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understanding management
Quantitative Techniques In Management 4th Edition N D VOHRA - Solutions
19. A large computer system has 100 identical components which are subject to random failure over time.The failure pattern is given as follows:Failed components have to be replaced immediately for the effective functioning of the computer. If they are replaced individually, as and when they fail,
18. An electronic machine has a component that is subject to failure and needs replacement immediately when this occurs. A total of 200 such machines are used in a company. The cost of each replacement is Rs 80 per item and for group replacement it is Rs 5,000 for all the 200 machines. Records of
17. The management of a large hotel is considering the periodic replacement of light bulbs fitted in its rooms. There are 500 rooms in the hotel and each room has 6 bulbs. The management is now following the policy ofreplacing the bulbs as they fail at a total cost of Rs 3 per bulb. The management
16. Goodlite Company has installed 2,000 electric bulbs of a certain brand. The company follows the policy of replacing the bulbs as and when they fail. Each replacement costs Rs 2. The probability distribution of the life of the bulbs is as given here:Determine the cost/week of the replacement
15. A manufacturer has to decide between two alternative machines M1 and M2, about which pertinent information is given below:Determine, (i) Optimal replacement period of M1 and of M2•(ii) Which of the two is a better alternative? (a) Cost (b) Maintenance cost (c) Scrap value (d) Cost of Capital
14. A piece of equipment costs Rs 7,500 initially and requires Rs 400 to be spent on its maintenance in the first Year. The maintenance cost would increase by Rs 500 per Year in each of the subsequent Years.Determine the optimal replacement for the machine when (i) future costs are not discounted,
For a machine, the following data are available:Determine the optimum period for replacement of the above machine. (CA, November, 1987) Year Cost of spares (Rs) Salary of maintenance staff (Rs) 1 2 3 4 5 6 200 400 700 1,000 1,400 1,600 1,200 1,200 1,400 1,600 2,000 2,600 Losses due to breakdown
12. A fleet owner finds from the past records that the costs per year of running a truck whose purchase price is Rs 60,000 are given as follows:At what age is a replacement due?Now, suppose thatthe truck owner in this case has three trucks, two of which are two Years old and the third one is one
11. A machine shop has a press which is to be replaced as it wears out. A new press is to be installed now.Further, an optimum replacement plan is to be found for the next 7 years after which the press is no longer required. The following data is given:Find an optimum replacement policy and the
10. A company is intending to purchase a small machine in the near future. It is not necessary that a new machine be purchased and for economic considerations estimates of selling and purchasing prices from new to 5 years' old have been obtained. These are displayed in the following table along
9. The maintenance costs and the resale price ofmachineMwhose purchase price is Rs 12,000 are given as:(i) Suggest optimal period for the replacement of the machine.(ii) When this machine is 2 Years old, another machine N, which is a new model of machine M, is available. The optimal period for
8. A truck owner finds from his past experience that the maintenance costs are Rs 200 for the first year and then increase by Rs 2,000 every year. The cost of the truck type A is Rs 9,000. Determine the best age at which to replace the truck. If the optimum replacement is followed, what will be the
7. A truck owner finds from the past records that the maintenance cost of a truck (whose purchase price is Rs 3,00,000) during the first 8 Years of its life and the resale prices at the end of each year, are as follows:Suggest optimal policy for the replacement of the truck. Year Maintenance cost
6. Determine the optimal replacement period and the average Yearly cost associated with it, in respect of a machine whose details are as follows:Cost of the machine including installation charges = Rs 4,000 Maintenance charges expected to be paid, Mt= 200 + lOOt + 10t2 (fort= 1, 2, ... , n)Resale
5. The cost of a machine is Rs 6,500 and its scrap value is only Rs 500 whenever disposed. The maintenance costs are found to be as under on the basis of experience:When should the machine be replaced to get maximum advantage? Year 1 2 3 4 5 6 7 8 Maintenance cost (Rs) 100 250 400 600 900 1,250
4. A firm is considering replacement of a machine, whose cost price is Rs 12,200; and the scrap value is only Rs 200. The maintenance costs are found as follows:When should the machine be replaced? Year 1 2 3 4 5 6 7 8 Maintenance cost (Rs) 200 500 800 1,200 1,800 2,500 3,200 4,000
3. Determine the age at which the following type of machine be replaced: Cost price Operating costs Resale value = Rs 8,000 Rs 1,000 for the first year, increasing by Rs 500 every year = Rs 4,000 for the first year, decreasing by Rs 500 every year
2. Determine the optimum replacement interval of an equipment which costs Rs 5,200 and whose resale values and running costs are as follows: Year 1 2 3 4 5 6 7 Resale value (Rs) 3,500 2,700 1,800 1,000 850 600 425 Running cost (Rs) 600 850 1,000 1,250 1,400 1,475 2,000
1. An electro-mechanical equipment has a purchase price of Rs 7,000. Its running costs per Year and resale values are given here:At which year is the replacement due? Year 1 2 3 4 5 6 7 8 Running cost (Rs) 2,000 2,100 2,300 2,600 3,000 3,500 4,100 4,600 Resale value (Rs) 4,000 3,000 2,200 1,600
5. Explain briefly the difference in replacement policies of items which deteriorate gradually and items which fail completely.
