# Ignou.de

Ignou Books , Notes , Study Material , Solved Papers ## Ms-51 question bank (8)

Ms-51 question bank

Sunday, 16 February 2014 15:47

### Ms-51 June , 2010 Operations Research

June, 2010

MS-51 : Operations Research

1. (a) "Operations Research (OR) is an aid for the executive in making his/her decisions by providing him/her with needed quantitative information based on the scientific method of analysis". Discuss the statement and give atleast two examples to illustrate how operations research is helpful in decision making.

(b) A manufacturing company is producing two products A and B. Each requires processing on two machines 1 and 2. Product A requires 03 hours of processing on machine 1 and 02 hours on machine 2. Product B requires 2 hours of processing on machine 1 and 6 hours on machine 2. The unit profits for product A and product B are Rs. 10 and Rs. 20 respectively. The available time in a given quarter on machine 1 and machine 2 are 1200 hrs and 1500 hrs respectively. The market survey has predicted that not more than 400 units of product A and not more than 250 units of product B can be sold in the given quarter.  The company wants to determine the product mix to maximize the profits. Formulate the problem as linear programming mathematical model and determine the profit.

2. (a) Why is the simplex method a better technique than a graphical approach for ost real cases ? Construct the dual to the following primal problem :

Max z = 6x1 + 10x2

Subject to the constraints

4x 1 +12x2 < 100

6x1 + 4x2 < 70

10x1 — 6x <  20

x2 <  20

x1, > x2 > 0

(b) In a grocery store, the daily demand of bread over a 100 days period has the following frequency distribution :

 Daily Demand 0 1 2 3 4 5 Number of Days 5 25 35 20 5 10

Using the above data, and random numbers  (27, 13, 80, 10, 54, 60, 49, 78, 66, 44), simulate a 10 - days sequence of the demand of bread.

3. (a) Suggest optimum assignment of 4 workers A, B, C and D to 4 Jobs I, II, III, and IV. The time taken by different workers in completing the different jobs is given below :

 JOBS I II III IV A 8 10 12 16 WORKERS B 11 11 15 8 C 9 6 5 14 D 15 14 9 7

Also indicate the total time taken in completing the jobs.

(b) Find the initial solution of the following transportation problem by using Vogel Approximation Method :

 DESTINATION P Q R S SUPPLY SOURCE A 21 16 25 13 11 B 17 18 14 23 13 C 32 17 18 41 19 DEMAND 6 10 12 15

Also find its optimal solution by using MODI method.

4. (a) What are the limitations of Game theory ? Show how a two persons zero - sum game problem can be formulated as a linear programming problem.

(b) For the following game, find the optimal strategies of A and B and the value of the game by using the principle of dominance :

 PLAYER B B1 B2 B3 B4 Al 7 6 8 9 PLAYER A A2 — 4 —3 9 10 A3 3 0 4 2 A4 10 5 —2 0

5. (a) "Small variations in optimal order size will not change the total cost appreciably".  Do you agree with this statement ? Give Justification in support of your answer.

(b) A purchase manager places an order each time for a lot of 500 units of product A. From the available data, the following results are obtained :

Inventory carrying cost = 40% of purchase cost

Ordering cost per order            = Rs.600

Cost per unit                             = Rs.50

Annual demand                         = 1000

Find out the loss to the organization due to his ordering policy.

6. Write short notes on any three of the following :

(a) Travelling salesman problem

(b) ABC Analysis

(c) Non-linear programming

(d) Similarities between dynamic programming and linear programming

(e) Branch and bound method

Sunday, 16 February 2014 15:47

### Ms-51 June , 2010 Operations Research

June, 2010

MS-51 : Operations Research

1. (a) "Operations Research (OR) is an aid for the executive in making his/her decisions by providing him/her with needed quantitative information based on the scientific method of analysis". Discuss the statement and give atleast two examples to illustrate how operations research is helpful in decision making.

