LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.A. DEGREE EXAMINATION – ECONOMICS

AC 4

THIRD SEMESTER – APRIL 2006

                                     ST 3100 – RESOURCE MANAGEMENT TECHNIQUES

(Also equivalent to STA 100)

 

 

Date & Time : 02-05-2006/1.00-4.00 P.M.   Dept. No.                                                       Max. : 100 Marks

PART – A

Answer all the questions.                                                                              10 ´ 2 = 20

 

1. Define slack and surplus variables in an LPP.
2. State any two applications of linear programming problem.
3. What is a transportation problem?
4. How to balance an unbalanced transportation problem?
5. What is the need for an assignment problem?
6. Define critical activity.
7. Explain i). Most likely time ii). Optimistic time in network analysis.
8. What is the objective of sequencing problem?
9. Define i). Holding cost, ii). Shortage cost.
10. What is an economic order quantity (EOQ) in inventory control?

PART – B

Answer any five questions.                                                                           5 ´ 8 = 40

 

11. A Company has 3 operational departments (weaving, processing and packing) with capacity to produce 3 different types of clothes namely suiting, shirting’s and woolens yielding a profit of Rs. 2, Rs. 4 and Rs. 3 per meter respectively. One meter of suiting requires 3 minutes in weaving, 2 minutes in processing and 1 minute in packing, similarly one meter of shirting requires 4 minutes in weaving, 1 minute in processing and 3 minutes in packing, one meter of woolen requires 3 minutes in each department. In a week, total time of each department is 60, 40 and 80 hours for weaving processing and packing respectively.

Formulate the linear programming problem to find the product mix to maximize the profit.

 

12. Solve graphically.

Max Z = 5x₁ + 3x₂

Subject to: x₁ + 2x₂ £ 18

x₁ + x₂ £ 9

0 £ x₂ £ 6

0 £ x₁ £ 4

 

 

13. Find the starting solution in the following transportation problem by least lost method.

Origin	D1	D2	D3	Supply
O1	16	20	12	200
O2	14	8	18	160
O3	26	24	16	90
Demand	180	120	150

 

14. A department head has 4 subordinate and 4 jobs to be performed. The time taken by each man to complete the job is given below.

Job	Men
	A	1	2	3	4
	B	18	26	17	11
	C	13	28	14	26
	D	38	19	18	15
	E	19	26	24	10

How should the jobs be assigned to minimize the time?

 

15. In a factory there are six jobs to perform, each of which should go through two machines A and B in the order A, B. the processing timings (hrs) for the jobs are given below.

Job	1	2	3	4	5	6
Machine A	1	3	8	5	6	3
Machine B	5	6	3	2	2	10

Find the sequence that would minimize the total elapsed time.

 

16. A small project consists of 7 activities for which the relevant data are given below.

Activity	Preceding Activities	Duration
A	———	4
B	———	7
C	———	6
D	A, B	5
E	A, B	7
F	C, D, E	6
G	C, D, E	5

Draw the arrow diagram and find the critical path.

 

17. Explain in detail ABC analysis in inventory control.
18. Explain how will you obtain the economic order quantity for a single item static model in inventory control.

PART – C

Answer any two questions.                                                               2 ´ 20 = 40

19. Solve the following linear programming problem by simplex method. Maximize Z = 4x₁ + 10x₂

Subject to 2x₁ + x₂ £ 50

2x₁ + 5x₂ £ 100

2x₁ + 3x₂ £ 90

x₁, x₂ ³ 0.

 

20. A manufacturer has distribution centers X, Y and Z. his retail outlets are A, B, C, D and E. the transport cost per unit between each center outlet is given below:

	Retail outlet
Distribution Center		A	B	C	D	E	Supply
	X	55	30	40	50	50	40
	Y	35	30	100	45	60	20
	Z	40	60	95	35	30	40
	Demand	25	10	20	30	15

Find the optimum solution to the given transportation problem.

 

21. A project consists of eight activities with the following relevant information.

Activity	Immediate predecessor	Optimistic time	Most likely time	Pessimistic time
A	——-	1	1	7
B	——-	1	4	7
C	——-	2	2	8
D	A	1	1	1
E	B	2	5	14
F	C	2	5	8
G	D, E	3	6	15
H	F, G	1	2	3

 

1. Draw the PERT network
2. Find the expected completion time and variance of each activity.

• Find the total float and free float.

