OMBD - QB Wth Answer - June 2012-1

VINAYAKA MISSIONS UNIVERSITY, SALEM FACULTY OF MANAGEMENT STUDIES – VMKV ENGINEERING COLLEGE MBA – II SEMESTER (MBA 2009 REGULATIONS)

47109203 - Optimization Models for Business Decisions QUESTION BANK UNIT-I: Linear Programming Programming Problem (LPP) Part – A (1 Mark) 1. De Defin finee Ope Opera ratio tions ns Rese Resear arch. ch.

“Operat “Ope rations ions Res Resear earch ch is the appl applicat ication ion of sci scienti entific fic met methods hods to com comple plex x prob problem lemss arising from operations involving large systems of men, materials, and money in industry, business, busines s, government government and defence”. defence”. -

UK Op Oper erat atio ions ns Re Rese sear arch ch So Soci ciet ety y

2. Wh What at are are the dif differ ferent ent pha phases ses in OR? OR?

(i). Judgment phase (ii). Research phase (iii). Action phase 3. Wha Whatt is a Linea Linearr Progr Programm amming ing Probl Problem? em?

Linear Line ar Pro Progra grammi mming ng is the mat mathem hematic atical al tec techniq hnique ue whi which ch invo involve lvess the all allocat ocation ion of scarce or limited resources in an optimal manner on the basics of a given criterion of optimality. 4. Define feasible region. A region in which all the constraints are satisfied, it is called as feasible region. It is also called as Solution Space. 5. Wha Whatt is altern alternativ ativee optim optimal al solutio solution n in LPP LPP? ?

If a LPP has more than one optimal solution, it is said to be an Alternative/Multiple optimal solution. 6. De Defin finee basic basic feas feasib ible le solut solution ion..

A feasible solution to an LPP which is also the basic solution is called the basic feasible solution. i.e., all basic variables assume non – negative values. 7. De Defin finee unb unbou ounde nded d sol soluti ution on..

When the value of decision variables in LPP is permitted to increase infinitely without violating the feasibility condition, then the solution is said to be unbounded solution. 8. Wh When en an an LPP LPP is sai said d to be be infeas infeasib ible? le?

MBA – OMBD Question Bank – 2012

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In LPP there are no points that satisfy all the constraints of the given problem, it is said to be infeasible (or) no feasible solution. 9. Wha Whatt are the metho methods ds used to solve solve an LPP LPP involving involving artific artificial ial variable variables? s?

a. Big M – Method Method (or) Method of Penalties Penalties (or) (or) Charnes Charnes Penalty Penalty Method b. Two - Phase Phase simplex simplex Method. Method. 10. State the fundamental fundamental conditions conditions in the basis of the simplex simplex method. method. 

The Feasibility condition: It ensures that if the starting solution is basic feasible, only

basic feasible feasible solutio solutions ns will be be obtained obtained during computa computations. tions. 

The Optimality condition: It guarantees that only better solutions (as compared to the

current solution) will be encountered. 11. What is key key column and and how is it selected? selected?

Key column is the column which gives the entering variable column and is selected by most negative value in the net evaluation (Z j – C j). It is also called as Pivot column. 12. When does the simplex simplex method indicate indicate that the LPP has unbounded solution? solution?

The indication of unbounded solution of LPP can be obtained if all the variables in the key column are negative. 13. Wha Whatt is a slack variabl variable? e?

Slack variable is a non – negative variable which is added to the left hand side of the constraint equation to convert the the inequality less than than or equal (≤) in to equality equation. Slack variables refer to the amount of unused resources like raw materials, labour and money. 14. What is is a surplus surplus variable? variable?

Surplus variable is a non – negative variable which is subtracted from the left hand side of the constraint to convert the inequality greater greater than or equal (≥) into an equation. Surplus variable is the amount of resources by which the left hand side of the equation exceeds the minimum limit. 15. What is is an artificial variable? variable?

Artificial variable is a non – negative variable introduced in the constraint greater than or equal (≥) in order to get the initial basic feasible solution. Artificial variables are temporary slack variables which are used for purposes of calculation, and are removed later. 16. Define Iso Profit Line. The obje objectiv ctivee func functio tion n of max maximi imizat zation ion is repr represe esented nted by ass assumi uming ng sui suitabl tablee out outcome come (revenue) and is known as Iso Profit line.

17. Defi Define ne Iso Cost Cost Line. Line.


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In LPP there are no points that satisfy all the constraints of the given problem, it is said to be infeasible (or) no feasible solution. 9. Wha Whatt are the metho methods ds used to solve solve an LPP LPP involving involving artific artificial ial variable variables? s?

a. Big M – Method Method (or) Method of Penalties Penalties (or) (or) Charnes Charnes Penalty Penalty Method b. Two - Phase Phase simplex simplex Method. Method. 10. State the fundamental fundamental conditions conditions in the basis of the simplex simplex method. method. 

The Feasibility condition: It ensures that if the starting solution is basic feasible, only

basic feasible feasible solutio solutions ns will be be obtained obtained during computa computations. tions. 

The Optimality condition: It guarantees that only better solutions (as compared to the

current solution) will be encountered. 11. What is key key column and and how is it selected? selected?

Key column is the column which gives the entering variable column and is selected by most negative value in the net evaluation (Z j – C j). It is also called as Pivot column. 12. When does the simplex simplex method indicate indicate that the LPP has unbounded solution? solution?

The indication of unbounded solution of LPP can be obtained if all the variables in the key column are negative. 13. Wha Whatt is a slack variabl variable? e?

Slack variable is a non – negative variable which is added to the left hand side of the constraint equation to convert the the inequality less than than or equal (≤) in to equality equation. Slack variables refer to the amount of unused resources like raw materials, labour and money. 14. What is is a surplus surplus variable? variable?

Surplus variable is a non – negative variable which is subtracted from the left hand side of the constraint to convert the inequality greater greater than or equal (≥) into an equation. Surplus variable is the amount of resources by which the left hand side of the equation exceeds the minimum limit. 15. What is is an artificial variable? variable?

Artificial variable is a non – negative variable introduced in the constraint greater than or equal (≥) in order to get the initial basic feasible solution. Artificial variables are temporary slack variables which are used for purposes of calculation, and are removed later. 16. Define Iso Profit Line. The obje objectiv ctivee func functio tion n of max maximi imizat zation ion is repr represe esented nted by ass assumi uming ng sui suitabl tablee out outcome come (revenue) and is known as Iso Profit line.

17. Defi Define ne Iso Cost Cost Line. Line.


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The objective function of minimization problem is represented by assuming suitable cost, a line, known as Iso Cost line. 18. List out the Model of OR. Models by Function Descriptive ptive model model  Descri 

Predictive Predic tive model model



Normative Normat ive model

Models by Structure or Physical Physical model model  Iconic or  

Analogue or Schematic Schematic models models Symbolic or Mathematical models

Models by nature of the Environment Deterministi inisticc models  Determ 

Probabilistic Probabi listic models

Models by degree of abstraction  Language Models 

Case studies

Models by the extent of Generality  General models 

Specific models

19. State the advantages advantages of of OR Models. Models. 

OR Models provides a logical and systematic approach to the problem.



