Resource management techniques lecture notes P.R.Engineering college

Resource management techniques lecture notes in Human resource management uploaded at P.R.Engineering college

Resource management techniques lecture notes in Human resource management at P.R.Engineering college P.R.Engineering college Staff uploaded in lecturenotes.net

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UNIT-I
LINEAR PROGRAMMING MODELS
PART-A 
1. Write the definition of operation research?  
2. Define optimal solution
3. Define a feasible solution. 
4. What are the phases of an operations research study?  
5. What is the difference between feasible solution and basic feasible solution? 
6.  Define unbounded solution. 
7. What do you mean by standard form of LPP? 
8. What are the limitations of LPP? 
9. Define slack and surplus variables? 
10. What is meant by decision variable? 
11. Define artificial variable. 
12. Write the methods used to solve an LPP involving artificial variables? 
13. What is meant by degeneracy in simplex method?
14. A paint company produces both interior and exterior paints from two raw materials
     M1 and M2 .The following table provides the basic data of the problem.
Raw material Exterior paint  Interior paint 
M1 6 4 24
M2 1 2 6
Profit per ton
(Rs in 1000’s) 5 4

PART-B
1. (a)  A company manufactures two products A and B. Each unit of B takes twice as long to 
            produce as one unit of A and if the company were to produce only a it would have time to     
            produce 2000 units per day. The availability of the  raw material is sufficient to produce 
           1500 units per day of both a and B   combined. Product B recurring a special Ingredient         
          only   600units can be  made per day. If A fetches a profit of Rs.2 per unit and B a profit of   
            Rs.4  per unit,   
                           (a) Formulate the optimum product minimum.                               (8)
                           (b)   List the phases of OR and explain them.                                  (8)  
2. (a) Explain the scope of OR.                                                                                   (8) 
 (b) A paper mill produces 2 grades of paper namely X and Y. Because of raw  material 
          restrictions, it cannot produce more than 400 tones of grade X and  300 tones of grade  Y 
          in a week. There are 160 production hours in a week. It Requires 0.2 and 0.4 hours to 
         produce a ton of products X and Y respectively   with Corresponding profits of Rs.200 and 
          Rs. 500 per ton. Formulate the   above as a  LPP to maximize profit and find the optimum 
          product mix.                                                                                                       (8) 
3.(a)  Use Graphical method to solve the following LP problem 
            Maximize Z= 5 x1+4 x2     
             Subject to the constraints:
                                             6x1+4x2  ≤ 24 , 
                                                x1+2x2   ≤ 6,   
                                               -x1+x2  ≤ 1,  
                                                 x2  ≤ 2 ;      and  x1, x2  ≥ 0                                                       
(b) Use graphical method to solve the LPP
                  Minimize Z = 20x1+10x2
                  Subject to the constraints
                                               x1+2x2≤ 40,
                                               3x1+x2 ≥30, 
                                               4x1+3x2 ≥60,    
                                                     x1, x2 ≥0. 
4. (a) Use simplex method to solve the following LPP  
                   Maximize Z = 7x1+5x2
                    Subject to the constraints
                                           x1+2x2 ≤  6,  
                                          4x1+3x2 ≤ 12 
                                           and x1, x2  ≥ 0                 
(b)Use simplex method to solve the following LPP
                    Maximize Z = 4x1+10x2
                   Subject to the constraints
                                         2x1+x2≤ 50,      
                                        2x1+5x2≤ 100,       
                                       2x1+3x2≤ 90,       
                                         x1, x2 ≥0 
5. Solve the following problem by simplex method 
                    Minimize Z = 8x1-2x2
                   Subject to the constraints
                                   -4x1+2x2  ≤  1,  
                                  5x1-4x2   ≤ 3, 
                                   and x1, x2,  ≥0 .