(b) A manufacturing company is producing two products A and B. Each requires processing on two machines 1 and 2. Product A requires 03 hours of processing on machine 1 and 02 hours on machine 2. Product B requires 2 hours of processing on machine 1 and 6 hours on machine 2. The unit profits for product A and product B are Rs. 10 and Rs. 20 respectively. The available time in a given quarter on machine 1 and machine 2 are 1200 hrs and 1500 hrs respectively. The market survey has predicted that not more than 400 units of product A and not more than 250 units of product B can be sold in the given quarter.  The company wants to determine the product mix to maximize the profits. Formulate the problem as linear programming mathematical model and determine the profit.

2. (a) Why is the simplex method a better technique than a graphical approach for ost real cases ? Construct the dual to the following primal problem :

Max z = 6x1 + 10x2

Subject to the constraints

4x 1 +12x2 < 100

6x1 + 4x2 < 70

10x1 — 6x <  20

x2 <  20

x1, > x2 > 0

(b) In a grocery store, the daily demand of bread over a 100 days period has the following frequency distribution :

 Daily Demand 0 1 2 3 4 5 Number of Days 5 25 35 20 5 10

Using the above data, and random numbers  (27, 13, 80, 10, 54, 60, 49, 78, 66, 44), simulate a 10 - days sequence of the demand of bread.

3. (a) Suggest optimum assignment of 4 workers A, B, C and D to 4 Jobs I, II, III, and IV. The time taken by different workers in completing the different jobs is given below :

 JOBS I II III IV A 8 10 12 16 WORKERS B 11 11 15 8 C 9 6 5 14 D 15 14 9 7

Also indicate the total time taken in completing the jobs.

(b) Find the initial solution of the following transportation problem by using Vogel Approximation Method :

 DESTINATION P Q R S SUPPLY SOURCE A 21 16 25 13 11 B 17 18 14 23 13 C 32 17 18 41 19 DEMAND 6 10 12 15

Also find its optimal solution by using MODI method.

4. (a) What are the limitations of Game theory ? Show how a two persons zero - sum game problem can be formulated as a linear programming problem.

(b) For the following game, find the optimal strategies of A and B and the value of the game by using the principle of dominance :

 PLAYER B B1 B2 B3 B4 Al 7 6 8 9 PLAYER A A2 — 4 —3 9 10 A3 3 0 4 2 A4 10 5 —2 0

5. (a) "Small variations in optimal order size will not change the total cost appreciably".  Do you agree with this statement ? Give Justification in support of your answer.

(b) A purchase manager places an order each time for a lot of 500 units of product A. From the available data, the following results are obtained :

Inventory carrying cost = 40% of purchase cost

Ordering cost per order            = Rs.600

Cost per unit                             = Rs.50

Annual demand                         = 1000

Find out the loss to the organization due to his ordering policy.

6. Write short notes on any three of the following :

(a) Travelling salesman problem

(b) ABC Analysis

(c) Non-linear programming

(d) Similarities between dynamic programming and linear programming

(e) Branch and bound method

Sunday, 16 February 2014 15:51

### Ms-51 December, 2009 Operations Research

December, 2009

Ms-51 : Operations Research

1. Solve the following problem through SIMPLEX method.

Minimize Z  = — 3x1+ x2+ x3

Subject to

x1 —2x2 + x3 < 11

—4x1+ x2 + 2x3 > 3

— 2x1       + x3 = 1

x1 > 0, x2 > 0 and x3 >0

2. (a) Discuss the queue parameters. How do you specify a querraing system ?

(b) A refuelling station is served by a single pump machine for providing service to the petrol vehicles. The arrival process has shown that the distribution of times between arrivals is negative exponential with a mean of 10 minutes. Similarly, service times were found to be adequately described by a negative exponential distribution with a mean of 6 minutes. Waiting space is unlimited. Determine:

(i) Probability that the customer has to wait.

