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1.what is operations research? “Operations Research is the application of scientific methods to complex problems arising from operations involving large systems of men, machines, materials and money in industry, business government and defence.”

2. State any four applications of operations research? (a)Assignment of jobs to applicants to maximize total profit or minimize total costs. (b)Replacement techniques are used to replace the old machines by new ones. ©Inventory control techniques are used in industries to purchase optimum quantity of raw materials. (d)Before executing a project, activities are sequenced and scheduled using PERT chart.

3.Define a feasible solution? Any solution to a LPP which satisfied the non-negativity restrictions of the LPP is called its feasible solution. 4.Define optimal solution? Any feasible solution which optimises (minimizes or minimizes)the objective function is called its optimal solution. 5.Define degenerate solution? A basic feasible solution is said to be degenerate if one or more basic variables are zero. 6.Define unbounded solution? If the value of the objective function Z can be increased or decreased indefinitely. Such solutions are called unbounded solutions. 7.What are limitations of LPP? 1.For larger problems having many limitations and constraints, the computational difficulties are enormous even when computer are used. 2.Many times it is not possible to express both the objective function and constraints in linear form.

3.The solution variables may have any values. Some times the solution variables are restricted to take only integer values. 4. This method does not take into account the effect of time 8.What do you understand by transportation problem? T.P is a special class of Linear Programming Problem in which we transport a commodity(single product) from the source to a destination in such a way that the total transportation cost is minimum. 9.Define the optimal solution to a T.P? The basic feasible solution to a T.P is said to be optimal if the minimises the total transportation cost. 10.what do you mean by degeneracy in a T.P.? If the number of occupied cells in a m X n T.P. is less than m + n - 1, then it is called a degeneracy in a T.P. 11.What do you mean by a project? A project is defied as a combination of inter-related activities all of which must be executed in a certain order for its completion. 12.What are the two basic planning and control techniques in a network analysis? (I) Programme Evaluation Review Technique(PERT) (ii)Critical Path Method.

13.What re the three main phases of a project? The three phases of a project are planning, scheduling and control. 14.What is a network? It is the graphic representation of logically and sequentially connected arrows and nodes representing activities and events of a project. 15.What do you mean by an activity of a project? An activity represents some action and as such is a time consuming effort necessary to complete a particular part of the overall project. 16.What is a dummy activity and when it is needed? Certain activities which neither consumes time nor resources but are used simply to represent a connection between events are known as dummies. When two activities have the same head and tail events, this cannot be represented in network diagram without using dummy activity. 17.What are the three types of floats? The three types of floats are (1) Total float (2)Free float (3) Independent float. 18.Define total float. The amount of time by which the completion of an activity could delalyed beyond the earliest expected completion time without affectring overall project duration time is called total

19.Define critical activity? An activity is said to be critical if a delay in its start will cause a further delay in the completion of the entire project. 20.What is the critical path? The sequence of critical activities in a network is called the critical path. 21.If the total float of an activity the latest and the earliest occurrence of the events 3 and 4 are 15,12 and 22, 10 respectively. What is free float? FF = TF -Head event slack 22.What is the independent float of the activity? IF = FF - Tail event slack 23.Define the expected variance of a project length? The expected variance of a project length also called the variance of the critical path, is the sum of the variances of all the critical activities. 24.Define a queue? The flow of customers from finite/infinite population towards service facility is called a queue (waiting line). 25.Define a customer? The arriving unit that requires some service to be performed is called a customer.

26.Define the following; 1.Banking: A condition in which a customer may leave the queue because the queue is too long and he has no time to wait or there is insufficient waiting space. 2.Reneging : This occurs when a waiting customer leaves the queue due to impatience. 3.Jockeying: Customers may jockey from one waiting line to another. 27.Define transient and steady state? A system is said to be in a transient state when its operating characteristics are dependent on time. When the operating characteristics of a system are independent of time, it is called a steady state. 28.Define traffic intensity of utilization factor? An important measure of a simple queue is its traffic intensity given by

p=

mean arrival rate mean service rate

=

λ µ

29.Explain the Kendall’s notation? Kendall’s notation is used for representing queuing models. Generally queuing model may be completely specified in the following symbol form (a/b/c);(d/e) a- inter-arrival time (arrival pattern) b- service pattern c-number of channels d-capacity of the system e-queue discipline 30.Define a game? The comparitive situation will be calle4d a game, if it has the following properties; 1.There is a finite number of participants called players. 2.Each player has a finite number of strategies available to him. 3.Every game results in an outcome. 31. Define strategy? The strategy of a player is the decision rule he uses for making the choice from his list of courses of action.

