- JOSEPHS COLLEGE OF COMMERCE (AUTONOMOUS)
END SEMESTER EXAMINATION – OCTOBER 2014
B.B.M. – V SEMESTER
OPERATIONS RESEARCH
Duration: 3 Hours Max. Marks: 100
SECTION – A
- Answer ALL the questions. Each carries 2 marks. (10 x2 =20)
- Give the meaning of Operations Research.
- In the context of transportation model, explain degeneracy and non-degeneracy.
- Describe the assignment problem giving suitable example. Give two areas of its applications.
- Explain the utility concept in case of decision theory.
- Introduce suitable variables for the expression to convert into standard form for simplex method (a) 2a+3b<= 5 (b) 5x+4y+3z>=10
- What is an Unbalanced Assignment Model? How is it solved by Hungarian Method?
- Bring out any two significant differences between PERT and CPM.
- Discuss unbounded solution and feasible solution in case of graphical method of solving LPP.
- What are floats or slack in a network diagram?
- “OR is an inter-disciplinary team approach”- Explain.
SECTION – B
- Answer any FOUR Each carries 5 marks. (4×5=20)
11.Draw the complete CPM network according to the following activities:
| DURATION (weeks) | STARTS AT EVENT | ENDS AT EVENT |
| 5 | 1 | 2 |
| 6 | 1 | 3 |
| 3 | 1 | 4 |
| 4 | 2 | 3 |
| 6 | 2 | 5 |
| 7 | 3 | 4 |
| 4 | 3 | 5 |
| 8 | 4 | 5 |
Determine the Critical Path.
- Solve the following problem by Least Cost Method and determine Initial Basic Feasible Solution.
| From/ To | D | E | F | Supply |
| A | 6 | 4 | 1 | 50 |
| B | 3 | 8 | 7 | 40 |
| C | 4 | 4 | 2 | 60 |
| Demand | 20 | 95 | 35 | ? |
- “OR has certain limitations. However, these limitations are mostly related to the problems of model building and time and money factors. ”—In this context briefly explain the demerits of OR with regard to application rather than it practical utility.
- Consider the following problem of assigning five jobs to five persons. The assignment costs are given below:
| PERSON/JOBS | I | II | III | IV | V |
| A | 8 | 4 | 2 | 6 | 1 |
| B | 0 | 9 | 5 | 5 | 4 |
| C | 3 | 8 | 9 | 2 | 6 |
| D | 4 | 3 | 1 | 0 | 3 |
| E | 9 | 5 | 8 | 9 | 5 |
Determine the optimum Assignment Schedule and Minimum Cost.
Note: Assignment cost is in thousands.
- A farmer is engaged in breeding pigs. The pigs are fed on various products grown on the farm. Because of the need to ensure nutrient constituents, it is necessary to buy additional one or two products, which we shall call A and B. the nutrient constituents (vitamins and proteins) in each of the product are given below:
| nutrient constituents | nutrient in the product | minimum requirement of nutrient constituents | |
| A | B | ||
| X | 36 | 6 | 108 |
| Y | 3 | 12 | 36 |
| Z | 20 | 10 | 100 |
Product A cost Rs. 20 per unit and Product B costs Rs. 40 per unit. Determine how much of products A and B must be purchased so as to provide the pigs nutrients not less than the minimum required, at the lowest possible cost. Formulate it as LPP.
- Write the dual of the following LPP and state the no. of decision variables and constraints in primal and dual of the problem:
Minimize Z= 5x1 – 6x2 + 4x3
Subject to Constraints:
3x1 + 4x2 + 6x3 >= 9
x1 + 3x2 + 2x3 >= 5
7x1 – 2 x2 – x3 <= 10
x1 – 2x2 + 4x3 >= 4
2x1 + 5x2 – 3x3 >= 3
Non- negativity constraints:
x1, x2, x3 >= 0
SECTION – C
III) Answer any THREE questions. Each carries 15 marks. (3×15=45)
- Use the graphical method to solve the following LPP.
Maximize Z = 5x1 + 2x2
Subject to constraints:
2x1 + 3x2 <= 150
3x1 <= 150
5x2 <= 200
Where, x1, x2 & x3 >=0
18.Given below the transportation problem, Answer the following questions:
| Factories/Warehouse | I | II | III | IV | Availability |
| A | 10 | 8 | 7 | 12 | 5000 |
| B | 12 | 13 | 6 | 10 | 6000 |
| C | 8 | 10 | 12 | 14 | 9000 |
| Demand | 7000 | 5500 | 4500 | 3000 | ? |
- Find the IBFS using VAM and is this solution feasible? (5marks)
- Is this solution degenerate? (1 mark)
- Is this solution optimal? If not find the optimal solution using MODI method. (9marks)
- A marketing manager has five salesmen and five sales districts. Considering the capabilities of the salesmen and nature of districts, the marketing managerestimates that sales per month (in hundred rupees) for each salesman in each district would be as follows:
| Salesmen | Districts | ||||
| A | B | C | D | E | |
| I | 32 | 38 | 40 | 28 | 40 |
| II | 40 | 24 | 28 | 21 | 36 |
| III | 41 | 27 | 33 | 30 | 37 |
| IV | 22 | 38 | 41 | 36 | 36 |
| V | 29 | 33 | 40 | 35 | 39 |
Find the assignment of salesmen to districts that will result in maximum sales using Hungarian method.
- 20. Solve using Big-M method for the following LPP.
Min Z: 500x + 200y
Subject to constraints:
3x + 2y <= 90
x >= 10
y >= 10
Non-negativity constraints:
x, y >= 0
21.(a)“Most of the OR techniques are simple and can be used without much mathematical complications. Hence, managers at various levels need not be scared of using these techniques”—In this context explain briefly the various techniques used in OR for taking decisions. (10 marks)
(b) Write a short note on Decision Tree Analysis with a diagrammatic representation. (5 marks)
SECTION – D
- IV) Case study- Compulsory questions. (15 marks)
- A construction company is preparing a PERT network for laying the foundation of a new art museum. Given the following set of activities, their predecessor requirements and three time estimates of completion time:
| Activities | pessimistic time | most likely time | optimistic time |
| 1-2 | 7 | 1 | 1 |
| 1-3 | 7 | 4 | 1 |
| 1-4 | 8 | 2 | 2 |
| 2-5 | 1 | 1 | 1 |
| 3-5 | 14 | 5 | 2 |
| 4-6 | 8 | 5 | 2 |
| 5-6 | 15 | 6 | 3 |
- Determine the expected time and variance for each activity.
- Draw the network and determine the project duration and critical path.
- Determine earliest time and latest time and total float for the same network.
- What is the probability that the project is completed 4 weeks earlier than expected?
- If the target time is 18 weeks what is the probability of meeting the target?
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