4. How would you deal with replacement of items that fail completely and suddenly?
3. In the replacement of items which deteriorate with time, prove that "Do not replace the item if the next period's cost is less than the weighted average of the previous costs."
2. Briefly explain the costs which are relevant to decisions for replacement of depreciable assets. Illustrate their behaviour and explain how the optimal time for replacement of an asset can be determined.
1. What is a replacement problem? Describe some important replacement situations and policies.
20. Staff replacement policies can be easily formulated because people retire at known times. Mark the statement as T (True) or F (False).
19. For a hotel with 2,000 bulbs, the replacement policy of"group replacement at fixed intervals together with individual replacements during the intervening period" would always be inferior to the policy of"replacement of individual failures as and when needed". Mark the statement as T (True) or F
18. Expected cost of a replacement policy of individual replacements can be obtained as follows:Expected cost per time period= (No. of units/Expected life of asset) x Replacement cost per unit Mark the statement as T (True) or F (False).
17. From the following probability distribution, it can be said that for a group of 1,000 bulbs, the number ofbulbs expected to fail in the first week are 1,000 x 0.10 = 100 and (1,000-100 =) 900 x 0.15 = 135 in the second week.Mark the statement as T (True) or F (False). Week 1 2 3 4 5 Probability
16. The optimal group replacement interval is determined by the point where the sum of group replacement per unit of time and the cost of individual replacements is the minimum. Mark the statement as T (True) or F (False).
15. No replacement policy can be laid for items that fail suddenly, because the failure time of each unit is uncertain. Mark the statement as T (True) or F (False).
14. The models relating to replacement of depreciable assets are based on rather unrealistic assumption that future costs and resale prices ofan equipment are predictable accurately. Mark the statement as T (True) or F (False).
13. When time value of money is considered, weighted average costs are obtained and the optimal policy is "Do not replace if the next period's cost is less than the weighted average of the previous costs, and replace if the next period's cost is greater than the weighted average of the previous
12. The present value factors serve as the weights when time value of money is considered. Mark the statement as T (True) or F (False).
11. Replacement models considered in the text are based on the assumption that replacements, individual or group, can be done only at fixed intervals of time.Mark the statement as T (True) or F (False).
10. Even if it is decided in principle to replace an existing machine with a new one, the replacement should be postponed up to the point where the old machine can be run at a relatively lower cost. Mark the statement as T (True) or F (False).
9. Timing of incurrence of costs is important when the time value of money is considered. Mark the statement as T (True) or F (False).
8. When the time value of money is considered, costs need to be discounted. Mark the statement as T (True) or F (False).
7. An optimal replacement interval of six Years indicates that the asset in question should be replaced at the beginning of every six years. Mark the statement as T (True) or F (False).
6. The replacement interval calculations are based on the implicit assumption that the replacement of the asset is repetitive in nature. Mark the statement as T (True) or F (False).
5. Optimal replacement interval is the minimum time elapsing between the successive replacements. Mark the statement as T (True) or F (False).
4. The total cost of a piece of equipment over a given period of n years would equal Purchase price+ maintenance cost for n years+ value of the asset after n years. Mark the statement as T (True) or F (False).
3. While total depreciation of depreciable assets increases with passage of time, the successive years'depreciation usually declines. Mark the statement as T (True) or F (False).
2. For the assets that deteriorate in performance over time, the maintenance costs usually rise significantly with time. Mark the statement as T (True) or F (False).
1. The replacement theory is concerned with replacement of assets when they stop working. Mark the statement as T (True) or F (False).