32.Define a saddle point? A saddle point is the position in the pay off matrix, where the maximum of row minima coincides with minimum of column maxima. 33.Define two-person zero sum game? A game with two players, where a gain of one player equals the loss of the other is known as a two-person zero sum game. 34.Distinguish between Pure and Mixed strategies? 1. A strategy is called pure, if one knows in advance of the play that it is certain to be adopted irrespective of the strategy the other may choose. The optimal strategy mixture of each player may be determine by assigning to each strategy its probability of being chose. These strategies are called mixed strategy. 2. A pure strategy is a special case4 of mixed strategy. A player may be able to choose only n pure strategies, where as he had infinite number of mixed strategies. 35.Define payoff? The gains resulting from a game is called payoff, and when it is presented in the form of a table it is called payoff matrix.

36.Define value of the game? The value of the game is defined as the expected gain to a player. 37.What is meant by minimax, maximin? Minimax is maximum of row minima, and maximin is minimum of column maxima. 38.When is the game fair? A game is fair if minimax value=maximin value=0 39.Define simulation. Why is it used? The representation of reality in some physical form or in some form of mathematical equations may be called as simulation, I.e, simulation is imitation of reality. This is used because one is satisfied with suboptimal results for decision making and also representation by a mathematical model is beyond the capabilities of the analyst. 40.Define random number? Random number is a number whose probability of occurrence is the same as that of any other number in the collection. 41.Explain Monte-Carlo technique It is a simulation technique in which statistical distribution functions are created by using a series of random numbers. This is generally used to solve problems which cannot be adequately represented by the mathematical models

42.What are the advantages of simulation? The advantages of simulation are 1.mathematically less complicated 2.flexible 3.modified to suit the changing environments of the real situation 4.can be used for training purposes 43.What are the limitations of simulation? 1.quantification of the variables may be difficult. 2.simulation may not yield optimum results. 3.simulation may not always be cheap. 4.simulation may not always be less time consuming. 5.the results obtained from simulation models cannot be completely relied upon 44.What do you mean unbalanced T.P.? Any T.P. is said to be unbalanced if m n

∑ai i=1

≠

∑bj j=1

45.What do you mean by a general LPP? The general LPP is given by Max or Min Z=C 1 X1 +C2 X2 +………..C n Xn … (1)

a11 a21

Subjected to

a12 a22

X1 + X1 +

X2 + ………..a1n X n(≤ = ≥)b1 X2 +………..a 2n Xn(≤ = ≥)b2

. ….(2)

.

a m1

X1 +

am2

X2 +………..amn Xn (≤ = ≥)bm x1,x2……..xn ≥ 0

….(3) 46.Define pseudo-random number? Random numbers are called Pseudo –random numbers when they are generated by some deterministic process and they qualify the predetermined statistical test for randomness.

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Transportation problem

Assignment problem

1

Number of sources and number of destinations need not be equal.

Number of sources and number of destinations are equal

2

Cost matrix need not a square matrix

Cost matrix must be square matrix

3

There is no restrictions on number of allotments in any row(column)

There is necessarily only one allotment in each row and column

4.

Optimal solution involves at most m+n-1 allotments

Optimal solution involves always m or n allotments

5

Problem is unbalanced if

Problem is unbalanced if it is not a square matrix

∑ ai ≠ ∑ bj

48.Difference between CPM and PERT

Critical path method

Program Evaluation Review Technique

i) Activity oriented

Event oriented

ii) Deterministic

probabilistic

iii) Time is fixed

Three time estimates namely optimistic, pessimistic, most likely are given such as Resources

iv) No limitation of resources

labour, equipments, materials are limited