AMIETE – ET/CS/IT (NEW SCHEME)   –   Code: AE62/AC62/AT62

 

Subject: OPERATIONS RESEARCH AND

ENGINEERING MANAGEMENT

Flowchart: Alternate Process: DECEMBER 2009Time: 3 Hours                                                                                                     Max. Marks: 100

 

 

NOTE: There are 9 Questions in all.

·      Question 1 is compulsory and carries 20 marks. Answer to Q.1 must be written in the space provided for it in the answer book supplied and nowhere else.

·      Out of the remaining EIGHT Questions answer any FIVE Questions. Each question carries 16 marks.

·      Any required data not explicitly given, may be suitably assumed and stated.

 

 

Q.1       Choose the correct or the best alternative in the following:                                  (210)

                

a.    The values of decision variables that satisfy all the constraints constitute a _____________

 

                  (A) basic solution                                  (B) optimal solution                                                          

                  (C) feasible solution                              (D) infeasible solution                                          

 

             b. For both the maximization and the minimization problems, the leaving variable is the ________ variable associated with the smallest non negative ratio, with strictly positive denominator.

       

                  (A)positive                                           (B) basic

                  (C)non basic                                         (D) negative

 

             c.  In the transportation problem, ____________ yields the best starting basic solution.  

 

                  (A) north west corner method               (B) least cost method

                  (C)Vogel’s approximation method        (D) row minima method

 

             d.  In PERT networks, most likely time ‘m’ which occurs, when execution is done under __________ conditions.

 

                  (A) extremely well                                (B) extremely poor

                  (C) normal                                            (D) optimistic

 

             e.  In game theory, graphical solution is suitable for games in which at least one player has exactly ____________ pure strategies.

                 

                  (A) one                                                (B) two

                  (C) zero                                               (D) multiple

 

             f.   ____________ distribution is used to describe the inter arrival time in the pure birth model and the inter departure time in the pure death model. 

 

                  (A) Poisson                                          (B) Normal

                  (C) Gaussian                                        (D)Exponential

             g. The main aim during the planning phase is to define the ___________ goals, objectives and policies of the corporation and the implementation steps and performance standards.

 

                  (A) short term                                       (B) long term

                  (C) medium term                                  (D) fixed

            

             h.  A corporate strategic plan is often long range.  It usually involves _________ levels of investment, in terms of capital and people which need time to develop.

 

(A)  low                                                (B)  high

                  (C) middle                                            (D)  zero

 

             i.   Decision making process was first defined by _________

 

                  (A) Vroom & Yetton                            (B) Maier

                  (C) Kepner & Tregoe                           (D) MC Kenney & Keen

 

             j.   Qualitative forecasting which is based on judgement of __________experience and future trends.

 

                  (A) past                                                (B) present                                                                        

                  (C) no                                                  (D) technical

 

 

Answer any FIVE Questions out of EIGHT Questions.

Each question carries 16 marks.

 

 

  Q.2     a.   Explain the different phases of an OR study.                                                       (6)

 

             b.   A firm plans to purchase at least 200 quintals of scrap containing high quality metal X and low quality metal Y.  It decides that the scrap to be purchased must contain at least 100 quintals of X-metal and not more the 35 quintals of Y-metal.  The firm can purchase the scrap from two suppliers A and B in unlimited quantities.  The percentage of X and Y metals in terms of weight in the scraps supplied by A and B is given below:

                  

Metals

Supplier A

Supplier B

X

25%

75%

Y

10%

20%

       

                   The price of A’s scrap is Rs.200 per quintal and that of B’s scrap is Rs.400 per quintal.  Formulate this problem as LP model and solve it graphically to determine the quantities that the firm should buy from two suppliers so as to minimize total purchase cost.                                                                   (10)

       

Q.3       a.   Define the following with reference to the Simplex method

                   (i)    Degeneracy                                  (ii)  Alternative optima

                   (iii)  Unbounded solutions                     (iv)  Infeasible solutions                           (4)

 

 

             b.   Solve the following LPP by using Big M-Method.                                             (12)

                   Minimize

                   Subject to constraints:

                  

                   and                                                                                                       

 

  Q.4     a.   A dairy firm has three plants located throughout a state.  The daily milk production at each plant is as follows:                                                           

                   Plant 1 :  6 million litres

                   Plant 2 :  1 million litres                       

                   Plant 3 :  10 million litres

                   Each day the firm must fulfil the needs of its four distribution centres.  Minimum requirement at each centre is as follows:

                   Distribution centre 1  :  7 million litres

                   Distribution centre 2  :  5 million litres

                   Distribution centre 3  :  3 million litres

                   Distribution centre 4  :  2 million litres

                   Cost of shipping one million litres from each plant to each distribution centre is given in the following table in hundreds of rupees.

                  

Distribution Centre

Plant

 

2

3

11

7

1

0

6

1

5

8

15

9

                   Find the initial basic feasible solution by Vogel’s approximation method, if the objective is to minimize the total transportation cost.                       (8)                                                             

             b.   Five men are available to do five different jobs.  From past records the time (in hours) that each man takes to do each job is known and is given in the following table:

                  

Job

Men

I

II

III

IV

V

A

2

9

2

7

1

B

6

8

7

6

1

C

4

6

5

3

1

D

4

2

7

3

1

E

5

3

9

5

1

                   Find the assignment of men to jobs that will minimize the total time taken.            (8)

            

  Q.5     a.   Explain the rules used for constructing the network.                                             (5)

                  

             b.  A small project consists of seven activities for which the relevant data are given below:

                  


 

Activity

Preceding activities

Activity duration (days)

A

-

4

B

-

7

C

-

6

D

A,B

5

E

A,B

7

F

C,D,E

6

G

C,D,E

5

                   (i)  Draw the network and find the critical path and project completion time.

                   (ii) Calculate earliest start, earliest finish, latest start and latest finish times for all the activities.

                   (iii) Calculate the total float for each activity.                                                     (11)

 

  Q.6     a.   Use the graphical method to solve the following game and find the value of the game.                      (8)

                                                               Player B

                                     Player A       

                                                           B1      B2       B3     B4

 

2

2

3

-2

4

3

2

6

                                               A1   

                                               A2

 

             b.   A road transport company has one-reservation clerk on duty at a time.  He handles information of bus schedules and makes reservations.  Customers arrive at a rate of 8 per hour and the clerk can service 12 customers on an average per hour.

                   (i)  What is the average number of customers waiting for the service of the clerk?

                   (ii) What is the average time a customer has to wait before getting service?          (8)

 

  Q.7     a.   What is management?  Briefly explain different management styles.                      (8)

 

             b.   Briefly explain a simple matrix-management scheme.                                           (8)

                                                                             

  Q.8     a.   Briefly explain the strategy formulation process.                                                  (8)

 

             b.   What is Forecasting?  Briefly explain the different qualitative forecasting methods.               (8)

       

  Q.9     a.   What is marketing?  Briefly explain the marketing’s role.                                     (8)

       

             b.   Briefly explain the different motivation techniques.                                               (8)