Operation Research TechniquesPart-A Questions1. Define unbounded solution

2. What do you mean by a general LPP?

3. Define feasible region.

4. Define constraint

5. State any three salient features of a LPP

6. Define infeasible solution

7. Define slack & surplus variable

8. Define optimal solution

9.Write the standard form of LPP in Matrix form.

10. What is degeneracy in LPP?

11. What is key column, key row? How is it selected.

12. Stat the condition for an unbounded solution of a LPP?

13. Define Artificial variable.

14. What is the use of artificial variable?

15. Give mathematical formulation of assignment problem.

16. List any three approaches used with transportation problem for

determining the starting solution.

17. What d you mean by transportation problem?

18. What is the use of MODI method?

19. Define degenerate and non-degenerate basic feasible solution of a transportation

problem.

20. What is unbalanced transportation problem? How to solve it?

21. Define an assignment problem.

22. How will you revise the opportunity cost matrix of a n assignment problem, if it does

not give the optimal solution?23. What do you mean by a project?

24. What do you mean by an activity of a project?

25. Define network.

26. Define EST & LFT.

27. In inventory models, What is mean by q and C3.

28. A Particular item has demand of 9,000 units/year. The cost of one procurement is Rs.100 and the holding cost per unit is Rs.2.40 per years. The replacement is instantaneous and no shortages are allowed. Determine the economic lot size.

29. Define Value of the game?

30. When Two-person zero sum game has a saddle point?

31. Differentiate PERT and CPM

32. Define pure strategy.33. Define group replacement.

34. What is travelling salesman problem?35. Define assignment problem.

36. What is an unbalanced transportation problem?

Part-B Questions

1.Solve the following LPP problem by simplex method

Maximize

Subject to

2. Solve the following L.P.P by the graphical method.

3. Solve the following LPP by Big-M method

4. Determine basic feasible solution to the following

transportation problem using North West Corner Rule

SinK

ABCDESupply

OriginP21110374

Q147218

R3948129

Demand 3 3 4 5 6 5. Find the starting solution of the following transporation

model by Least Cost method1267

04212

31511

101010

6. Find an optimal solution by MODI method of the following matrix using VAM for finding the initial solution1234Supply

I2116251311

II1718142313

III2718414119

Demand10121515

7. A machine operator has to perform two operations,turning and threading on a number

of different jobs. The time required to perform these operations (in minutes) for each

job is known. Determine the order in which the jobs should be processed in order to

minimize the total time required to turn out all the jobs.

JobTime for turning

(minutes)Time for threading

(minutes)

138

21210

359

426

593

6111

7. Draw the network and determine the critical path for given data

Jobs1-21-32-43-43-54-54-65-6

Duration651034629

8. Construct the network for the project whose activities are given below and compute the

total, free and independent float of each avtivity and hence determine the critical path

and project duration.

Activity0-11-21-32-42-53-43-64-75-76-7

Duration (in weeks)38126338538

9. A particular item has a demand of 9,000 units/year. The cost of one procurement is

Rs.100 and the holding cost per unit is Rs.2.40 per year. The replacement is

isntantaneous and no shortages are allowed. Determine

i) the economic lot size.

ii) the number of orders per year

iii) the between orders

iv) the total cost per year if the cost of one units is Re.1

10. An item is produced at the rate of 50 items per day. The demand occurs at the rate of

25 items pr day. If the setup cost is Rs.100 per setup and holding cost is Re.0.01 per

unit of item per day, find the economic lot size for one run, minimum total cost for

one run.

11. Using the principle of Dominance solve the following game

12. Solve the following game by graphical method

13. Reduce the game by dominance and find the game value

IIIIIIIV

I3240

II3424

III4240

IV0408

14. Solve the transportation problem using VAM and find the optimal solution whose

cost, demand, supply are given by the following tableW1W2W3W4W5Supply

P1202832557050

P24836404425100

P33555224548150

Demand10070504040

15. An item is produced at the rate of 50 units per day. The demand is at the rate of 25

units per day. The set up cost is 100 per unit per day. Find the EOQ and the minimum

annual inventory cost. After how many days should production be stopped during each

run?16. A manufacturer has a supply 12000 units of a product per year to his customer. Shortages are not permitted and there is no lead time. The inventory holding cost is Rs.0.20 per unit per month and the set up cost per run is Rs.350. Determine the economic lot size, the period of one run, the minimum annual inventory cost.

17. In a game of matching coins with two players, suppose A wins one unit value when there are two heads, wins nothing there are two tails, and losses units value when there are one head and one tail. Determine the payoff matrix, the best strategy for each palyer,and the value of the game.18. Use simplex method to

Min Z=x2-3x3+2x5

Subject to

19. Solve the following game by graphical method

20. Solve the following game

21. Find the sequence for the following eight jobs, that will minimize the total elapsed

time for the completion of all the jobs. Each job is processed in the same order

C, A, B. Entries give the time in hours on machines

Jobs12345678

Times on Machine A46745362

Times on Machine B81078118913

Times on Machine C5623491511

22. A project consists of the tasks A, B, C,D,E ,F,G, H, I with the following data

ActivityABCDEFGHI

Preceeding activity------AAB,DCBF,G

Duration2382016241819410

Construct network. Find critical path. Also find Total, Independent and Free floats23. Solve the following traveling salesman problem. A salesman is planning to tour cities

B,C, D,E starting from his home city A.

The inter-city distances are shown in the following table

CityABCDE

A--10318813638

B103--26217652

C188262--85275

D13617685--162

E3852275162--

_1396268087.unknown

_1396768083.unknown

_1410596955.unknown

_1396867118.unknown

_1396687321.unknown

_1381561807.unknown

_1396267617.unknown

_1381562123.unknown

_1381559396.unknown