OR Models indicates the scope as well as limitations of a problem.



OR Models helps in finding avenues for new research and improvements in a system.



OR Models makes the overall structure of the problem more comprehensible and helps in dealing with the problem in its entirety.

20. Write the the standard standard form of LPP. Standard Form of LPP

Objective function is Maximize or Minimize, Z = c1 x1 + c 2 x 2 + ................ + c n x n Subject to constraints constraints,,

ai 1 x1 + a i 2 x 2 + ................ + ai n x n = bi ,

i = 1, 2, 3, ……….., n

x1 , , x2 , , x3 ,………x ,………xn ≥ 0


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21. Define Redundant Constraint.

The constraint does not affect the solution space, it is said to be redundant constraint. 22. Define degeneracy of LPP.

If the minimum positive ratio for two or more rows are same, tie exist. If there is a tie, selection of key row is very difficult. In such case the problem is said to be degenerate. It can be solved by choosing the key row arbitrarily. 23. When does an LPP possess a Pseudo-optimal Solution? An LPP possesses a pseudo-optimal solution if at least one artificial variable is in the basis at positive level even though the optimality conditions are satisfied. 24. What is the indication of alternative optimal solution in simplex table?

In optimal simplex table, in the net evaluation (Z j – C j) row if zero occurs for non-basic variables it indicates that LPP has alternate solution. 25. List out the limitations of LPP? 

Linear programming is applicable only to problems where the constraints and objective function are linear i.e., where they can be expressed as equations which represent straight lines. In real life situations, when constraints or objective functions are not linear, this technique cannot be used.



Factors such as uncertainty, weather conditions etc. are not taken into consideration.



This method doesn’t take into account the effect of time.



When the constraint equations are more, the computational difficulties are enormous even when computers are used.

Part – B (8 marks)

1. A firm manufactures two products A & B on which the profits earned per unit are Rs.3/- & Rs. 4/- respectively. Each product is processed on two machines M1 and M2. Product - A requires one minute of processing time on M1 and two minutes on M2, while B requires one minute on M1 and one minute on M2. Machine M1 is available for not more than 7 hrs. 30minutes while machineM2 is available for 10 hours during any working day. Find the number of units of products A & B to be manufactured to get maximum profit. 2. Naga & Co has two bottling plants, one located at Gandhi Nagar and another at Nehru Nagar. Each plant produces three drinks, whisky, beer and fruit juices named A, B and C respectively. The numbers of bottles produced per day are as follows.


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Plant at Gandhi Nagar Nehru Nagar Whisky (A) 1500 1500 Beer (B) 3000 1000 Fruit Juices (C) 2000 5000 A market survey indicates that during the month of April, there will be a demand of Products

20,000 bottles of whisky, 40,000 bottles of beer and 44,000 bottles of fruit juices. The operating costs per day for plants at Gandhi Nagar and Nehru Nagar are 600 and 400 monetary units. For how many days each plant be run in April so as to minimize the production cost, while still meeting the market demand? 3.

(i) A farmer has 1000 acres of land on which he can grow corn, wheat or soyabeans. Each

acre of corn costs Rs.100 for preparation, requires 7 man-days of work and yields a profit of Rs.30. an acre of wheat costs Rs.120 to prepare 10 man – days of work and yields a profit of Rs.40. an acre of soybeans costs Rs.70 to prepare 8 man – days of work and yields a profit of Rs.20. if the former has Rs1, 00,000 for preparation and can count on 8,000 man – days of work. Formulate this as an LPP.

(4 Marks)

(ii) Solve the following LPP graphically

Min. Z = 4X1 + 5X2 Subject to the constraints X1 + X2 ≥ 10 2X1 + 5X2 ≥ 35 & X1, X2 ≥ 0

(4 Marks)

4. (i) A person wants to decide the constituents of a diet which will fulfill his daily requirements of proteins, fats, carbohydrates at the minimum cost. The choice is to be made from four different types of foods. The yields per unit of these foods are given below. Food type

Proteins

Yield per unit Fats Carbohydrates

Cost per unit (Rs)

A

3

2

6

45

B

4

2

4

40

C

8

7

7

85

D

6

5

4

65

Minimum requirement 800 200 700 Formulate the linear programming model for the problem.

(4 Marks)

(ii) Solve the following LPP graphically MBA – OMBD Question Bank – 2012

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Maz. Z = 3X1 + 2X2 Subject to the constraints X1 - X2 ≤ 1 X1 + X2 ≥ 3 & X1, X2 ≥ 0

(4 Marks)

5. Use Simplex method to solve the following LPP Max. Z = 100X1 + 200 X2 + 50X3 Subject to the constraints 5X1 + 5X2 + 10X3 ≤ 1000 10X1 + 8X2 + 5X3 ≤ 2000 10X1 + 5X2

≤

500

and X1, X2, X3 ≥ 0 6. Use the simplex method to solve the LPP Min

Z = -X1 + X2 -3X3

Subject to the constraints X1 + X2 + X3 ≤ 10 -2X1 + X3 ≥ -2 2X1 -2X2 + 3X3 ≤ 0 and X1, X2, X3 ≥ 0 7. A firm manufactures two types of products P1 and P2 and sells them at a profit of Rs.2/- on type P1 and Rs. 3/- on type P2. Each product is processed on two machines G and H. Type P1 requires one minute of processing time on G and two minutes on H; type P2 requires one minute on G and one minute on H. The Machine G is available for not more than 6 hours 40 minutes while Machine H is available for 10 hours during any working day. Formulate the problem as a LPP and solve graphically. 8. Use two phase simplex method to solve the following LPP Max.Z = 5X1 + 3X2 Subject to the constraints 2X1 + X2 ≤ 1 X1 + 4X2 ≥ 6 and X1, X2 ≥ 0 MBA – OMBD Question Bank – 2012

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9. Show that there does not exists any feasible solution to the following LPP Max. Z = 2X1 + 3X2 + 5X3 Subject to the constraints 3X1 +10 X2 + 5X3 ≤ 15 33X1 -10 X2 + 9X3 ≤ 33 X1 + 2X2 + X3 ≥ 4 and X1, X2, X3 ≥ 0 10. Show that the following LPP has an unbounded solution. Max. Z = 4X1 + X2 + 3X3 + 5X4 Subject to the constraints 4X1 - 6X2 - 5X3 - 4X4 ≥ - 20 3X1 -2X2 + 4X3 + X4 ≤ 10 8X1 - 3X2 + 3X3 + 2X4 ≤ 20 and X1, X2, X3,X4 ≥ 0

Unit – II: Transportation and Assignment problems Part - A (1 Mark) 1. Define a transportation problem.

TP is a special kind of LPP in which goods are transported from a set of sources to a set of destinations subject to the supply and demand of the source and destination, respectively, such that the total cost of transportation is minimized. 2. Write the mathematical form of a transportation problem. m

Minimize Z

n

∑ ∑ i =1

C ij X ij

j =1

Subject to n

∑ X ij

= ai ; i = 1,2...m

j =1 m

∑ xij

= b j ; j = 1,2....n

i =1

xij ≥ 0, i = 1,2...m, j = 1,2......n

3. Define basic feasible solution.


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A feasible solution is called a basic feasible solution if the number of non – negative allocations is equal to m + n – 1 where m is the number of rows, n is the number of columns in a TP table. 4. Define optimal solution.