(ii) Mean number of customer in the system.

(iii) Percentage utilisation of the service station.

(iv) Steady - state probability of having four customers in the system.

3. (a) Define Operations Research. Discuss its application in manufacturing and non - manufacturing sectors.

(b) State and explain Bellman's Principle of optimality.

4. (a) Write the general form of LP problem in matrix notation.

(b) The demand of an item is uniform at a rate of 25 units per month. The fixed cost is Rs. 30/- each time a production is made. The production cost is Rs. 2/- per item and rinventory carrying cost is 50 paisa per unit per month. If the shortage cost is Rs. 3/-per item per month, determine how often to make a production and of what size ?

5. Write short notes on any three of the following :

(a) GOAL Programming

(b) GOMORY'S cutting plane Algorithm

(c) Selective Inventory Control

(d) Pure and Mixed Strategy

(e) Sensitivity Analysis

(f) Monte Carlo Simulation

Sunday, 16 February 2014 15:47

### Ms-51 June , 2010 Operations Research

June, 2010

MS-51 : Operations Research

1. (a) "Operations Research (OR) is an aid for the executive in making his/her decisions by providing him/her with needed quantitative information based on the scientific method of analysis". Discuss the statement and give atleast two examples to illustrate how operations research is helpful in decision making.

(b) A manufacturing company is producing two products A and B. Each requires processing on two machines 1 and 2. Product A requires 03 hours of processing on machine 1 and 02 hours on machine 2. Product B requires 2 hours of processing on machine 1 and 6 hours on machine 2. The unit profits for product A and product B are Rs. 10 and Rs. 20 respectively. The available time in a given quarter on machine 1 and machine 2 are 1200 hrs and 1500 hrs respectively. The market survey has predicted that not more than 400 units of product A and not more than 250 units of product B can be sold in the given quarter.  The company wants to determine the product mix to maximize the profits. Formulate the problem as linear programming mathematical model and determine the profit.

2. (a) Why is the simplex method a better technique than a graphical approach for ost real cases ? Construct the dual to the following primal problem :

Max z = 6x1 + 10x2

Subject to the constraints

4x 1 +12x2 < 100

6x1 + 4x2 < 70

10x1 — 6x <  20

x2 <  20

x1, > x2 > 0

(b) In a grocery store, the daily demand of bread over a 100 days period has the following frequency distribution :

 Daily Demand 0 1 2 3 4 5 Number of Days 5 25 35 20 5 10

Using the above data, and random numbers  (27, 13, 80, 10, 54, 60, 49, 78, 66, 44), simulate a 10 - days sequence of the demand of bread.

3. (a) Suggest optimum assignment of 4 workers A, B, C and D to 4 Jobs I, II, III, and IV. The time taken by different workers in completing the different jobs is given below :

 JOBS I II III IV A 8 10 12 16 WORKERS B 11 11 15 8 C 9 6 5 14 D 15 14 9 7

Also indicate the total time taken in completing the jobs.

(b) Find the initial solution of the following transportation problem by using Vogel Approximation Method :

 DESTINATION P Q R S SUPPLY SOURCE A 21 16 25 13 11 B 17 18 14 23 13 C 32 17 18 41 19 DEMAND 6 10 12 15

Also find its optimal solution by using MODI method.

4. (a) What are the limitations of Game theory ? Show how a two persons zero - sum game problem can be formulated as a linear programming problem.

(b) For the following game, find the optimal strategies of A and B and the value of the game by using the principle of dominance :

 PLAYER B B1 B2 B3 B4 Al 7 6 8 9 PLAYER A A2 — 4 —3 9 10 A3 3 0 4 2 A4 10 5 —2 0

5. (a) "Small variations in optimal order size will not change the total cost appreciably".  Do you agree with this statement ? Give Justification in support of your answer.