A large computer installation contains 2,000 components of identical nature which are subject to failure as per probability distribution that followsComponents which fail have to be replaced for efficient functioning of the system. If they are replaced as and when failures occur, the cost of
A group of process plants in an oil refinery are fitted with valves. Over a period of time, the failure pattern of these 400 valves has been observed and it is as follows:It costs Rs 100 to replace each valve individually. If all the valves are replaced at a time, it costs Rs 50 per valve.The
The cost of a new car is Rs 10,000. Compare the optimum moment of replacement assuming the following cost informationsAssume that the repairs are made at the end of each year only if the car is to be retained and are not necessary if the car is to be sold for its salvage value. Also assume that the
Consider Example 11.4 again. Suppose that there is another machine Y which costs Rs 8,000. It requires maintenance cost equal to Rs 200 in the first year, which increases by Rs 400 in each succeeding year. Assuming that other conditions are same, determine the optimal replacement time for machine
A firm has a machine whose purchase price is Rs 20,000. Its maintenance cost and resale price at the end of different years are as given here:(a) Obtain the economic life of the machine and the minimum average cost.(b) The firm has obtained a contract to supply the goods produced by the machine,
The Mini Transport Company owns three mini buses, two of which are two years old while the third one is only a year old. Each of these buses was purchased for Rs 80,000. The company contemplates replacing the three buses by two full-sized buses, each such bus containing 50% more seating capacity
The data on the operating costs per year and resale prices of equipment A whose purchase price is Rs 10,000 are given here:(a) What is the optimum period for replacement?(b) When equipment A is 2 years old, equipment B, which is a new model for the same usage, is available.The optimum period for
A company plans to have a strength of 80 sales persons over time. The people employed by the company leave their job, the distribution of which is assumed to be as follows:Using this information, answer the following questions:(a) What recruitment level per annum would be necessary to maintain this
A large establishment has an installation with 1,000 bulbs of a certain type. From the past data, it has observed the failure rates of these bulbs as detailed here:It is given that the cost of replacing an individual bulb is Rs 3 while if the entire group of bulbs is replaced, the cost would be Re
A machine X costs Rs 5,000. Its maintenance cost is Rs 1,000 in each of the first four years and then it increases by Rs 200 every year. Assuming that the machine has no salvage value and the maintenance cost is incurred in the beginning of each year, determine the optimal replacement time for the
(a) A machine M1, costing Rs 9,000 has a maintenance cost of Rs 200 in the first year of its operation which rises by Rs 2,000 in each of the successive years. Assuming that the machine replacement can be done only at the end of a year, determine the best age at which the machine be replaced.(b)
The Simple Engineering Company has a machine whose purchase price is Rs 80,000. The expected maintenance costs and resale price in different years are as given here:After what time interval, in your opinion, should the machine be replaced? Year Maintenance Cost Rs: Resale Value ('000 Rs): 1 1,000
A firm is using a machine whose purchase price is Rs 13,000. The installation charges amount to Rs 3,600 and the machine has a scrap value of only Rs 1,600 because the firm has a monopoly of this type of work. The maintenance cost in various years is given in the following table.The firm wants to
19. A large firm has on an average, 30 pieces ofan equipment requiring repairs per week. The probability of an equipment failure is approximately constant so that the arrivals are distributed according to the Poisson law. The repair time is exponentially distributed. The down-time cost of the
12. In the central railway station 15 computerised reservation counters are available. A customer can book his/her ticket in any train on any day in any one of these computerised reservation counters. The average time spent on each customer by each clerk is five minutes. Average arrivals per hour
30. The probability of n customers arriving during a time interval T, according to the Poisson law, is given byMark the statement as T (True) or F (False). e-m m" P(n) = where m = T. n!
36. A certain queuing system has a Poisson input with a mean arrival rate of two calling units per hour.The service time distribution is exponential with a mean of0.4 hour. The marginal cost of providing each server is Rs 4 per hour, where it is estimated that the cost which is incurred by having
35. If the mean arrival rate is 24 per hour, consider from the customers's point of view, the time spent in the system, whether three channels in parallel with a mean service rate of 10 per hour is better or worse than a single channel with mean service rate of 30 per hour.