6. Use Big M method to    
                        Minimize Z = 4x1+3x2
                          Subject to the constraints
                                                   2x1+x2 ≥10,  
                                                 -3x1+2x2 ≤ 6, 
                                                     x1+x2 ≥6,
                                                 and   x1, x2  ≥ 0                                                             (16) 
7. Use Two Phase Simplex method to   
                           Maximize Z = 5x1-4x2+3x3
                            Subject to the constraints
                                                 2x1+x2-6x3 = 20,  
                                                6x1+5x2+10x3 ≤ 76, 
                                              8x1-3x2+6x3 ≤ 50,     
                                               and   x1, x2, x3 ≥0                                                        (16) 
8. Use Penalty method
                               Maximize Z = 6x1+4x2      
                                Subject to the constraints
                                                2x1+3x2≤ 30,       
                                                 3x1+2x2≥ 24
                                                  x1+x2 ≥3,       
                                                  x1, x2≥0 
9. Use Two Phase Simplex Method to
                               Maximize Z = 5x1+8x2
                                  Subject to the constraints
                                             3x1+2x2≥3,      
                                               x1+4x2≥ 4,   
                                               x1+x2≤ 5,   
                                                x1, x2, ≥0 
10. Solve the following linear programming problem.
                                Maximize Z = 8x2
                               Subject to the constraints
                                               x1-x2≥0,      
                                             2x1+3x2 ≤-6,    
                                              and  x1, x2 are unrestricted.

UNIT-II
       TRANSPORTATION MODEL AND ASSIGNMENT MODEL 
PART-A
1. How do you convert the unbalanced T.P into a balanced one?
2. What do you understand by transportation problem? 
3. What do you mean by an unbalanced assignment problem?
4. What do you mean by degeneracy in a T.P?
5. Define transportation problem? 
6. What are the methods for determining an IBFS in T.P?  
7. What is an assignment problem?
 8. Explain how the profit maximization transportation problem can be converted  to an      
      equivalent cost minimization transportation problem 
 9. State the difference between the T.P and A.P. 
10. How do you convert the maximization assignment problem into a minimization one?
                                                        PART-B
  1. Find the non-degenerate basic feasible solution for the following transportation problem 
        using:
                a) North-west corner Rule 
                b) Least cost Method 
                c) Vogel’s Approximation method.

To                                          Supply    
                                  2          11             10         3         7             4
         From                1           4               7           2         1             8 
                                  3           9              4            8         12           9
      Demand                 3           3            4             5          6                                  (16)
                                               
2. A company has 3 plants A,B, and C , three warehouses X,Y,Z. A number of units  available at 
         the plants is 60,70,80 and the demand at X,Y,Z are 50,80,80 respectively. The unit cost of 
          the transportation is given in the following table  
 X Y Z
A 8 7 3
B 3 8 9
C 11 3 5

Find the allocation so that the total transportation cost is minimum.                     (16)

D1   D2 D3 D4 Supply
O1 11     13      17     14   250
O2 16 18 14 10 300

O3 21 24 13 10 400

Demand 200 225 275 250 950

3.  Find an optimal solution to the  TP    :                                                                 (16)

4. A company has 4 machines to do 3 jobs. Each job can be assigned to one and only one 
         machine. The cost of each job on each machine is given below. Determine the job 
          assignments which will minimize the total cost.                                           (16) 
                                             .
5. Solve the transportation problem.                                                                                  (16)
                                        Destination
                                                                A      B          C    D

1               11         20  7   8                          
                             Source      2             21           16            20           12
                                               3                8             12            18             9
6. Obtain an optimum basic feasible solution to the following transportation problem.
                                                                   To                              Available
                                                         7     3   2  2
                                   From        2    1   3  3
                                               3    4         6                    5          (16)
                                       Demand        4    1   5