(b) A purchase manager places an order each time for a lot of 500 units of product A. From the available data, the following results are obtained :

Inventory carrying cost = 40% of purchase cost

Ordering cost per order            = Rs.600

Cost per unit                             = Rs.50

Annual demand                         = 1000

Find out the loss to the organization due to his ordering policy.

6. Write short notes on any three of the following :

(a) Travelling salesman problem

(b) ABC Analysis

(c) Non-linear programming

(d) Similarities between dynamic programming and linear programming

(e) Branch and bound method

Sunday, 16 February 2014 15:44

### Ms-51 June, 2011 Operations Research

June, 2011

MS-51 : Operations Research

1.  (a)   Discuss the historical background of Operations Research (O.R). Explain its significance and scope in Management Des ci s ion Ma king. Enumerate the limitations of O.R.

(b) Solve the following Linear Programming Problem graphically.

Maximize Z = 4x1  + 6x2

Subject to constraints

x1+x2 =5

x1  2

x2 ≤ 0

x1, x2  0

2.(a) Derive the equation for Economic Batch Quantity (EBQ) for simultaneous production and consumption

(b) The annual demand for an item is 3200 units.  The unit cost is Rs. 6/- and inventory carrying cost is 25% per annum.  If the cost of one procurement is Rs. 150/- find out.

(i)  Economic Order Quantity

(ii)  No. of orders per year

(iii)  Time between two consecutive orders

(iv)  The optimal cost Mention assumptions made, if any.

3.(a) Discuss the application of dynamic programming in decision making. How is this different from linear programming ?

(b) An organization has three consultants. Each consultant can work upto 160 hours during next month during which three projects roust be completed. Project 1 will take 130 hours, Project 2 will take 140 hours and Project 3 will take 160 hours. The mount (l's.) per hour that can be billed for assigning each consultant to each project is given below:-

 Consultant Project 1 2 3 1 1200 1500 1900 2 1400 1300 1200 3 1600 1400 1500

Formulate this as a transportation problem and find the optimal solution. What is the

maximum total billing for next month ?

4.  (a) Explain the meaning of Dominance Principle in Game Theory. Illustrate with a small example.

(b)  A bakery keeps stock of a popular brand of cakes. Previous experience shows the daily pattern for the item with associated probabilities as given :

 Daily Demand (Nos) 0 10 20 30 40 50 Probability 0.1 0.2 0.15 0.5 0.02 0.03

Use the following sequence of random numbers to simulate the demand for next 10 days. Also find the average demand per day. Random Nos. 25, 39, 65, 76, 12, 05, 73, 89, 19, 49.

5.  (a)  Discuss the parameters of Queuing Problem.

(b)  A self - service store employs one cashier at its counter. Nine customers arrive on an average every 5 minutes while the cashier can serve 10 customers in 5 minutes. Assuming Poisson distribution for arrival rate and exponential distribution for service rate, find

(i)  Average number of customers in the system.

(ii)  Average number of customers in queue or average queue length.

(iii)  Average time a customer spends in the system.

(iv)  Average time a customer waits before being served.

6.  Write short notes on any four of the following :

(a)  Branch and bound algorithm

(b)  Goal Programming

(c)  Non - linear Programming

(d)  Assignment Problem

(e)  Dual Linear Programming Problem

(f)  Traveling salesman problem

Sunday, 16 February 2014 15:44

### Ms-51 June, 2011 Operations Research

June, 2011

MS-51 : Operations Research

1.  (a)   Discuss the historical background of Operations Research (O.R). Explain its significance and scope in Management Des ci s ion Ma king. Enumerate the limitations of O.R.

(b) Solve the following Linear Programming Problem graphically.

Maximize Z = 4x1  + 6x2

Subject to constraints

x1+x2 =5

x1  2

x2 ≤ 0

x1, x2  0

2.(a) Derive the equation for Economic Batch Quantity (EBQ) for simultaneous production and consumption

(b) The annual demand for an item is 3200 units.  The unit cost is Rs. 6/- and inventory carrying cost is 25% per annum.  If the cost of one procurement is Rs. 150/- find out.