1. What is the probability of completing the project in time?

 

22. a). Explain the various problems involved in the inventory management.

b). Explain in detail a single item static model with one price break with the necessary diagrams

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034      B.A. DEGREE EXAMINATION – ECONOMICS

AB 03

THIRD SEMESTER – NOV 2006

        ST 3100 – RESOURCE MANAGEMENT TECHNIQUES

(Also equivalent to STA 100)

 

 

Date & Time : 28-10-2006/9.00-12.00      Dept. No.                                                       Max. : 100 Marks

 

 

PART – A

Answer all questions.                                                                 (10 x 2 = 20 Marks)

 

1. Define slack and surplus variables.
2. Explain linear programming problem.
3. When do you say that a transportation problem is unbalanced? How to make it balanced?
4. Express a transportation problem as a linear programming problem.
5. What is the objective of a sequencing problem?
6. Write any two uses of an assignment problem.
7. State any two differences between CPM and PERT.
8. Define: a) Network             b) Activity
9. What are the components of a cost function in an inventory model?
10. Define: i) Optimistic time            ii) Pessimistic Time

 

 

PART – B

Answer any Five questions.                                                       (5 x 8 = 40 Marks)

 

11. A firm manufacturers two products A and B on which the profit earned per unit are Rs.3 and Rs.4 respectively. Each product is processed on two machines M₁ and M₂ product A requires one minute of processing time on M₁ and 2 minutes on M₂ while B requires one minute on M₁ and one minute on M₂.  Machine M1 is available for not more them 7 hours and 30 minutes, while machine M₂ is available for 10 hours during any working day.  Formulate the problem as a linear programming problem.
12. Find all the basic solutions to the following system of linear equations:

x₁ + 2x₂ + x₃  =  4

2x₁ + x₂ + 5x₃  =  5

 

13. Obtain the initial basic feasible solution for the following transportation problem using north-west corner method.

D₁        D₂        D₃        D₄        D₅        D₆    Supply

 

O₁        6         4          8         4          9         6         4

O₂        6         7          13        6          8         12        5

O₃        3         9          4         5          9         13        3

O₄        10        7          11        6          11        10        9

Demand          4         4          5          3          2         3

 

 

 

14. Four professors are capable of teaching any one of 4 different courses. Class preparation time in hours for different topics varies from professor to professor and is given in the table below.  Each professor is assigned only one course.  Determine an assignment schedule so as to minimize the total course preparation time for all courses.

 

Professor       Subject 1          Subject 2         Subject 3         Subject 4

A                     2                    10                     9                     7

B                     15                    4                      14                    8

C                     13                   14                     16                    11

D                     4                    15                     13                    9

 

15. Determine the optimal sequences of jobs that minimizes the total elapsed

time based on the following processing time on machines given in

hours and passing is not allowed.

 

Job

1          2          3         4          5

A    3          8          7         5          2

Machine   B     3          4          2         1          5

C    5          8          10        7          6

 

16. Draw the network and find the critical path for the project comprising of 9 activities

 

Activity              A         B         C         D         E          F          G         H         I

 

Immediate

Predecessor      __        __        __        A         B         C         D, E     B         H, F

 

Estimated time

(weeks)              3          5          4          2          3          9          8          7          9

 

17. Explain ABC Analysis in inventory control.

 

18. Neon lights in a campus are replaced at the rate of 100 units per day. The physical plant orders the neon lights periodically.  It costs Rs.100 to initiate a purchase order.  A neon light kept in storage is estimated to cost about Rs.2 per day.  The lead-time between placing and receiving an order is 12 days.  Determine the optimal inventory policy for ordering the neon lights.

 

PART – C

Answer any Two questions.                                                       (2 x 20 = 40 Marks)

 

19. Use simplex method to

Maximize  Z = 3x₁ + 2x₂ + 5x₃

Subject to

x₁ + 2x₂ + x₃  £ 430

3x₁ + 2x₃  £  460

x₁ + 4x₃  £ 420

x₁, x₂, x₃  ³ 0

20. A manufacturer has distribution centers at X, Y and Z. These centers have availability 40, 20 and 40 units respectively of his product.  His retail outlets at A, B, C, D and E requires 25, 10, 20 30 and 15 units respectively.  The transport cost (in rupees) per unit between each centers and outlet is given below.

Retail outlet

Distribution centre         A        B          C       D        E

X                     55        30        40       50        50

Y                     35        30        100      45        60

Z                      40        60        95        35        30

 

Determine the optimal distribution to minimize the cost of transportation.