7. Find the optimum basic feasible solution to the following Matrix using least cost method for  
         finding the critical solution
                                                     Market
                                       A B C D E  Available
                          P    4 1 2 6 9       100
Factory    Q    6 4 3 5 7                120
                           R    5 2 6 4 8       120
         Demand                40 50 70 90 90  (16)
8. A department has five employees with five jobs to be performed. The time (in hours) each man 
          will take to perform each job is given in the cost matrix.
     Employees
                                     I II III IV V
                    A   10 5 13 15 16
        B  3 9 18 13 6
Jobs        C  10 7 2 2 2 
         D  7 11 9 7 12
           E  7 9 10 4 12
      How should the jobs be allocated, one per employee, so as to minimize the total man-hours?
9. A company has a team of four salesman and there are four districts where the company wants to its 
         business. After taking into account the capabilities of salesman and the nature of district, the 
        estimates that the profit per day in rupees for each salesman in each salesman in each district is                      
         as below.
    1 2 3 4 
   A 16 10 14 11 
   B 14 11 15 15 
   C 15 15 13 12
   D 13 12 14 15
Find the assignment of salesman to various districts which yield maximum profit.

UNIT-III
INTEGER PROGRAMMING MODELS
PART-A
1. Define integer programming problem? 
2. What are the methods used in solving IPP  
3.  Define a mixed integer programming problem. 
4.  Differentiate between pure and mixed IPP. 
5. Explain Gomorian constraint (or) Fractional Cut constraint. 
6. Where is branch and bound method used?

PART B
1. Solve the following mixed integer programming problem by using Gomory’s cutting plane 
         method  
                    Maximize Z = x1+x2
                   Subject to the constraints
                                         3x1+2x2 ≤ 5,  
                                         x2 ≤  2 
                                        and x1,x2 ≥0,    x1  is an integer  
                                                     
 2. Solve the following integer programming problem 
                    Maximize Z = 2x1+20 x2-10x3
                     Subject to the constraints
                                        2x1+20x2+4x3 ≤ 15,  
                                         6x1+20x2+4x3   = 20,               
                                          x1, x2, x3  ≥ 0  and are integers
     
3. Find an optimum integer solution to the following LPP
                       Maximize Z = x1+2x2     
                       Subject to the constraints
                                            2x2≤ 7,     
                                             x1+x2≤ 7        
                                             2x2≤ 11       
                                               x1, x2≥0 , x1, x2 are integers 
4. Solve the following all integer programming problem using the Branch and bound method. 
                           Minimize Z = 3x1+2.5x2
                            Subject to the constraints
                                                              x1+2x2 ≥ 20,  
                                                             3x1+2x2 ≥ 50 
                                                               and x1,x2  are nonnegative integers

5. Use Branch and Bound technique to solve the following  
                                  Maximize Z = x1+4x2
                                  Subject to the constraints
                                                                    2x1+4x2≤ 7,  
                                                                     5x1+3x2≤15 
                                                                      and x1, x2 ≥0 and are integers  
6. Solve the following mixed integer programming problem.
                                 Maximize Z = x1+x2
                                 Subject to the constraints
                                                              2x1+5x2≤ 16,  
                                                             6x1+5x2≤30
                                                              x2 ≥0,    x1, Non – negative integers  .
                            
UNIT-IV
SCHEDULING BY PERT AND CPM
PART-A
   
  1. What are the three types of float? 
  2. What is a network?
  3. Define the cost time slope of an activity. 
  4. Define crash time and crash cost  
  5.  Distinguish between PERT and CPM
  6. What is total float? 
  7. Define critical activity and critical path.
  8. Define activity.
  9. Define Dummy activity
 10. Define Dandling.
 11. Write down the formulae for computing earlier start, Latest start, earliest finish, Latest finish?
 12. Define optimistic time estimate.
 13. What is pessimistic time estimate?
 14. Define most likely estimate. 
 15. Define free float.