(i)  Economic Order Quantity

(ii)  No. of orders per year

(iii)  Time between two consecutive orders

(iv)  The optimal cost Mention assumptions made, if any.

3.(a) Discuss the application of dynamic programming in decision making. How is this different from linear programming ?

(b) An organization has three consultants. Each consultant can work upto 160 hours during next month during which three projects roust be completed. Project 1 will take 130 hours, Project 2 will take 140 hours and Project 3 will take 160 hours. The mount (l's.) per hour that can be billed for assigning each consultant to each project is given below:-

 Consultant Project 1 2 3 1 1200 1500 1900 2 1400 1300 1200 3 1600 1400 1500

Formulate this as a transportation problem and find the optimal solution. What is the

maximum total billing for next month ?

4.  (a) Explain the meaning of Dominance Principle in Game Theory. Illustrate with a small example.

(b)  A bakery keeps stock of a popular brand of cakes. Previous experience shows the daily pattern for the item with associated probabilities as given :

 Daily Demand (Nos) 0 10 20 30 40 50 Probability 0.1 0.2 0.15 0.5 0.02 0.03

Use the following sequence of random numbers to simulate the demand for next 10 days. Also find the average demand per day. Random Nos. 25, 39, 65, 76, 12, 05, 73, 89, 19, 49.

5.  (a)  Discuss the parameters of Queuing Problem.

(b)  A self - service store employs one cashier at its counter. Nine customers arrive on an average every 5 minutes while the cashier can serve 10 customers in 5 minutes. Assuming Poisson distribution for arrival rate and exponential distribution for service rate, find

(i)  Average number of customers in the system.

(ii)  Average number of customers in queue or average queue length.

(iii)  Average time a customer spends in the system.

(iv)  Average time a customer waits before being served.

6.  Write short notes on any four of the following :

(a)  Branch and bound algorithm

(b)  Goal Programming

(c)  Non - linear Programming

(d)  Assignment Problem

(e)  Dual Linear Programming Problem

(f)  Traveling salesman problem

Sunday, 16 February 2014 15:41

### Ms-51 December 2011 Operations Research

December, 2011

Ms-51 : Operations Research

1.  (a)  A company produces two products A and B, each of which requires three types of

processing. -The length of time for processing each unit and the profit per unit are given in the following table :

 Process \$ Product A (hr/unit) Product B (hr/unit) Available capacity per day (hr) Process I 120 120 8,400 Process II 30 60 3,000 Process III 80 40 4,800 Profit per unit (Rs) 50 70

How many units of each product should the company produce per day in order to maximize the profit ? (Use simplex method to solve the problem)

(b) What is the concept of Operations Research ? "Operations Research (OR) is useful only if applied with Information Technology". Comment.

2.  (a)  What functions does inventory perform ? State the two basic inventory decisions

management must make in order to accomplish the functions of inventory just describe by you.

(b)  A repair and maintenance company is engaged in providing service to a particular brand of popular vehicle. It uses 8000 units of a moving parts per year as replacements of the old parts. Each part costs Rs. 250/-. The setup costs are estimated at Rs. 100 and the inventory carrying cost is the average of such inventory at 20% of the price. Supply of the part is at the rate of 80 per day. Calculate the following :

(i) Optimal order quantity

(ii) Optimal number of set ups,

(iii) Total variable costs based on optimal policy.

Assume 310 working days in a year.

3.  (a)  Discuss various steps of Goal Programming model formulation. How does GP help in decision making ?

(b) A repair shop attended by a single machine has an average of four customers an hour who bring small appliances for repair. The mechanic inspects them for defects and quite often can fix them right away or otherwise render a diagnosis. This takes him six minutes, an average. Arrivals are Poisson and service time has exponential distribution. Determine

(i) the portion of time during which the shop is empty.

(ii) the probability of finding at least 1 customer in the shop.