Optimal solution is a feasible solution (not necessarily basic) which minimizes the total cost. 5. Define non – degeneracy in a transportation problem.

A basic feasible solution to a (m X n) TP that contains exactly m + n – 1 non – negative allocations in independent position. 6. What do you understand by degeneracy in a transportation problem?

A basic feasible solution to a (m X n) TP that contains less than m + n – 1 non – negative allocations is called degeneracy in a TP. 7. How to resolve the degeneracy in a transportation problem?

This degeneracy in a TP can be resolved by adding one (more) empty cell having the least cost and is of independent position with a non – negative allocation (ε >0). 8. Define balanced transportation problem.

A TP is said to be balanced, if the total supply from all the sources is equal to the total

demand in all the destinations. i.e.,

m

n

i =1

j =1

∑ ai = ∑ bj

9. How do you convert an unbalanced transportation problem in to a balanced one?

The unbalanced TP is converted into a balanced one by adding a dummy row (source) or dummy column (destination) whichever is necessary. The unit TP cost for the dummy row/column elements are assigned zero. Then the problem is solved by the usual procedure. 10. List out the methods used to obtain an IBFS in a transportation problem.

a. North – West Corner Rule (NWC) b. Row Minima Method (RMM) c. Column Minima Method (CMM) d. Least Cost Method (LCM) e. Vogel’s Approximation Method (VAM) 11. List out the methods used to obtain an optimal solution in a transportation problem. 

Stepping Stone Method



MODI method


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12. State the necessary and sufficient condition for the existence of a feasible solution to a TP.

The necessary and sufficient condition for the existence of a feasible solution is a solution that satisfies all conditions of supply and demand. 13. When does a TP have a unique solution?

While doing optimality test, if the entire empty (non-basic) cell evaluation,

Δ j

= Cij – (ui + v j) are positive, then the problem is said to have an unique solution. 14. What is the indication for an alternate optimal solution in TP? While performing optimality test, if some of empty (non-basic) cell evaluation, Δ j = Cij – (ui + v j) = 0, then the problem is said to have an alternate optimal solution. 15. Vogel’s Approximation Method results is the most economical initial basic solution? Why?

Yes, it is true. In this method we are allocating the items only at the least cost and hence this method reduces the number of iterations towards optimality. Also it gives near optimal solution. Some time it may be optimal solution. 16. List the merits and demerits of using North-West Corner Rule. Merits: Since the cost factor is not considered in each time, this method is easy to compute the

total transportation cost. Demerits: Since the allocations have been made without considering the unit cost, the solution

obtained may not be the best solution. Therefore, to get an optimal solution it requires more number of iterations. 17. What is an assignment problem?

The assignment problem is a special type of allocation problem in which a number of operations are to be assigned to an equal number of operators, where each operator performs only one operation at a minimum cost or maximum profit. 18. What is a traveling salesman problem?

In this model a salesman has to visit ‘n’ cities. He has to start from a particular city (home city), visit each city once and then return to his starting point (home city), 19. State the objectives of traveling salesman problem.

The main objective of a salesman is to select the best sequence in which he visited all cities in order to minimize the total distance traveled or minimize the total time. 20. When is there an indication of an alternate solution in an assignment problem?

If the final cost matrix contains more than the required number of zeros for assignment at independent position, then it indicates that the problem has an alternate optimal solution. MBA – OMBD Question Bank – 2012

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21. State the difference between the TP and the AP. 

The cost matrix in TP is not necessarily a square matrix, whereas in AP, it is

a square matrix. 

Supply and demand at any source and at any destination may be positive

quantity ai, b j in TP, whereas in AP it will be 1 i.e., ai = b j = 1. 

The allocations Xij in the case of TP can take any positive values satisfying

the rim requirements, whereas in AP, Xij will take only two possible values 1 or 0. 

TP will not provide degeneracy always, whereas in AP will always provide

degeneracy. 22. Write the mathematical form of AP.

Minimize Z

n

n

i =1

j =1

∑ ∑ C ij X ij

Subject to n

X ij ∑

=1; i =1, 2..., n

j = 1 n

xij ∑

=1; j =1, 2...., n

i= 1

and xij =0or 1∀ i , j 23. How do you solve the maximization case of AP? To solve the maximization problem, first we convert the given maximization matrix into an equivalent minimization matrix form by subtracting all the elements in the given profit matrix from the highest element in that matrix. Then the problem is a minimization and can be solved by the usual assignment method (Hungarian Method). 24. Give any two applications of assignment problem in Business. 

AP is used in production environment in which the number of jobs are assigned to number of workers or machines in such a way that the total time (or cost) to complete all the jobs will be minimum.



AP is used in traveling salesman problem.

25. Why can the TP technique or the simplex method not be used to solve an assignment problem?

The TP technique or the simplex method not be used to solve an assignment problem because of degeneracy. MBA – OMBD Question Bank – 2012

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Part – B (8 Marks)

1. A company has 3 plants A, B, C and three warehouses X, Y, Z. The number of units available at the plants are 60, 70, & 80 and the demand at X, Y, & Z are 50, 80, & 80 respectively. The unit cost of transportation has been displayed in the table. X Y Z A 8 7 3 B 3 8 9 11 3 5 C Formulate the above data as transportation modal and obtain an optimum solution.

2. A product is manufactured by 4 factories A, B, C, & D. Their unit production costs are 2/-, Rs. 3/- Re.1/- and Rs. 5/- respectively. Production capacity of the factories are 50,

Rs. 70,

40, and 50 units respectively. The product is supplied to four stores S1, S2, S3, & S4, requirements of which are 25, 35, 105, and 20 units respectively. Unit transportation costs are given below. S1

S2

S3

S4

A

2

4

6

11

B

10

8

7

5

C

13

3

9

12

D

4

6

8

3

Find the transportation plan such that the total production and transportation cost is minimum. 3. There are four jobs to be assigned to the machines. Only one job could be assigned to one machine. The amount of time in hours required for the jobs in machines are given below. Machine

Job

A

B

C

D

E

1

4

3

6

2

7

2

10

12

11

14

16

3

4

3

2

1

5

4

8

7

6

9

6


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Find an optimum assignment of jobs to the machines to minimize the total processing Find for which machine no job is assigned. What is the total processing time to

time.

complete

all the jobs?

