantages of Preventive Replacement Over Routine Replacement: Routine

replacement means carrying out minor replacement jobs at regular intervals. It involves minor jobs such

as lubrication, minor adjustment of pressure and tightening of loose parts etc. Preventive maintenance is the planned maintenance of plants and equipments in

order to prevent or minimize breakdowns and depreciation rates. PM incudes all types

of jobs like

(a) Major jobs like overhauling and reconditioning etc.

(b) Replacement of consumables like gaskets, belts, seal, bearings etc.

.. . .(c) Internal cleaning of equipments, lubrication and oil changing.

Q. 9.7. What is the difference between age maintenance and preventive maintenance? Ans. Age replacement is a subset of preventive maintenance.


20/26

Age Replacement: It is the replacement of item at fixed interval (as per its technical characteristics)irrespective to its condition at that time.

Condition basedMaintenance : It is based on the fact that whenever any failure is to occur it gives sometypes of waining. CBM is the use of advanced technology to sense machinery operating characteristicssuch as vibration, temp., pressure etc. and to compare the measured values of these characteristics withhistorical data as per established criteria to assess machinery condition. CBM permit conditiOn basedrather than age based initiation of maintenance efforts to correct the any problem identified

Inventory Models

Q. 10.1 What is inventory?

Ans. An inventory consists of usable but idle resources such as men, machines material or money Whenresources involved are a material, the inventory is called stock.

Q. 10.2. Define lead time and reader point in inventory problems.

Ans. Lead time : It is the time period between the placement of order and receipt

of goods. /

2. Recorder level It is the level of stock at which replenishment order is placed and is equal to the lead

time multiplied with the demand during lead time. Q. 10.3. What are the uses of maintaining inventories?

Ans. 1. It helps in smooth and efficienf running of an enterprise.

2. It provides service to the customer at a short notice.

3. It reduce product costs since there is an added advantage of batching and long uninterruptedproducion run.

Due to absence of stock, the company may have to pay high prices because of piece wise purchasing.

Inventory helps in maintaining the economy by absorbing some of the fluctuations when the demandfor an item fluctuates.

Q. 10.4. What are the disadvantages of maintaining inventories

Ans. 1. A production foreman who has large in process inventory may be able to hide poor planning sincthere is always something to manufacture.

Inventory does not add any value to the product. Inventory means unproductive tied up capital of theenterprise.

With large inventory there is always likelihood of absolescence etc.


21/26

For maintaining inventory additional money to be spent on personnel, equipment, insurance etc.

Q. 10.5. What are the different costs that are involved in inventory model?

Ans. 1. Inventory carrying or stock holding costs.

(a) Capital tied up in inventories.

(b) Cost of storage space.

(c) Depreciation and deterioration cost.

(d) Pilferage cost.

(e) Obsolescence cost.

(I) Handling cost.

(g) Record keeping cost.

(h) Taxes and Insurance.

2. Procurement costs or set up costs.

3. Shortage cost or stock out costs.

Q. 10.6. What is the advantages (need) of inventory control in organization?

Ans. 1. Inventory, control ensures an adequate supply of items to customers and avoids the shortage asfor as possible at the minimum cost.

2. It makes use of available capital in a most effective way and avoids an unnecessary expenditure onhigh inventory etc.

3. The risk of loss due to change in prices of items is reduced.

4. It ensures smooth and efficient running of organization. 5. It provides advantages of quality discounts on bulk purchases.

6. It eliminates the possibility of duplicate ordering.

7. It helps to minimize the loss due to deterioration obsolescence, damage or pilferage etc.

8. It helps in maintaining the economy by absorbing some of the fluctuations when the demand for anitem fluctuates.

Q. 10.7. How the term inventory may be classified?

Or

Distinguish between direct and indirect inventories.

Ans. Direct inventories : The items, which play a direct role in the manufacture and become an integralpart of finished goods, are known as direct inventories. They are further divided into four types

(a) Raw material inventories.

(b) Walk in process inventories.


22/26

(c) Finished good inventories.

(d) Spare parts inventories.

Indirect inventories : Those items which are necessarily required for manufacturing but do not becomethe component of finished production, like oil, grease, lubricants, petrol etc.

Q 10.8. What is inventory problem? Ans Inventory problem is to decide when to order and how much to order so that total cost of the

system should be mimmum

Q 10.9 Define EOQ Write the formula for finding EOQ

Ans EOQ is the size of the order which mmimizes total annual cost of carrying

Q. 10.10. What are price breaks in inventory model?

Ans. Inventory problems in which the item cost is variable and depends upon the quantitymanufactured or purchased, This usually happens when discounts are offered for the purchase of largequantities. These discounts are known as price break in inventory model.

