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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 :

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 :

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 :

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 :

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

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

x_1, 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:-

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 :

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 

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

x_1, 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:-

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 :

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 

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 :

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 :

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.

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 

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

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 

December, 2009

Ms-46 : Management of Financial Services

1. "External risk arises mainly due to certain developments that take place outside the financial services company. The sources of these risks vary for different services". Explain this statement and discuss these sources of risk that are applicable to different services.

2. What are the main aspects which the merchant banker takes into consideration while selecting a public issue proposal. Discuss the various pre-issue activities undertaken by merchant banker for raising funds from the capital markets.

3. What are the various debt instruments issued by companies, Non-Bank Finance companies and Financial Institutions to raise funds from the market ? Describe their main features.

4. Explain the concept of credit cards ? In addition to credit facility what other facilities and services, are extended by credit card organisations to their customers.

5. What are the principal and other contingencies covered under the life insurance contract ?

6. Discuss the embedded options that are available under life insurance policies. What is leasing ? Classify leasing based on the terms and conditions on which an asset is leased ? Discuss the rights and obligations of the lessor and lessee in a lease contract.

7. Explain the following statements :

(a) 'Transacting the depository way is more advantageous than transacting the traditional way'.

(b)  'Life insurance plans are effective ways of saving taxes'.

(c)  'Credit rating of debt instruments helps the investors in managing credit risk in investment decisions'.

(d) 'Venture capital is quite distinct from other forms of finances ?

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

(a) Acceptance house

(b) Financial Restructuring

(c) Self Regulation

(d) Securitisation of housing loan

(e) Employer - employee Liability

(f) Mutual Funds

June, 2010

MS-46 : Management of Financial Services

1. Discuss the different types of risks faced by the financial services firms ? Explain the strategies available to manage the credit risk ?

2. What are the distinctive characteristics of financial services ? In what way does information technology affect the financial services sector from the providers' point of view ? Discuss.

3. Explain the concept of securities depositories ? Discuss the importance and functioning of the securities depository system.

4. What do you understand by Initial Public Offer ? Describe its process of public issues and the salient features of the SEBI guidelines regarding the Initial Public Offer.

5. What do you mean by securitisation of Assets ? Describe the process of securitisation. Emphasize the role of Special Purpose Vehicle (SPV) and other parties in the transaction of assets securitisation.

6. Discuss the functions undertaken by National Housing Bank. What restrictions are imposed by it on housing finance companies regarding acceptance of deposits ?

7. Define insurance and explain its basic characteristics ? Discuss in detail the different

types of insurable risks.

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

(a) Income funds

(b) Investment banks

(c) Certificates of deposits

(d) Utility ratings

(e) Public liability insurance

(f) Hire purchase system

June, 2011

MS-46 : Management Of Financial Services

1.  "In recent past Indian debt market has become more vibrant." Critically evaluate this statement

2.  Discuss different types of risks associated with financial services.

3.  Insurance Regulatory and Development Authority (IRDA) has its prime objective to protect the interest of policy holders. What regulations have been evolved by it to attain this objective.

4.  Write notes on :

(a)  Green Shoe Option

(b)  Forfeiting

(c)  Liability Insurance

(d)  Whole life policy

5.  Discuss the process, benefits and limitations of credit rating.

6.  What do you understand by Venture Capital ? Discuss the various modes of financing by Venture Capital funds. Explain the difference exist routes available to a Venture Capitalist from an investee company.

7.  Explain the mechanism of factoring and components of 'cost of factoring'. Discuss the present position of factoring services in India.

8.  What is the role of Assets Management Company in a Mutual fund ? Discuss the working mechanism and functions of Assets Management Companies. 

December, 2011

Ms-46 : Management of Financial Services

1.  How does the Securities and Exchange Board of India (SEBI) regulate brokers and sub-brokers in financial market ?

2.  Write notes on :

(a) Marine insurance

(b) Export factoring

(c) Capital Restructuring

(d) Commercial Bill market.

3.  Explain Book Building Process of public issue of securities. Discuss the rules prescribed by SEBI in this regard.

4.  Describe the role of Central Bank of a country in financial system of a country.

5.  Explain :

(a) OTCEI

(b) Rolling Settlement System

6.  Critically evaluate regulations for Credit Rating Agencies in India.

7.  "SEBI regulations made trustees of mutual funds more responsible in comparison with their AMCs" Discuss.

8.   What do you mean by Venture Capital ? Explain the special features of Venture Capital. Discuss the various modes of finance provided by Venture Capital funds. 

December, 2012

Ms-46 : Management Of Financial Services

1. Discuss in detail the risks affecting the business of fund based services. What are the strategies followed by them to manage these risks ?

2. Discuss in detail about the "Participants in Money Market" in India. Mention the names of instruments traded in this market.

3. What is factoring ? Explain the mechanism of factoring.

4. Discuss the role of Government Securities Market in Indian financial system.

5. Explain the Depository system and the terms

(a) Fungibility and

(b) depository participants in detail.

6. Explain in detail the process used for making an IPO of Equity shares of a company. Explain the term 'Book Building' in this regard.

7. Explain the process of Credit Rating. How does SEBI regulate credit rating agencies in India ?

8. What do you understand by securitisation of Assets ? Discuss its mechanism and the

advantages to the parties concerned.