(iii) the average number of customers in the system.

(iv) the average time spent, including service.

4.  (a)  What is a transportation problem ? How is it useful in business and industry ? Explain the differences and similarities between MODI method and stepping stone method used for solving transportation problem.

(b)  A department head has four subordinates and four tasks to be performed. Subordinates differ-in efficiency and tasks differ in their intrinsic difficulty. His estimate of time each man would take to perform each task is given in the matrix below :

 TASKS SUBORDINATE 1 2 3 4 A 8 26 17 11 B 13 28 14 26 C 38 19 18 15 D 19 26 24 10

How should the tasks be allotted, one to a man, so as to minimize the total manhours ?

5.  (a)  What do you understand by simulation ? How is a simulation technique better than

mathematical models in solving problems of business and industry ? Discuss taking suitable examples.

(b)  Solve the following game by using the dominance method.

 PLAYER B B1 B2 B3 PLAYER A Al 3 6 8 A2 —3 3 8 A3 4 3 6

6.  Write short notes on any four of the following :

(a) A B C Analysis

(b) Dual of an LPP

(c) Saddle point in Game Theory

(d) Degeneracy in LP problem

(e) Periodic Review System

(f) Dynamic Programming

Sunday, 16 February 2014 15:42

### Ms-51 December 2012 Operations Research

December, 2012

Ms-51 : Operations Research

1. (a) Experts believe that OR is a technique which help in resolving conflicts between Production, Finance, Marketing and Personnel functions of a manufacturing unit. Do you agree ? Justify your answer with the help of suitable examples.

(b) A company produces product A and B and has a total production capacity of 9 tons per day. A and B require the same production capacity. The company has a permanent contract to supply at - least 2 tons of A and at least 3 tons of B per day to another company. Each ton of A requires 20 machine hours production time and each ton of B requires 50 machine hours production time. The daily maximum possible number of machine hours is 360. All the firm's out put can be sold and the profit made is Rs. 80 per tons of A and Rs. 120 per tons of B. Determine the production schedule for maximum profit and also calculate the profit.

2. (a) What functions does inventory perform ? State the two basic inventory decision management must make as they attempt to accomplish the function of inventory described by you.

(b) A drug manufacturing company uses batch production process and uses material X for its famous brand of drug. Material X is being produced by the company in 10 batches of 1500 units each. All the material is being used in the production of the drug. The plant operates for 2800 hours in a year. The set up costs of the machine are Rs. 100/-and is independent of the batch size. The cost of the material is Rs. 200 per unit and holding cost is 20%. Is the existing production strategy adopted by the management economical ? Justify your answer.

4. (a) What is a queue ? Give an example and explain the basic concept of queue. Also

discuss the queue parameters.

(b) A repair man is to be hired to repair machines which break down at an average rate of 3 per hour. The break down follows Poisson distribution. Non - productive time of a machine is considered to cost Rs. 10 per hour. Two repairmen have been interviewed - one is slow but cheap, while the other is fast but expensive. The slow repairman charges Rs. 5 per hour and he services break down machines at the rate 4 per hour. The fast repairman demand Rs. 7 per hour, and he services at an average rate of 6 per hour. Which repairman should be hired ?

5. (a) Explain in brief Gomory's method for solving an integer linear programming problem.

(b) Four different jobs can be done on four different machines. The set up and take -down time are assumed to be prohibitively high for changeovers. The matrix below gives the cost in rupees of producing job i on machine j.

MACHINES

 Mi M2 M3 M4 J1 J1 5 7 11 6 Jobs J2 8 5 9 6 J3 4 7 10 7 J4 10 4 8 3

Assign the Jobs to the various machines so that the total cost gets minimized.

6. Write short notes on any four of the following :

(a) ABC Analysis

(b) Travelling Salesman Problem

(c) Dual of an LPP

(d) Bellman's Principle of Optimality

(e) Dynamic Programming