 

21. A project is composed of 11 activities. The time estimates (in days) for which are given below:

Activity           Optimistic time           Pessimistic time           Most likely time

(1, 2)                            7                                 17                                9

(1, 3)                            10                                60                                20

(1, 4)                            5                                 15                                10

(2, 5)                            50                              110                                65

(2, 6)                            30                                50                                40

(3, 6)                            50                                90                                55

(3, 7)                            1                                 9                                 5

(4, 7)                            40                                68                                48

(5, 8)                            5                                 15                                10

(6, 8)                            20                                52                                27

(7, 8)                            30                                50                                40

 

• Draw the network diagram for the project.

1. Find the expected value and variance for each activity.

• Find the critical path.

1. Find the total float and free float for each activity.

• What is the probability of completing the project in 125 days?

22. Explain in detail a single item static inventory model with one price break with suitable diagrams.

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

BA 03

   B.A. DEGREE EXAMINATION – ECONOMICS

THIRD SEMESTER – November 2008

ST 3103 / ST 3100 – RESOURCE MANAGEMENT TECHNIQUES

 

 

 

Date : 11-11-08                     Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

PART-A

 Answer ALL the following:                                                                          (10X2=20)

 

1) Define an optimal solution.

2) When do you say that there is no feasible solution in graphical method of solving  L.P.P?

3) What is the need for an artificial variable in a L.P.P?

4) Briefly explain transportation problem.

5) Give an example for an unbalanced assignment problem and state how to make it   balanced.

6) Define a two machines and n jobs sequencing problem.

7) What is meant by idle time in a sequencing problem?

8) Distinguish pessimistic and optimistic time.

9) Define storage cost and setup cost.

10) What are the factors influencing the inventory models?

 

                                                                 PART – B

Answer any FIVE of the following:                                                           (5 X 8 = 40)

 

11(a) Write down the standard form of the general L.P.P.

(b) A firm can produce three types of cloth say A, B, C, three kinds of wool are  required for it, say red

wool, green wool and blue wool. One unit length of type A  cloth needs 2 yards of red and 3 yards of blue wool; One unit length of type B cloth  needs 3 yards of red, 2 yards of green wool and 2 yards of blue wool; One unit  length of type C cloth needs 5 yards of green wool and 4 yards of blue wool. The  firm has only a stock of 8 yards of red wool, 10 yards of green wool and 15 yards of blue wool. It is assumed that the income obtained from one unit length of type A  is Rs. 3, of type B cloth is Rs. 5 and that of type C cloth is Rs.4. Determine how the  firm should use the available material, so as to maximize the total income from the  finished cloth. Formulate the above problem as a L.P.P.    ( 3+5)

 

12) A company produces two types of a product: A and B. Each product of A type  requires twice as much

labour time as B type. If all the products are of B type only,  the company can produce 500 of these products per day. The market limit daily sales of A and B types are 150 and 250 respectively. Assuming that the profits per product  of A and B types are Rs.8 and Rs.5 respectively. Solve the L.P.P by  graphical method to maximize the profit.

 

13) Use simplex method to solve the following L.P.P:

Maximize Z = 5x₁+ 4x₂

subject to the constraints: 4x₁+5x₂ £ 10

3x₁+2x₂ £ 9

8x₁+3x₂ £ 12

x₁ , x₂ ³ 0 .

 

 

 

 

 

14) Obtain the Initial Basic Feasible Solution for the following transportation problem

using North-West corner rule and Least cost method  :

Destination

Origin	Calicut	Bangalore	Mumbai	Pune	Availability
Cochin	1	2	1	4	30
Chennai	3	3	2	1	50
Hyderabad	4	2	5	9	20
Requirement	20	40	30	10

(4+4)

15) Solve the following assignment problem:

 

	I	II	III	IV	V
1	11	17	8	16	20
2	9	7	12	6	15
3	13	16	15	12	16
4	21	24	17	28	26
5	14	10	12	11	15

 

16) Find the sequence that minimizes the total elapsed time required to complete the

following tasks on two machines:

 

Task	A	B	C	D	E	F	G	H	I
Machine  I	2	5	4	9	6	8	7	5	4
Machine II	6	8	7	4	3	9	3	8	11

 

17) A project consists of a series of tasks with the following relationships. With this

notation construct the network diagram having the following constraints:

A < D,E;     B,D <F ;     C<G;      B,G <H;       F,G <I

Find also the minimum time of completion of the project, when the time of

completion of each task is as follows:

 

Task	A	B	C	D	E	F	G	H	I
Time	23	8	20	16	24	18	19	4	10

 

18) An electrical appliance manufacturer wishes to know what the economic quantity

should be for a plastic impeller when the following information is available. Plastic

impellers are replaced at the rate of 100 units per day. It costs Rs.100 to initiate a

purchase order. One impeller kept in storage is estimated to cost about Rs.2 per day.

