Exam Details
| Subject | Operations Research | |
| Paper | ||
| Exam / Course | Management Programme | |
| Department | School of Management Studies (SOMS) | |
| Organization | indira gandhi national open university | |
| Position | ||
| Exam Date | December, 2015 | |
| City, State | new delhi, |
Question Paper
What are the main characteristics of operations research? Explain with suitable examples. Discuss its scope and limitations.
What is buffer stock? List the reasons for keeping a buffer stock Suppose the lead time for procurement of a product gets doubled, will you recommend doubling its buffer stock? Justify your answer.
Find the initial basic feasible solution of the following transportation problem by Vogetl's approximation method. The availability at the factories, the requirement of the warehouses and the various associated unit transportation cost are presented in the following table:
<img src='./qimages/14736-2a.jpg'>
A toy manufacturer uses 48,000 rubber wheels per year for its popular dump truck series. The firm makes its own wheels, which it can produce at a rate of 800 per day. The toy trucks are assembled uniformly over the entire year. Carrying cost is RS 10 per wheel a year. Set up cost for a production run of wheels is RS 450. The firm operates 240 days per year.
Determine each of the following.
Optimal run size
Minimum total annual cost for
carrying and set up
Cycle time for the optimal run size
Run time
Suggest optimum assignment of 4 workers C and D to 4 jobs II, III and IV. The time taken (hours) by different workers in completing the different jobs is given below:
Jobs
Workers
A 8 10 12 16
B 11 11 15 8
C 9 6 5 14
D 15 14 9 7
Also, find the total time taken m completing the jobs.
A vending machine dispenses hot chocolate or coffee. Service time is 30 seconds per cup and is constant. Customers arrive at a mean rate of 80 per hour, and this rate is Poisson -distributed.
Determine:
The average number of customers waiting in line.
The average time customers spend in the system.
The average number in the system.
A manufacturer of toys makes two types of toys, A and B. Processing of these two toys is done on two machines X and Y. The toy A requires two hours on machine X and six hours on machine Y. Toy B requires four hours on machine X and five hours on machine Y. There are sixteen hours of time per day available on machine X and thirty hours on machine Y. The profit obtained on both the toys is the same, i.e., RS 5 per toy. Formulate this problem as an integer LP problem.
Find the optimum strategies for A and Band the value of the game.
B
A
1 7 2 4
0 3 7 8
5 2 6 10
A company machines and drills two castings X and Y. The time required to machine and drill one casting including machine set -up time is as follows:
Casting Machine Hours Drilling Hours
X 4 2
Y 2 5
There are two lathes for machining and three drilling machines. The working week is of 40 hours; there is no lost time and over time. Variable costs for both castings are RS 120 per unit while total fixed costs amount to RS 1000 per week. The selling price of casting X is RS 300 per unit and that of Y is RS 360 per unit. There are no limitations on the number of X and Y casting that can be sold. The company wishes to maximize its profit.
Formulate a linear programming model for the problem
What are the advantages and disadvantages of Monte Carlo simulation as a problem solving technique?
6. Write short notes on any four of the following:
Degeneracy in L.P. Problem
Periodic review system in inventory control
Travelling sales man problem
Bellman's Principle of Optimality
Non-Linear Programming
Impact of Internet on OR
What is buffer stock? List the reasons for keeping a buffer stock Suppose the lead time for procurement of a product gets doubled, will you recommend doubling its buffer stock? Justify your answer.
Find the initial basic feasible solution of the following transportation problem by Vogetl's approximation method. The availability at the factories, the requirement of the warehouses and the various associated unit transportation cost are presented in the following table:
<img src='./qimages/14736-2a.jpg'>
A toy manufacturer uses 48,000 rubber wheels per year for its popular dump truck series. The firm makes its own wheels, which it can produce at a rate of 800 per day. The toy trucks are assembled uniformly over the entire year. Carrying cost is RS 10 per wheel a year. Set up cost for a production run of wheels is RS 450. The firm operates 240 days per year.
Determine each of the following.
Optimal run size
Minimum total annual cost for
carrying and set up
Cycle time for the optimal run size
Run time
Suggest optimum assignment of 4 workers C and D to 4 jobs II, III and IV. The time taken (hours) by different workers in completing the different jobs is given below:
Jobs
Workers
A 8 10 12 16
B 11 11 15 8
C 9 6 5 14
D 15 14 9 7
Also, find the total time taken m completing the jobs.
A vending machine dispenses hot chocolate or coffee. Service time is 30 seconds per cup and is constant. Customers arrive at a mean rate of 80 per hour, and this rate is Poisson -distributed.
Determine:
The average number of customers waiting in line.
The average time customers spend in the system.
The average number in the system.
A manufacturer of toys makes two types of toys, A and B. Processing of these two toys is done on two machines X and Y. The toy A requires two hours on machine X and six hours on machine Y. Toy B requires four hours on machine X and five hours on machine Y. There are sixteen hours of time per day available on machine X and thirty hours on machine Y. The profit obtained on both the toys is the same, i.e., RS 5 per toy. Formulate this problem as an integer LP problem.
Find the optimum strategies for A and Band the value of the game.
B
A
1 7 2 4
0 3 7 8
5 2 6 10
A company machines and drills two castings X and Y. The time required to machine and drill one casting including machine set -up time is as follows:
Casting Machine Hours Drilling Hours
X 4 2
Y 2 5
There are two lathes for machining and three drilling machines. The working week is of 40 hours; there is no lost time and over time. Variable costs for both castings are RS 120 per unit while total fixed costs amount to RS 1000 per week. The selling price of casting X is RS 300 per unit and that of Y is RS 360 per unit. There are no limitations on the number of X and Y casting that can be sold. The company wishes to maximize its profit.
Formulate a linear programming model for the problem
What are the advantages and disadvantages of Monte Carlo simulation as a problem solving technique?
6. Write short notes on any four of the following:
Degeneracy in L.P. Problem
Periodic review system in inventory control
Travelling sales man problem
Bellman's Principle of Optimality
Non-Linear Programming
Impact of Internet on OR
Other Question Papers
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