St. Joseph’s College of Commerce (Autonomous)
End Semester Examination- APRIL 2014
MIB – II Semester
OPERATIONS RESEARCH FOR BUSINESS DECISIONS
Duration: 3 Hrs Max. Marks: 100
SECTION – A
- I) Answer any SEVEN Each carries 5 marks. (7 x 5 = 35)
- Explain with reasons which of the following statements are true or false:
- a) Emotions and guesswork is not part of Operation Research
- b) The purpose of using simulation technique is to understand properties and operating characteristics of complex real life problems.
- c) An assignment problem cannot have multiple optimal solution.
- The Mapple Store sells Mapple Computers and printers. The computers shipped are in 12 cubic foot boxes and printers in 8 cubic foot boxes. The Mapple store estimates that at least 30 computers can be sold each month and the number of computers sold will be at least 50% more than the number of printers. The computers cost the store $1000 each and are sold for a profit of $1000. The printers cost the store $300 and are sold for a profit of $350.the store has a storeroom that can hold 1000 cubic feet and can spend $70,000 each month on computers and printers. How many computers and how many printers should be sold each month to maximize profit? What is the maximum profit? Solve by graphical method.
- Define Operation Research. Explain the methodology of OR.
- Imagine yourself to be the Executive Director of a 5 Star hotel which has four banquet halls that can be used for all functions including weddings. The halls were all the same size and facilities in each hall differed. During a heavy marriage season, 4 parties have approached you to reserve a hall for the marriage to be celebrated on the same day. These marriage parties were told that the first choice among these halls would cost Rs10, 000 for the day. They were also required to indicate the second, third and fourth preferences and the price they were willing to pay. Marriage party A and D indicated they were not interested in Halls 3 and 4. Other particulars are given in the table below:
| MARRIAGE PARTY | REVENUE HALL | |||
| 1 | 2 | 3 | 4 | |
| A | 10,000 | 9000 | X | X |
| B | 8000 | 10,000 | 8000 | 5000 |
| C | 7000 | 10,000 | 6000 | 8000 |
| D | 10,000 | 8000 | X | X |
Decide on an allocation that will maximize the revenue of the hotel.
- Arrival of cars at a filling station is considered to be Poisson with an average time of 4 min in between one arrival and the next. Service time is considered to be poison with an average time of 3 min. the length of filling is assumed to be distributed exponentially with mean of 0.05 hours.
- a) What is the arrival rate?
- b) What is the service rate?
- c) What is the equipment utilization rate?
- d) What is the average time an arrival spends in the system (waiting and servicing time)?
- Solve the game whose pay-off matrix is given below:
| PLAYER A | PLAYER B | |||
| B1 | B2 | B3 | B4 | |
| A1 | 1 | 7 | 3 | 4 |
| A2 | 5 | 6 | 4 | 5 |
| A3 | 7 | 2 | 0 | 3 |
- A project consists of 9 jobs A to I with the following precedence relationships and estimates of time. Draw a project network and find the critical path with project duration
| JOB | A | B | C | D | E | F | G | H | I |
| PREDECESSOR | – | – | A,B | A,B | B | D,E | C,F | D,E | G,H |
| DURATION(DAYS) | 15 | 10 | 10 | 10 | 5 | 5 | 20 | 10 | 15 |
- The occurrence of rain in a city on a day is dependent upon whether or not it rained on the previous day. If it rained on the previous day the rain distribution is given by
| EVENT | PROBABILITY |
| NO RAIN | 0.50 |
| 1 CM | 0.25 |
| 2CM | 0.15 |
| 3CM | 0.05 |
| 4CM | 0.03 |
| 5CM | 0.02 |
If it did not rain the previous day, the rain distribution is given by:
| EVENT | PROBABILITY |
| NO RAIN | 0.75 |
| 1CM | 0.15 |
| 2CM | 0.06 |
| 3CM | 0.04 |
Simulate the city’s weather for 10 days and determine by simulation the total days without rain as well as the total rainfall during the period. Use the following: 67, 63, 39, 55, 29, 78, 70, 06, 78, 76 for simulation. Assume that for the first day of the simulation it had not rained the day before.
- Medicare hospital has the following minimum daily requirement for nurses
| PERIOD | CLOCK TIME (24 HRS) | MINIMAL NUMBER OF NURSES REQUIRED |
| 1 | 6 am – 10 am | 2 |
| 2 | 10 am – 2 pm | 7 |
| 3 | 2 pm – 6 pm | 15 |
| 4 | 6 pm – 10 pm | 8 |
| 5 | 10 pm – 2 am | 20 |
| 6 | 2 am – 6 am | 6 |
Nurses report to the hospital at the beginning of each period and work for 8 consecutive hours. The hospital wants to determine the minimal number of nurses to be employed so that there will be sufficient number of nurses available for each period. Formulate this as a linear programming problem.
- Define any five terms :
- Degeneracy b. Duality c. Reneging d. Unbounded solution
- Dangling Error f. Saddle point
SECTION- B
- II) Answer any THREE questions. Each carries 15 marks. (3×15 = 45)
- A company manufactures two products A and B. Both products are processed on two machine centres, M1 and M2.
| PRODUCTS | HOURS REQUIRED PER UNIT | ||
| M1 | M2 | PROFIT | |
| A | 1 | 3 | 30 |
| B | 2 | 2 | 20 |
| CAPACITY | 80 | 120 | |
Solve the problem using simplex method to determine number of units of A and B to be produced per week to maximize profit. Is there an alternate solution? If yes, find it.
- National Oil Co. has three refineries and 4 depots. Transportation costs per ton and requirements are given below:
| D1 | D2 | D3 | D5 | CAPACITY | |
| P1 | 5 | 7 | 13 | 10 | 700 |
| P2 | 8 | 6 | 14 | 13 | 400 |
| P3 | 12 | 10 | 9 | 11 | 800 |
| REQUIREMENT | 300 | 600 | 700 | 400 |
Determine optimal allocation of output.
- With a view to improving the quality of customer services, a Bank is interested in making an assessment of the waiting time of its customers coming to one of its branches located in a residential area. This branch has only one tellers counter. The arrival rate of the customer and the service rate of the teller is given below:
| Time between two consecutive arrivals of customers( in min) | Probability |
| 3 | 0.17 |
| 4 | 0.25 |
| 5 | 0.25 |
| 6 | 0.20 |
| 7 | 0.13 |
| Service time by the teller (in min) | Probability |
| 3 | 0.10 |
| 4 | 0.30 |
| 5 | 0.40 |
| 6 | 0.15 |
| 7 | 0.05 |
You are required to simulate 10 arrivals of customers in the system starting from 11 am ans show the waiting time of customers and idle time of the teller.
Use the following random numbers taking the first two random numbers in two digits each for the first trial and so on: 11,56,23,72,94,83,83,02,97,99,83,10,93,34,33,53,49,94,37 and 97.
- Define an OR model. Discuss the various classification schemes of models.
- What is game theory? Explain with examples the concept of dominance in game theory. What are the major limitations of game theory?
Section – C
III) Compulsory Question. (1×20=20)
- 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 | Duration |
| 1-2 | 3 |
| 1-3 | 8 |
| 2-4 | 9 |
| 3-5 | 6 |
| 4-5 | 0 |
| 4-6 | 10 |
| 4-7 | 14 |
| 5-7 | 11 |
| 7-9 | 10 |
| 6-8 | 5 |
| 8-10 | 4 |
| 9-10 | 1 |
REQUIRED:
- Draw the CPM Network.
- Compute the total float for each activity and determine the critical path using forward pass 7 backward pass
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