4. Solve the following TP, Warehouse Factory

W1

W2

W3

W4

Capacity

F1

19

30

50

10

7

F2

70

50

40

60

9

F3

40

8

70

20

18

Requirement

5

8

7

14

5. Solve the transportation problem with unit TP cost in rupees and units of demand and supply as given below. Destination D1

D2

D3

D4

Capacity

Source S1

10

13

11

8

65

S2

9

12

12

10

44

S3

13

9

11

9

41

Requirement

60

40

55

45

6. A company produced two products B and C. These products are marketed in four cities. The following table gives you the sales figures of the firm. Find the transportation plan to maximize the sales. Cities

Trichy

Salem

Madurai

Chennai

Supply

B

90

90

100

110

200

C

50

70

130

85

100

Demand

75

100

100

30

Product

7. A Marketing student has to select one and only one elective in each semester and the same elective should not be selected in different semesters. Due to various reasons, the expected grades in each subject if selected in different semesters, vary and they are given below. MBA – OMBD Question Bank – 2012

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Semester

Subject Marketing Services Retail Event Research Marketing Management Marketing I F E D C II E E C C C D C A III IV B A H H The grade points are H = 10, A = 9, B = 8, C = 7, D = 6, E = 5, and F = 4. How will the

student select the electives in order to maximize the total expected points and what will be his maximum expected total points?

8. The processing time in hours for the jobs when allocated to the different machines is given below. Assign the machines for the jobs so that the total processing time is minimum. Mechines

M1

M2

M3

M4

1

5

7

11

6

2

8

5

9

6

3

4

7

10

7

4

10

4

8

3

Jobs

9. A department head has four tasks to be performed and three subordinates, the subordinates differ in efficiency. The estimates of the time, each subordinate would take to perform, is given below in the table. How should he allocate the tasks one to each man, so as to minimize the total man hours? Men

A

B

C

I

9

26

15

II

13

27

6

III

35

20

15

IV

18

30

20

Task


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10. A head of department in a college has the problem of assigning courses to teachers with a view to maximizing educational quality in his department. He has available to him one professor, two associate professors and one teaching assistant (TA). Four courses must be offered and, after appropriate evaluation, he has arrived at the following relative ratings (100 = best rating) regarding the ability of each instructor to teach each of the four courses. Teachers

Course - I

Course - II

Course - III

Course - IV

Professor -1 60 40 60 20 60 50 Asso. Prof - 1 Asso. Prof – 2 20 30 40 T.A 30 10 20 How should he assign his staff to the courses to realize his objective?

11. A salesman has to visit five cities A1, A2, A3,……., A5.

70 70 60 40

The distances given in kilometers

between the five cities are as follows. To

A1

A2

A3

A4

A5

A1

-

4

10

14

2

A2

12

-

6

16

4

A3

16

14

-

8

14

A4

24

8

12

-

10

From

2 6 4 16 A5 If the salesman starts from city A1 and has comeback to city A1, which route should he select so that the total distance traveled by him is minimized.

Unit – III: Sequencing problem and Game theory Part - A (1 Mark) 1. What is a sequencing problem?

The selection of an appropriate order for number different tasks to be performed on a finite number of service facilities in order to make effective use of available facilities and achieve greater output is called sequencing. 2. Define total elapsed time.

Total elapsed time is the time between the starting time of the first job and completion time of the last job. 3. List out the types of sequencing problems.


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

Processing n jobs through 2 machines



Processing n jobs through 3 machines



Processing n jobs through m machines



Processing 2 jobs through m machines

4. Define the term idle time.

Idle time is the time for which a machine remains idle during the total elapsed time. 5. Define processing time.

Processing time is the time required by each job on each machine. 6. Write any two assumptions in sequencing problem.  

No machine can process more than one operation at a time. Each operation, once started, must be performed till completion.

7. Write the conditions for applying Johnson’s Algorithm for finding the optimal sequencing order of ‘N’ jobs through 3 machines.

The following conditions (either one or both) must be satisfied. 

Minimum processing time on Machine A ≥ Maximum Processing time on Machine B



Minimum processing time on Machine C ≥ Maximum Processing time on Machine B

If any one of the conditions satisfied, the given three machines problem can be converted into two machines problems namely G & H. where G = A + B and H = B + C 8. Write the conditions for applying Johnson’s Algorithm for finding the optimal sequencing order of ‘N’ jobs through ‘M’ machines.

The following conditions (either one or both) must be satisfied. 

Min. processing time on M/C. M1 ≥ Max. Processing time on M/C [M2, M3, …, Mm-1]



Min. processing time on M/C. Mm ≥ Max. Processing time on M/C [M2, M3, …, Mm-1]

If any one of the conditions satisfied, the given M machines problem can be converted into two machines problems namely G & H. Where, G = M1 + M2 +……. + Mm-1 and H = M2 + M3 +……..+Mm 9. Define a game.

The competitive situation with a finite number of competitor’s with conflicting interests and where the action of one depends upon the action taken by the other. (or)


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Game is defined as an activity between two or more persons involving activities by each person according to a set of rules, at the end of which each person receives some befit or satisfaction or suffers loss (negative benefit).

10. Distinguish between pure and mixed strategies.

If a player plays only one particular course of action all the time, he is said to be adopting pure strategy, whereas player plays each of his course of action a certain part of the time (i.e., in fixed proportion), he is said to use mixed strategies. 11. Define a saddle point.

A saddle point is that position in the payoff matrix where the maximin value of the row coincides with minimax value of the column. 12. What is a two persons zero sum game?

A game with two players, where the sum of the points won equals the sum of the points lost (i.e., gain of one player equals the loss of the other) is known as Two-person zero sum game. 13. Define zero sum game. Give an Example.

A game wherein the gain of one player equals the loss of other is called zero sum game. For example, A and B are the players, A’s gain is equal the loss of the player B. two person zero sum game is always zero sum game. 14. What is meant by minimax principle?

Minimax principle is the principle minimizes the maximum losses. Minimax is the maximum of each column and take the minimum among the maximum values (i.e., maximum of row minima). 15. State the rules of dominance.

(i) If all the elements in a column (say K th

column) are greater than or equal to he

corresponding elements in another column (R th column), K th column is dominated by R th column. (ii) If all the elements in a row (say I th row) are less than or equal to the corresponding elements in another row (say Jth row), Ith row is dominated by Jth row. 16. What are the types of games that can be solved graphically?

The games in which the payoff matrix is of the form (m X 2) and (2 X n) are solved graphically. 17. Define the term players.

Finite number of participants (competitors) in a game is called players. The players may be any two companies competing for tenders, two persons bidding in a game etc… MBA – OMBD Question Bank – 2012

16

18. When do you say a game is stable?

A game is sad to be stable, if there is a saddle point.

19. Define value of the game.

The value of the game is defined as the expected outcome of the game when players follow their optimal strategies. 20. What kind of games are solved graphically?

The games in which the payoff matrix in the form of (m x 2) or (2 x n), they can b solved by using graphical method.

21. Find the Dominating row and Dominating column in the payoff Matrix

5 -2 -4

4 1 8

2 -1 5

Row II is dominated by row I and Column II is dominated by Column III. 22. What is meant by fair game?

A game is fair, if the value of minimax and the value of maximin is equal to zero

i.e.,

Minimax = Maximin = 0. 23. When do you say a game is strictly determinable?

A game is strictly determinable, if the value of maximin and minimax is equal to the game value. i.e., Maximin = V = Minimax. 24. Define Strategy.

Strategy is a set of rules (Programmes) that specifies which of the available courses of action the player should make at each play. (Or)

Strategy is defined as a complete set of plans of action specifying precisely what the player will do under every possible future contingency that might occur during the play of the game. 25. When do players apply mixed strategies?