Chapter 11 : Network Models

Q 11.1 Define critical path and critical activities

Ans Critical path the path containing critical activities (with zero float) is known

as critical path.

Critical activity the activity, which can not be delayed without delaying the

project duration, is known as critical activity

Q 11.2 Differentiate between supercritical and subcritical activities


23/26

Ans Supercritical an activity having negative float is known as supercritical

activity.

Subcritical An activity having positive float is known as subcritical activity This

activity may be delayed without any delay m the project

Q 11.3 Differentiate between slack and float

Ans Slack It is the time by which occurrence of an event can be delayed

Q. 11.4. Enlist four types of floats used in network analysis.

Ans. (a) Total float.

(b) Free float

(c) Independent float

(d) Interfering float

Q 11.5 Define Free Float, Independent float, Interfering float as used in PERT chart.

Ans. Freefloat : Portion of the total float within which an activity can be manipulated

without affecting the floats of subsequent activities.

Independent float: Portion of the total float within which an activity can be delayed

without affecting the floats of proceeding activities.

Interfering float : It is equal to the difference between the total float and the free float of the activity.

Q. 11.6. What do you mean by dummy activity?

Ans. Dummy activity : An activity, which only determines the dependency of one

activity on the other, but does not consume any time, is called a dummy activity.

Q. 11.7. Define dummy arrow used in network.

Ans. Dummy arrow: It represent the dummy activity in the network. It only represents the dependencyof one activity on the other. It is denoted by dash/dotted

line.

Q 11.8. Define dangling and looping in net-work models.


24/26

Ans. Dangling : The disconnection of an activity before the completion of all the

activities in a network diagram is known as dangling.

Looping (cycling) : Looping error is also known as cycling error in a network diagram. Drawing an endlessloop in a network is known as error of looping.

Q. 11.9. Differentiate between event and activity.

Ans. Event: The beginning and end points of an activity are called events or nodes. Event is a point intime and does not consume any resources.

Activity : It is physically identifiable part of a project which require time and resources for its execution.An activity is represented by an arrow, the tail of which represents the start and the head, finish of theactivity.

Q. 11.10. Define (i) Network (ii) Path terms used in network.

Ans. (i) Network: It is the graphical representation of logically and sequentially connected arrows andnodes representing activities and events of a project.

(ii) Path : An unbroken chain of activity ,arrows connecting the initial event to

some other event is called path.

Q. 11.11. Differentiate between CPM and PERT.

Ans. CPM.:

1. CPM is activity oriented i.e., CPM network is built on the basis of activities.

2. CPM is a deterministic model. It does not take into account in uncertainties involved in the estimationof time.

3.

CPM places dual emphasis on project time as well as cost and finds the trade off. between project timeand project cost.

4. CPM is primarily used for projects which are repetitive in nature and comparatively small in size.

PERT

1.PERT is event oriented.

2.PERT is a probabilitic model.


25/26

3.PERT is primarily concerned with time only.

4. PERT is used for large one time reserach and development type of projects.

Q 11.12. Define crashing in network mode1s.

Ans. Crashing: The deliberatic reduction of activity normal time by puffing an

extra effort is called crashing. The crashing is being done by allocating more manpower or bysubcontracts.

Q. 11.13. Differentiate between:

(i) Crash project time and optimum project time

(ii) Normal cost and crash cost.

Ans.

(i) Crash project time: It is the minimum time by which the prOject may be completed.

Optimum project time: The time corresponding to minimum project cost for completion of the project isknown as optimum project time.

(ii) Normal cost : The cost associated when the project completed with normal time

Crash cost: The cost associated when the project completed with crash time is known as crash cost.

Q.11.14. Briefly explain resource allocations. Distinguish between Resource smoothing and Resourcelevelling.

Ans. The resource allocation procedure mainly consists of two activities:

(z) Resource smoothing

(ii) Resource levelling.

Resource smoothing If the project duration could not be changed then the resource allocation only smoothen the demand on resources in order that the demand

for any resource is uniform as possible The periods of maximum demand for resource

are located and the activities are accordmg to their float values are shifted for balancing

the availability and requirement of resources. The intelligent utilization of floats can

smoothen the demand of resources to the maximum possible extent is called resource


26/26

smoothing.

Resource Levelling : There are various activities in a project demanding varying

levels of resources.

The demand on certain specified resources should not go beyond the prescribed

level is know as resource levelling.

Important Questions of AOR

Documents

Transcript of Important Questions of AOR