The lead time between placing and receiving an order is 12 days. Determine the

optimal inventory policy for ordering the plastic impellers.

 

PART – C

Answer any TWO of the following:                                                           (2 X 20 = 40)

 

19) Use penalty method to

Minimize z = x₁ + 4x₂

subject to the constraints:

x₁ + 3x₂ ³ 4000

x₁ + 2x₂ £ 3500

x₁ + 2x₂ ³ 2000

x₁, x_2,  ³ 0.                                                                  (20)

 

 

• (a) A departmental stores wishes to purchase the following quantities of dress and

tenders are submitted by 4 different manufactures who undertake to supply more

than the quantities mentioned in the table. The store estimates that its profit per

dress material will vary with the manufactures as shown in the following table:

Dress

Manufactures	A	B	C	D	E	Availability
W	275	350	425	225	150	300
X	300	325	450	175	100	250
Y	250	350	475	200	125	150
Z	325	275	400	250	175	200
Demand	150	100	75	250	200

How should the orders be placed?

(b) We have 4 jobs each of which has to go through the machines Mj_, j =1, 2,…6 in the

order M_1,M₂, .., M_6. Processing time is given below:

Machines

Jobs	M1	M2	M3	M4	M5	M6
A	18	8	7	2	10	25
B	17	6	9	6	8	19
C	11	5	8	5	7	15
D	20	4	3	4	8	12

Determine a sequence of these four jobs that minimizes the total elapsed time T.

 

• (a)Five jobs are to be processed and five machines are available. Any machine can

process any job with the resulting profit as follows:

Machines

Jobs	A	B	C	D	E
1	32	38	40	28	40
2	40	24	28	21	36
3	41	27	33	30	37
4	22	38	41	36	36
5	29	33	40	35	39

What is the maximum profit that may be expected if an optimum assignment is made?

(b) The data for a PERT network is displayed in the table given below. Determine the critical path and

the expected duration of completion of the entire project. Give answers to the following:

(i) What is the probability that the project duration will exceed 60 days?

(ii) What is the chance of completing the project between 45 days and 54 days?

Time duration (days)

Activity nodes	a	m	b
1-2	2	4	6
1-3	6	6	6
1-4	6	12	24
2-3	2	5	8
2-5	11	14	23
3-4	15	24	45
3-6	3	6	9
4-6	9	15	27
5-6	4	10	16

 

22) Explain and derive the single static model with price break.                      (20)

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.A. DEGREE EXAMINATION – ECONOMICS

YB 06

THIRD SEMESTER – April 2009

ST 3103 / 3100 – RESOURCE MANAGEMENT TECHNIQUES

 

 

 

Date & Time: 17/04/2009 / 1:00 – 4:00      Dept. No.                                                        Max. : 100 Marks

 

 

SECTION- A

Answer all the questions.                         10 x 2 =  20 marks

1. Write any two applications  of  operations  research.
2. Define basic solution for a linear programming problem.
3. Distinguish between slack and surplus variables.
4. Express a transportation problem as a linear programming problem.
5. Why is assignment problem viewed as a particular case of transportation problem?
6. What is a sequencing problem?

7 . Provide any two differences between PERT and CPM.

8. When is an activity called critical in network analysis?

9 . Write a note on   (i) setup cost    (ii) holding cost.

10 .State the assumptions of  classic EOQ model.

                                           SECTION- B                                                          

                                      Answer any five questions                               5 x 8 = 40 marks

 

11.The owner of  Metro sports wishes to determine how many advertisements to place in

the selected three monthly magazines A,B and C. His objective  is to advertise in such

a way that total exposure to principal buyers of expensive sports good is maximized.

Percentages of readers for each magazine are known. Exposure in any particular

magazine  is the number of advertisements placed multiplied by the number of

principal buyers. The following data may be used .