Players apply mixed strategies when there is no saddle point in the given payoff matrix.


17


1. There are five jobs each of which has to go through four machines M1, M2, M3, & M 4. in the order M1 - M2 - M3 - M4. Processing times are given below. Job

Machine

A

B

C

D

E

M1

11

13

9

16

17

M2

4

3

5

2

6

M3

6

7

5

8

4

M4 15 8 13 9 11 Find the optimal sequence and the total minimum elapsed time. And also calculate idle

time of the machines. 2. Use graphic method to find the minimum elapsed total time sequence of 2 jobs and

five

Machines, when we are given the following information. Machines Job-1

Job-2

Sequence

A

B

C

D

E

Time (in hrs)

2

3

4

6

2

Sequence

C

A

D

E

B

Time (in hrs)

4

5

3

2

6

3. (i) Find the sequence that minimizes the total elapsed time (in hrs) required to complete the following jobs on 2 machines in the order M1 - M2. Job

:

A

B

C

D

E

F

G

Machine M1 :

8

6

10

11

10

14

4

Machine M2 :

5

3

7

12

8

6

7

Also find out the idle time for the machines. (ii) Solve the following game

(5 Marks) (3 Marks)

Player B I I


3

II 2

18

Player A

II

-2

-3

III

-4

-5

4 (i) Consider the game G with the following pay - off Player B I

Player A

II

I

2

6

II

-2

λ

a) Show that G is strictly determinable, whatever λ may be b) Determine the value of G.

(4 Marks)

(ii) Two players A & B match coins. If the coins show two heads, A wins Rs.2/-, if there are

two tails A wins nothing, and loses Re.1/-. When there are one head and one tail. Determine the optimum strategies for the players and the value of the game.

(4 Marks)

5. Find the sequence that minimizes the total elapsed time (in hrs) required to complete the following jobs on 3 machines in the order M1 - M2 - M3. Job

:

A

B

C

D

E

F

G

Machine M1 :

3

8

7

4

9

8

7

Machine M2 :

4

3

2

5

1

4

3

Machine M3 :

6

7

5

11

5

6

12

Also calculate the idle time for the machines. 6. Find an optimal sequence for the following problem. There are four jobs, each of which must go through five machines in the prescribed order. (Passing is not allowed). Processing times (in hours) are given below. Machines Jobs

A

B

C

D

E

1

7

5

2

3

9

2

6

6

4

5

10

3

5

4

5

6

8

4

8

3

3

2

6

Also find the total minimum elapsed time and idle time. 7. Using dominance property to solve the game

Player B MBA – OMBD Question Bank – 2012

19

I

Player A

II

III

IV

I

-5

3

1

20

II

5

5

4

6

III

-4

-2

0

-5

8. Using graphical method solve the rectangular game. Player B I

II

III

IV

V

I

2

-1

5

-2

6

II

-2

4

-3

1

Player A

0

9. Using graphical method solve the rectangular game. Player B I

Player A

II

I

6

5

II

3

6

III

8

4

10. Solve the following rectangular game by using graphical method. Player B

I

I

II

III

IV

3

3

4

0

4

3

7

Player A II

5

Unit – IV: Network Project Scheduling & Replacement theory Part - A (1 Mark) 1. What do you mean by Project?

Project is a combination of interrelated activities all of which must be executed in a certain order before the entire task can be completed to achieve a set goal. 2. What is a network?

Network is a graphical representation of a project’s operations and is composed of all the events and activities in sequence, along with their inter relationships and inter dependence. 3. Define an activity. MBA – OMBD Question Bank – 2012

20

An activity is any portion of a project which consumes time or resources and has a definable beginning and ending. It is denoted by an arrow with description and time estimates within parenthesis along the arrow.

4. What do you mean by concurrent activities?

Activities which can be accomplished concurrently or together are called concurrent activities. 5. Define the term total float.

Total float is the amount of time within which an activity can be delayed without affecting the project completion time. It is the difference between the LST and EST of the same activity. 6. Define earliest start time.

Earliest start time (EST) for an activity represents the time at which an activity can begin at the earliest. 7. Define latest finish time.

The latest finish time (LFT) of an activity represents the latest by which an activity must be completed without delaying the completion of the project. 8. What is slack time in a network?

It is a free time in a network. It is equal to the difference between the latest finish time and the earliest finish time (or) the difference between latest start time and the earliest start time of the activity. 9. Define Optimistic time.

It is the smallest time taken to complete the activity if every thing goes on well or under best possible conditions. 10. Define total float.

Total float is the amount of time by which the completion of an activity can be delayed beyond the earliest expected completion time without delaying the overall project. It is the difference between the late start and early start times of the same activity. 11. Define critical path.

The critical path in a network diagram is the longest continuous chain of activities (a path along which it takes the longest possible time duration) through the network starting from first to the last event. 12. State the relationship among the floats.

Independent Float ≤ Free Float ≤ Total Float 13. State any one difference between direct cost and indirect cost.


21

Direct costs are directly dependent upon the amount of resources involved in the execution of all the activities of the project. Increase in direct cost will decrease in project duration. Indirect cost is associated with general and administrative expenses, insurance cost, taxes etc…. Increase in indirect cost will increase in project duration.

14. Define the cost-time slope of an activity.

The cost slope represent the rate of increase in the cost of performing the activity per unit decrease in time and is called cost-time slope (or) cost-time trade off. It varies from activity to activity. Cost slope =

Crash Cost - Normal Cost Normal Time - Crash Time

15. Define Crashing.

The deliberate reduction of activity time by putting an extra effort is called crashing the activity. 16. Define crash time.

Crash time is the absolute minimum time required to achieve the crash cost i.e., possible and any attempts to further crash would only raise the activity cost without reducing the time. 17. Define Crash cost.

Crash cost is the least cost of completing an activity by employing all possible means like overtime, additional resources etc… i.e., the activity cost corresponding to the crash time is called the crash cost. 18. Define optimum duration of a project.

The total project cost is the sum of direct cost and indirect cost. It is the time duration of a project at which the total project cost associated it is minimum. (Or)

Optimum duration of a project is the duration, for which the total cost associated with it is minimum. 19. Define the least duration of a project.

Least duration of a project is the minimum duration beyond which no more crashing the activity is possible. Here, the total cost associated with it is not necessarily minimum. 20. What is resource scheduling?

Resource scheduling is the effective allocation of available resources to various activities in such a manner that the allocation is considered as acceptable under the given situation. MBA – OMBD Question Bank – 2012

22

21. What is resource leveling?

Resource leveling refers to the scheduling of activities within the limits of the available floats in such a way that the variations in resource requirements are minimized. (Or)

There are various activities in a project demanding varying levels of resources. The overall resources of the organization are limited. The demand on certain specified resources should not go beyond the specified level. This operation of resource allocation is called resource leveling or Load leveling. 22. What is replacement Problem?