PART B
1. A project schedule has the following characteristics  
  
  Activity 1-2 1-3 2-4 3-4 3-5 4-9 5-6 5-7
Time(days) 4 1 1 1 6 5 4 8
Activity 6-8 7-8 8-10    9-10    
Time(days) 1 2 5 7    
                From the above table  
                             (1) Construct a network diagram 
                             (2) Compute the earliest event time and latest event time 
                             (3) determine the critical path and total project duration 
                             (4) Compute total float, free float for each activity.
                                                     
2.   Listed in the table are the activities and sequencing requirements necessary for the     
       completion of research report. 
Activity   A B C  D  E F G H I J K L M
Duration 4 2 1 12 14 2 3 2 4 3 4 2 2
Immediate 
Predecessors  E A B K - E F F F I,L C,G,H D I,L

Find the critical path and also find the total float and the free float for each non-critical   
          activity            
                                                                                    
  3. A small maintenance project consists of the following jobs whose precedence    
         relationships is given below  
Job 1-2 1-3         2-3 2-5 3-4 3-6         4-5 4-6        5-6 6-7
Duration 15 15 3 5 8 12 1 14 3 14
(days)          
                    (i) Draw an arrow diagram representing the project 
                    (ii) Find the total float for each activity 
                    (iii) Find the critical path and the total project duration     
                                        
4.    (a)  Explain in detail about various phases of project management.                          
       (b). Calculate the earliest start, earliest finish, latest start and latest finish of each activity of   
              the project given below and determine the critical path of the project 
       Activity : 1-2       1-3     1-5      2-3       2-4        3-4       3-5     3-6       4-6        5-6 
       Duration :  8          7       12       4          10          3          5         10        7            4

5. The following table shows the jobs of a network along with their time estimates 
Job 1-2 1-6 2-3 2-4 3-5 4-5 6-7  5-8 7-8  
a(days) 1 2 2 2 7 5 5  3 8  
m(days) 7 5 14 5 10 5 8  3 17  
b(days) 13 14 26 8 19 17 29  9 32

Draw the project network and find the probability that the project is completed in 40 days.                                                                                                                     
 6. A Project has the following activities and other characteristics:
 Estimated Duration (in weeks)
Activity Optimistic Most likely Pessimistic
(i-j)   
1-2 1 1 7
1-3 1 4 7
1-4 2 2 8
2-5 1 1 1
3-5 2 5 14
4-6 2 5 8
5-6 3 6 15

(i)   What is the expected project length? 
(ii)  What is the probability that the project will be completed no more than 4 weeks later than expected time? 
7. The following data is pertaining to project with normal time and crash time 
         Jobs  Normal   Crash
  Time  Cost  Time  Cost
         1-2 8  100  6  200
        1-3 4  150  2  350
       2-4 2  50  1  90
       2-5 10  100  5  400
       3-4 5  100  1  200
      4-5  3  80  1  100
                   a) If the indirect cost is Rs.100 per day. Find the least cost Schedule
                   b) What is the minimum duration?
                                                   UNIT V
QUEUING MODELS
PART A
1. Define a queue
2. Define transient and steady state 
3 Explain the queue discipline and its various forms 
4. Explain Kendall’s notation.
5. People arrive at a theatre booth in poison distributed arrival rate of 25 per hour. Service time is  
        constant at 2minutes.Calculate the mean number in the waiting line.
6. What are the basic characteristics of a queuing system?
     
PART – B
1. Arrivals of a telephone booth are considered to be poisson with an average  time of 10 min.     
        between one arrival and the next. The length of a phone call is assumed to be distributed 
        exponentially with mean 3 min. 
               (i) What is the probability that a person arriving at the booth will have to wait?  
               (ii) The telephone department will install a second booth, when convinced that an arrival  
                      has to wait on the average for at least 3 min. for phone. By how much the flow of   
                     arrivals should increase in order to justify a second booth?        
              (iii) What is the average length of the queue that forms time to time?   
              (iv)  What is the probability that it will take him more than 10 minutes altog

Title:
Resource management techniques lecture notes

Subject:
Human resource management

Institute:
P.R.Engineering college

Resource management techniques lecture notes P.R.Engineering college

Resource management techniques lecture notes in Human resource management uploaded at P.R.Engineering college

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