————————————————————————————————————

                                                                                   Magazine

———————————————————————————————————

A                                  B                        C

 

Readers                                                1 lakh                          0.6 lakh             0.4 lakh

Principal buyers                                   20%                            15%                   8%

Cost per advertisement(Rs.)                 8000                            6000                  5000

————————————————————————————————————

The budgeted amount is at most   Rs.1 lakh for the  advertisements . The owner has

already decided that magazine A should have no more than 15 advertisements and that

B and C each have at least  80 advertisements. Formulate an LP model for the problem.

 

12. Use the graphical method to solve the following LPP:

Maximize     Z = 2x₁ + 3x₂

Subject to the constraints:

x₁ + x₂  ≤  30  ,  x₁ -x₂ ≥ 0  ,  x₂ ≥ 3  ,

0≤ x₁≤ 20  and  0 ≤ x₂  ≤ 12.

 

 

 

13. Find all the basic feasible solutions of the equations:

2x₁ + 6x₂ + 2x₃ + x₄   = 3

6x₁ + 4x₂ + 4x₃ + 6x₄ = 2

 

14. Find an initial basic feasible solution of the following transportation problem using

Vogel’s approximation method:

I                     II                III             IV      Supply

A                  11                   13                17             14        250

B                  16                    18                14             10       300

C                  21                   24                13              10       400

Demand               200                225               275            250

 

15. Consider the problem of assigning five machines. The assignment costs are given

below :

Machines

Operators                 A                  B                   C                      D                      E

I                        10                 3                   10                      7                        7

II                         5                  9                    7                      11                       9

III                      13                 18                    2                       9                       10

IV                      15                  3                     2                     12                      12

Assign the   operators   to   different machines so that total cost is minimized.

 

16. Determine the optimal sequence of jobs that minimizes the total elapsed time based

on the following information processing time on machines given in hours and

passing is not allowed .

Job                :      1                   2                        3                         4                       5

Machine A    :      3                   8                        7                         5                       2

Machine B    :      3                   4                        2                         1                       5

Machine C    :      5                   8                        10                       7                       6

Also find the  idle  time  of machines A ,B and C.

 

17. The following table gives the activities in a construction project and time duration :

Activity                         Preceding activity                     Normal time (days)

1-2                                           –                                                20

1-3                                           –                                                25

2-3                                         1-2                                              10

2-4                                         1-2                                              12

3-4                                    1-3,   2-3                                            5

4-5                                    2-4  , 3-4                                          10

 

• Draw the activity network of the project .
• Determine the critical path and the project duration.
• Find the total float and free float for each activity.

 

18. Derive the classic EOQ model clearly stating the assumptions.

 

 

SECTION- C

                             Answer any two questions                                       2 x 20 = 40 marks

19. Use simplex method to

Minimize Z = x₁ – 3x₂ + 2x₃

Subject to

3x₁ – x₂ + 2x₃    ≤ 7

-2x₁ – x₂ + 2x₃    ≤ 12

-4x₁ + 3x₂ + 8x₃  ≤ 10

x₁ ≥ 0, x₂ ≥ 0, x₃ ≥ 0 .

 

20. National oil company (NOC) has three refineries and four depots. Transportation cost

per ton ,capacities and requirements are given below:

________________________________________________________________________

D1             D2            D3          D4        Capacity (tons)

________________________________________________________________________

R1                               5               7               13           10               700

R2                                          8                6               14           13               400

R3                             12              10                9           11               800

Requirement (tons)  200            600             700        400

 

Determine optimum allocation of output.

 

21. A project is composed of eleven activities, the time estimates for which are given

Below:

Activity               optimistic time        normal time          pessimistic time

       1-2                              7                              9                                  17

1-3                             10                           20                                  60

1-4                              5                            10                                  15

2-5                            50                            65                                110

2-6                            30                            40                                  50

3-6                            50                            55                                  90

3-7                              1                              5                                    9

4-7                            40                            48                                  68

5-8                              5                            10                                  15

6-8                            20                            27                                  52

7-8                            30                            40                                  50

(a) Draw the network diagram for the project.

(b) Calculate total and free floats.

(c) Determine the critical path.

(d) What is the probability of completing the project in 125 days?

 

22. (a) Derive the classic EOQ model with price break.

(b) Neon lights in an industrial park are replaced at the rate of 100 units per day.

The physical plant orders the neon lights periodically. It costs $.100 to initiate a

purchase order,  A neon light kept in storage is estimated to cost about $.0.02 per

day. The lead time between placing and receiving an order is 12 days. Determine

the optimum inventory policy for ordering the neon lights.

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