The replacement problems are concerned with the situations that arise when some items such as men, machines, electric light bulbs, etc… need replacement due to their decreased efficiency, failure of breakdown. Such decreased efficiency or complete breakdown may either be gradual or all of a sudden. (Or)

Efficiency of certain items decreases due to wear and tear and require expensive maintenance cost. Certain items like bulb fail suddenly. In such cases the old items have to be replaced by new ones to prevent any further increase in expenditure. This is called replacement. 23. Mention any two situations where the replacement of items is necessary? 

The old item has become in worse condition and works badly or requires expensive maintenance.



The old item has failed due to accident or otherwise and does not work at all, or the old item is expected to fail shortly.



A better or more efficient design of machine or equipment has become available in the market.

24. What is salvage value?

Salvage value is the actual worth or cost of machine at the given period of time. When the age of the machine increases, the salvage value decreases. It is also known as resale value. 25. What is meant by running cost?

The cost which is required to maintain and run to operate the machine is called running cost. 26. Define optimum replacement policy.

Replace the equipment at the end of n years, if the maintenance cost in the (n + 1) th year is more than the average total cost in the nth year and the nth year’s maintenance cost is less than the previous year’s average total cost. 27. What are the types of failures? MBA – OMBD Question Bank – 2012

23



Gradual failure



Sudden failure o

Progressive failure

o

Regressive failure

o

Random failure

28. Define group replacement.

Under this policy we take decisions as to when all the items should be replaced, irrespective of whether they have failed or not, with a provision that if any item fails before the replacement time it may be replaced individually. 29. What are the types of failures in replacement theory? (a) Replacement of items with gradual deterioration 

Replacement of items that deteriorate with time, ignoring time value of money.



Replacement of items that deteriorate with time, considering time value of money.

(b) Replacement of items that fail suddenly 

Individual Replacement Policy



Group Replacement Policy

30. What is discount factor?

Let r% be the rate at which money value decreases. The present worth factor of unit amount to be spend after one year is given by V = (1 + r)-1 where, V is called the discount factor. It is also called present worth factor. (Or)

The present worth factor of unit amount to be spent after one year is given by V = (1 + r) -1, where r is the interest rate, then V is called discount factor or discount rate.


1. Consider a project consisting of 7 jobs A, B, …….., G with the following precedence relations and time estimates(days). Job Predecessors a m b A 2 5 8 B A 6 9 12 C A 5 14 17 D B 5 8 11 E C, D 3 6 9 F 3 12 21 G E, F 1 4 7 Draw the project network and find the probability that the project will be completed, MBA – OMBD Question Bank – 2012

24

(i) 4 days earlier than expected. (ii) Not more than 4 days later than expected (iii) If the project due date is 30 days, find the probability of meeting the due date. (iv) If the project due date is 35 days, find the probability of meeting the due date. 2. (i) Distinguish between PERT and CPM.

(4 Marks)

(ii) Construct a network for each of the projects whose activities and their precedence

relationships are given below.

(4 Marks)

Activity A B C D E F G H Predecessor A B B C D 3. (i) Identify the critical path for the following network diagram. 4

2

J H,I

K F,G (4 Marks)

6 1

2

1

I E

2

5

3

1

4

7

3

8

9

8 5 3

4

5

(ii) A firm is considering replacement of a machine whose cost price is Rs.17500 and the

scrap value is Rs.500. The maintenance costs (in Rs.) are found from experience to be as follows. Year

:

1

2

3

4

5

6

7

8

:

200

300

3500

1200

1800

2,400 3,300 4,500

Maintenance Cost (Rs.)

When the machine should be replaced?

(4 Marks)

4. (i) The cost of equipment is Rs.10, 000. The annual operation and maintenance cost; and resale values are given below. Year

1

2

3

4

5

6

7

8

O & M cost (Rs.)

1000

1200

1400

1700

2000

2500

3000

3500

Resale value (Rs.) 6000 4000 3200 2600 Determine at what time it could be replaced?

2500

2400

2000

1600 (4 Marks)

(ii) A machine cost is Rs.500/- . Operation and maintenance costs are zero for the first year

and increase by Rs.100/- every year. If money is worth 5% every year determine the best age at which the machine should be replaced. The resale value of the machine is negligibly MBA – OMBD Question Bank – 2012

25

small. What is the weighted average cost of owning and operating the machine? (4 Marks)

5. A project consists of a series of labeled A, B, C, …….., H, I with the following relationships [W< X, Y means X & Y can not start until W is completed; X, Y
:

Time :

A

B

C

D

E

F

G

H

I

23

8

20

16

24

18

19

4

10

6. Calculate 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, Total float, Independent float and free float. Activity

1-2

1-3

1-5

2-3

2-4

3-4

3-5

3-6

4-6

5-6

3

5

10

7

4

Duration 8 7 12 4 10 (in weeks) 7. A project schedule has the following characteristics. Activity

1- 2

2- 3

2- 4

3- 5

4- 5

4- 6

5- 7

6- 7

7- 8

7- 9

8- 10

9- 10

to

1

1

1

3

2

3

4

6

2

4

1

3

tm

2

2

3

4

3

5

5

7

4

6

2

5

tp

3

3

5

5

4

7

6

8

6

8

3

7

a) Construct a PERT network diagram. b) Identify the critical path and compute the expected project completion time. c) What is the probability factor for completing the project in 30 weeks? 8. The following mortality rates have been observed for a certain electric bulb. Week

1

2

3

4

5

6

7

8

Percentage of failure 5 13 25 43 68 88 96 100 There are 1000 bulbs in a factory and its costs Rs. 4/- to replace individual bulb. If all

bulbs are replaced simultaneously then the cost would be only Re.1/- per bulb. Determine the best replacement policy.


26

9. The following failure rate have been observed for certain items 1

Month End

2

3

4

5

0.10 0.30 0.55 0.85 1.00 Probability of failure to date The cost of replacing an individual item is Rs.1.25. The decision is made to replace all items simultaneously at fixed intervals and also to replace an individual item as they fail. If the cost of group replacement is 30 paise, what is the best interval of group replacement? 10. The yearly cost of two machines A & B when the money neglected is as follow. Year 1 2 3 MA 2900 2600 2700 3400 2100 2700 MB Find their cost patterns if money value is 10% worth and hence find which machine is

most economical.

Unit – V: Decision Theory Part - A (1Mark) 1. What is decision making?

Decision making is an integral part of any business organization. It involves by choosing the best among several alternative decisions through a proper evaluation to achieve desired outcome. 2. List out the different environments in which decisions are made. 

Decision - making under certainty



Decision - making under uncertainty



Decision - making under risk



Decision - making under conflict.

3. Define payoff.

It is the effectiveness associated with specified combination of course of action and state of nature. It is also known as profits or conditional values. 4. Define opportunity loss table.

Opportunity loss table is a payoff table which represents the cost or loss incurred because of failure to take the best possible action. It is the numerical difference between the optimal outcome and the actual outcome for a given decision. 5. Define uncertainty.

Uncertainty refers to a completion when one cannot specify the relative probability distribution of the outcomes of his decision. (Or) MBA – OMBD Question Bank – 2012

27

State of knowledge in which one or more alternatives result in a set of possible specific outcomes, but where the probabilities of the outcomes are neither known nor meaningful. 6. Define certainty.

An environment in which the decision maker is in a position to know exactly what will happen by his decision during the period in which such a decision is made. 7. Define risk.

Risk refers to a situation in which one can specify the relative probability distribution of the outcomes of his decision. 8. Define the term “Act”.

The acts are the alternative courses of action of strategies that are available for decision maker. The objective is to choose the best alternative from the available alternatives. Decision alternatives are also called Action or Strategies or Courses of action. 9. Define the term “Event”.

Events are the occurrences which affect the achievement of the objectives. Events are also called States of nature or outcomes for the decision problem. The events constitute a mutually exclusive and exhaustive set of outcomes, which describe the possible behaviour of the environment in which the decision is made. 10. Define decision maker.

Decision maker is a person who is responsible for making decision. He has to select one from a set of possible courses of action. 11. What are the approaches that are used in decision environment with risk?

Expected Monetary Value Criterion (EMV) Expected Opportunity Loss Criterion (EOL) Expected Value of Perfect Information Criterion (EVPI) 12. What is Expected Monetary Value?

The expected monetary value for a given course of action is the expected value of the conditional payoff for that action. The conditional payoffs are obtained for each action by considering various act-event combinations. 13. What are the methods used for decision making under uncertainty?

Maximax (or) Minimin criterion - Criterion of Optimism Maximin (or) Minimax criterion – Criterion of Pessimism Laplace criterion – Equally likely decision Criterion of regret (savage Criterion)


28

Hurwicz criterion – Criterion of realism 14. Define Laplace criterion.

The Laplace criterion uses of all information by assigning equal probabilities to the possible payoff for each action and then selecting that alternatives which corresponds to the maximum expected payoff. It is an equally likely decision criterion. 15. Define decision tree.

A decision tree is a graphical representation of various decision alternatives, states of nature, probabilities attached to the states of nature and the conditional benefits and losses. (Or)

Type of tree-diagram used in determining the optimum course of action, in situations having several possible alternatives with uncertain outcomes. The resulting chart or diagram (which looks like a cluster of tree branches) displays the structure of a particular decision, and the interrelationships and interplay between different alternatives, decisions, and possible outcomes. 16. Define states of nature.

States of nature are the occurrences which affect the achievement of the objectives. It is also known as events. The events constitute a mutually exclusive and exhaustive set of outcomes. A future event not under the control of decision maker. 17. What is maximin principle?

The maximin criterion is based upon the conservative approach to assume that the worst possible is going to happen. The decision maker considers each strategy and locates the minimum payoff for each; and then selects that alternative which maximizes the minimum payoff. 18. State the relationship between decision and decision making.

Decision making is the systematic process of selecting the suitable course of action among the several alternatives where as decision is the final outcome of decision making process. 19. What are the steps involved in decision making process?

Determine the various alternative course of action from which the final decision is to be made. Identify the possible outcomes called the states of nature which are available to the decision maker. Tabulate the payoff function for all the decision alternatives with respect to the states of nature from different combinations. Construct the regret or opportunity loss table. Select the optimum decision criterion which results in largest payoff.


29

20. What is Expected Opportunity Loss Criterion?

The Expected Opportunity Loss (EOL) is the cost of not picking the best solution. In other words, it's the amount lost by not picking the best alternative. The minimum expected opportunity loss is found by constructing an opportunity loss table and computing EOL for each alternative. 21. What is EVPI Criterion?

The expected profit with perfect information is the expected return, in the long run, if we have perfect information before a decision is made. It may be defined as the maximum amount one would be willing to pay, to acquire effect information as to which event would occur. 22. Define Hurwicz criterion.

Hurwicz criterion stipulates that a decision maker’s view may fall somewhere between the extreme pessimism and the extreme optimism of the maximum criterion. It is made by assigning weights with certain degrees of optimism and pessimism. 23. Distinguish between decision under certainty and decision under uncertainty.

If the decision maker knows with certainty the consequences of every alternative or decision choice, the problem is a decision problem under certainty. If the decision maker faces multiple states of nature but he has no means to arrive at probability values to the likelihood of occurrence of these states of nature, the problem is a decision problem under uncertainty. 24. What are the steps involved in Maximin criterion?

Following steps are involved in Maximin criterion Determine the minimum assured payoff for each alternative. Choose that alternative which corresponds to the maximum of the above minimum payoffs. 25. What are the steps involved in EMV criterion?

Following steps are involved in EMV Criterion List conditional profit for each act-event combinations, along with the corresponding event probabilities. For each act, determine the expected conditional profits. Determine EMV for each act. Choose the act at which corresponds to the optimal EMV.


30


1. Under an unemployment promotion program, it is proposed to allow sale of news papers on the buses during the off peak hours. The vendor can purchase the news paper at a special concessional rate of 25 paise per copy against the selling price of 40 paise. Any unsold copies are, however a dead loss. A vendor has estimated the following probability distribution for the number of copies demanded. Number of copies

15

16

17

18

19

20

Probability 0.04 0.19 0.33 0.26 0.11 0.07 (a) How many copies should he order so that his expected profit will be maximum?

(b) Compute EPPI. (c) The vendor is thinking of spending on a small market survey to obtain additional information regarding the demand levels. How much should he be willing to spend on such a survey? 2. (i) A decision problem has been expressed in the following payoff table. Customer Category

Supplies level A1

A2

A3

A4

E1

7

12

20

27

E2

10

9

10

25

E3

23

20

14

23

E4

32

24

21

17

Using Hurwicz principle to find optimal solution [ α =0.5]

(4 Marks)

(ii) The details for two competing alternatives are shown in table below. Alternative - I Annual Revenue

Alternative - II

Probability

Annual Revenue

Probability

2000

0 .15

4000

0. 3

3000

0.2

2500

0.4

5000

0.4

3500

0.2

4000 0.25 1200 Find the best alternative, when the interest rate is 0%.

0.1 (4 Marks)

3. The research department of Hindustan lever has recommended to the marketing department to launch a shampoo of three different types. The marketing manager has to decide one of


31

the types of shampoo to be launched under the following estimated payoffs for various levels of sales. Estimated Levels of Sale(units) Types of shampoo

15,000

10,000

5,000

Egg Shampoo

30

10

10

Clinic Shampoo

40

15

5

Deluxe Shampoo 55 20 3 What will be the marketing manager’s decision if (i) Maximin (ii) Minimax

(iii) Maximax

(iv) Minimin (v) laplace and (vi) Hurwicz criterion [α =0.5] is applied?

4. A motor parts dealer finds that the cost of a particular item in stock for a week is Rs.20/- and the cost of a unit shortage is Rs. 50/-. The probability distribution of weekly sales in terms of hundreds is as follows. Weekly sales (’00 Units)

0

1

2

3

4

5

6

Probability

0.1

0.1

0.2

0.2

0.2

0.15

0.05

How many units per week should the dealer order? Also find the expected value of perfect information. 5. The parker flower shop promises its customers delivery within four hours on all flower orders. All flowers are purchased on the previous day and delivered to parker by 8.00AM. the next morning. Parker’s daily demand for roses is as follows Demand

7

8

9

10

Probability

0.1

0.2

0.4

0.3

Parker purchases roses for Rs.10.00 per dozen and sells them for Rs.30.00. All unsold roses are donated to a local hospital. How many dozens of roses should parker order each evening to maximize its profits? What is the optimum expected profit? 6. An ice-cream retailer buys ice-cream at a cost of Rs.5 per cup and sells it for Rs.8 per cup; any remaining unsold at the end of the day can be disposed of at a salvage price of Rs. 2 per cup. Past sales have ranged between 15 and 18 cups per day; there is no reason to believe that sales volume will take on any other magnitude in future. Find the EMV if the sale history has the following probabilities.


32

Market size

15

16

17

18

Probability

0.1

0.2

0.4

0.3

7. A company is going to develop a new product in the market. Three alternative decisions are available for the management. A1: Advertising in a television. Advertising cost is Rs. 3000/- per day A2: Appointing salesmen for marketing. Cost is Rs. 1200/- per day A3: Conducting exhibition cost Rs. 900/- per day. The unit price is fixed at Rs. 25/- product and the cost of units associated with the respective decision alternatives are 9, 5 and 11. The expected demands for the item are as follows. Demand

200

300

400

500

Probability

0.3

0.2

0.4

0.1

The company has to decide the best alternative decisions among the three decisions.

8. Dhana & Co is currently working with a process which after paying for materials, labour, etc… brings a profit of Rs. 12,000. The following alternatives are made available to the company. a) The company can conduct research (R 1) which is expected to cost Rs. 10,000 having

90% chances of success, the company gets a gross income of Rs. 25,000 b) The company conduct research (R 2) which is expected to cost Rs. 8,000 having a

probability of 60% success, the gross income will be Rs. 25,000. c) The company can pay Rs. 6000 as royalty for a new process which will bring a gross

income of Rs. 20,000. d) The company continues the current process.

Because of limited resources, it is assumed that only one of the two types of research can be carried out at a time. Use decision tree analysis to locate the optimal strategy for the company.

9. A department store with a bakery section is faced with the problem of how many cakes to buy in order to meet the day’s demand. The departmental store prefers not to sell day old cakes in competition, left over cakes are therefore, a complete loss. On the other hand, if a customer desires a cake and all of them have been sold, the customer will buy elsewhere and the sales MBA – OMBD Question Bank – 2012

33

will be lost. The store has therefore, collected information on the past sales based on selected 100 day period as shown in table below. Sales per day 15 16 17 18 20 40 30 10 No. of days Probability 0.2 0.4 0.3 0.1 Construct the conditional profit and the opportunity loss tables. What is the optimal number of

cakes that should be bought each day? A cake costs Rs. 2/- and sells for Rs. 2.50. 10. The research department of consumer products division has recommended to the marketing department to launch soap with three different perfumes. The marketing manager has to decide the type of perfume to launch under the following estimated payoff for the various levels of sales. Estimated Levels of Sale(units) Types of Perfume

20,000

10,000

2,000

I

250

15

10

II

40

20

5

III 60 25 3 Examine which type can be chosen under (a) Maximax; (b) Minimax; (c) Maximin;

(d)

Laplace and (e) Hurwicz criterion [use α =0.5] -------------------

VINAYAKA MISSIONS UNIVERSITY, SALEM MBA – OMBD Question Bank – 2012

34

FACULTY OF MANAGEMENT STUDIES (MBA 2009 REGULATION)

II SEMESTER

Optimization Models for business decisions Model Question Paper Duration: 3 hrs

Max Marks: 50 Answer all questions. All questions carry equal marks Part – A (10 X 1 = 10 Marks)

1. Define Operations Research. 2. What is a slack variable? 3. Define non – degeneracy in a transportation problem. 4. State the objectives of travelling salesman problem. 5. Define the term idle time. 6. Define zero sum game. Give an Example. 7. Define an activity. 8. What are the types of failures in replacement theory? 9. List out the different environments in which decisions are made. 10. Define state of nature. Part – B (5 X 8 = 40 Marks)

11. (a) Naga & Co has two bottling plants, one located at Gandhi Nagar and another at Nehru Nagar. Each plant produces three drinks, whisky, beer and fruit juices named A, B and C respectively. The numbers of bottles produced per day are as follows. Plant at Gandhi Nagar Nehru Nagar Whisky (A) 1500 1500 Beer (B) 3000 1000 Fruit Juices (C) 2000 5000 A market survey indicates that during the month of April, there will be a demand of Products

20,000 bottles of whisky, 40,000 bottles of beer and 44,000 bottles of fruit juices. The operating costs per day for plants at Gandhi Nagar and Nehru Nagar are 600 and 400 monetary units. For how many days each plant be run in April so as to minimize the production cost, while still meeting the market demand? (Or) (b) Show that there does not exists any feasible solution to the following LPP MBA – OMBD Question Bank – 2012

35

Max. Z = 2X1 + 3X2 + 5X3 Subject to the constraints 3X1 +10 X2 + 5X3 ≤ 15 33X1 -10 X2 + 9X3 ≤ 33 X1 + 2X2 + X3 ≥ 4 and X1, X2, X3 ≥ 0

12. (a) Solve the transportation problem with unit TP cost in rupees and units of demand and supply as given below. Destination D1

D2

D3

D4

Capacity

Source S1

10

13

11

8

65

S2

9

12

12

10

44

S3

13

9

11

9

41

Requirement

60

40

55

45

. (Or) (b) A department head has four tasks to be performed and three subordinates, the subordinates

differ in efficiency. The estimates of the time, each subordinate would take to perform, is given below in the table. How should he allocate the tasks one to each man, so as to minimize the total man hours? Men

A

B

C

I

9

26

15

II

13

27

6

III

35

20

15

Task

18 30 20 IV 13. (a) Find the sequence that minimizes the total elapsed time (in hrs) required to complete the following jobs on 3 machines in the order M1 - M2 - M3.

Job

:

A

B

C

D

E

F

G

Machine M1 :

3

8

7

4

9

8

7

Machine M2 :

4

3

2

5

1

4

3


36

Machine M3 :

6

7

5

11

5

6

12

Also calculate the idle time for the machines. (Or) (b) Using dominance property to solve the game Player B I

Player A

II

III

IV

I

-5

3

1

20

II

5

5

4

6

III

-4

-2

0

-5

14. (a) Consider a project consisting of 7 jobs A, B, …….., G with the following precedence relations and time estimates(days). Job Predecessors a m b A 2 5 8 B A 6 9 12 C A 5 14 17 D B 5 8 11 E C, D 3 6 9 F 3 12 21 G E, F 1 4 7 Draw the project network and find the probability that the project will be completed,

(i) 4 days earlier than expected. (ii) Not more than 4 days later than expected (iii) If the project due date is 30 days, find the probability of meeting the due date. (iv) If the project due date is 35 days, find the probability of meeting the due date. (Or)

(b) The yearly cost of two machines A & B when the money neglected is as follow. Year 1 2 3 2900 2600 2700 MA MB 3400 2100 2700 Find their cost patterns if money value is 10% worth and hence find which machine is

most economical.


37

OMBD - QB Wth Answer - June 2012-1

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