34. A post office has two clerks, either of whom averages 1.5 minutes per customer transaction (the service time being distributed exponentially). The arrival rate of the customers to the post office is one customer per minute. Compute(a) the probability that both the clerks would be idle.(b) the
33. (a) The arrivals at a desk are Poisson distributed with a mean of one customer every two minutes.The service times are exponentially distributed with an average of 15 seconds per customer. You are required to calculate:(i) Overall system utilisation.(ii) Expected number of customers in the
32. The customers arrive into a large departmental store and wander around the place selecting items of household and other use, and then proceed to checkout stands with a basket of items. There are 4 checkout counters each of which can serve a customer in six minutes, on the average. Assume that
31. A steel fabrication plant was considering the installation of a second tool crib in the plant to save walking time of the skilled craftsmen who check out equipment at the tool cribs. The Poisson/exponential assumptions about arrivals are justified in this case. The time of the craftsman is
30. The customers in the Raja Ji Departmental Store, which is being renovated, order their requirements in the different sections, pay cash at the cash counters and then, finally, obtain delivery from the 'delivery counter'. After taking delivery, the customers queue up to leave through a checkout
29. A post office has two counters, the first one handles moneY-orders and registration letters, while the second handles all other business. It has been found that service time distributions for both the counters are exponential with a mean service time of 4 minutes per customer. The customers are
28. Customers arrive at a barber's shop according to Poisson distribution. The average time between successive arrivals is 6 minutes. There are three barbers, all of same efficiency. The service time of the customers is exponentially distributed with a mean equal to 10 minutes per customer. Find
27. An insurance company has three claim adjusters in its Delhi branch office. Claimants against the company are found to arrive in a Poisson fashion, at an average rate of 20 per 10-hour day. The amount of time a server (the adjuster) spends with a customer is found to be exponentially distributed
26. Two typists have identical jobs. Each types letters dictated by a manager. Suppose that letters to be typed arrive at random (following Poisson distribution) at a rate of three per hour for each typist.Suppose that each typist can type four letters on the average per hour (following exponential
25. A company has two manufacturing shops and two tool cribs, one for each shop. Both the tool cribs handle almost identical jobs, gauges, and measuring instruments. Analysis of service time shows a negative exponential distribution with a mean of 2.5 minutes per workman. Arrivals of workmen
24. Patients arriving in the OPD of the Delhi Institute of Medical Sciences are registered at the counter after which they can be attended to by any one of the panel of 5 equally efficient doctors. The patients arrive at an average interval of 1.5 minutes and the arrival rate follows the Poisson
23. A telephone exchange has two long distance operators. It is observed that, during the peak load, long distance calls arrive in a Poisson fashion at an average rate of 15 per hour. The length of service on these calls is approximately exponentially distributed with mean length of 5 minutes.(i)
22. A laundry has six washing machines which breakdown randomly and the average time interval between successive breakdowns is 4 hours. The machines breaking down require, on an average, forty-five minutes to repair, the service time being exponentially distributed. Using this information, you are
21. The Hi-Power Company provides electric power, supplied by four big generators, to an industrial area. The generators are subject to an occasional breakdown and, from the past data, it is known that a generator develops problem, on an average, once in every 12 months. The company has a repair
20. A mechanic is to be recruited to repair scooters that breakdown at an average rate of 6 per hour. The breakdowns follow a Poisson distribution. Non-productive time of a scooter costs Rs 40 per hour.Mechanics A and B have been interviewed for the purpose. Mechanic A charges Rs 20 per hour, and
18. PQR Company has been experiencing machine breakdown for sometime and now wants to hire a mechanic on a permanent basis as against the present practice of engaging a mechanic as and when a breakdown occurs. The company has a large number of machines and, on an average, two machines breakdown per
17. Unique Tyre Company decided to hire a new mechanic to handle all tyre changes for customers ordering a new set of tyres. Two mechanics applied for the job. One mechanic has limited experience, can be hired for Rs 14 per hour, and can service an average of three customers per hour. The other
16. In an engineering workshop, motors breakdown at an average rate of 5 per day, the number of breakdowns being Poisson distributed. The present unqualified mechanic can repair motors at an average rate of 6 per day and is paid a daily wage of Rs 100. A qualified mechanic offers his services at a
15. At a tool counter, the supply clerk is paid daily wage at Rs 100 per day for an 8-hour working day. The employees who come to him to take and return the tools, their daily charges are Rs 120 per day. On an average, 25 workers come to the counter every hour for replacing the tools. The supply
14. Arrivals at the enquiry counter of Roshanara Transport Company are Poisson distributed with an average of six per hour. The time that the customers spend in seeking information from the clerk stationed at the counter is known to be exponentially distributed with an average of three
13. A repair shop attended to by a single mechanic 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, on the average. Arrivals are
11. Customers arrive to a typist, who is known for quality typing, according to Poisson probability law with an average inter-arrival time of20 minutes. The customers wait if the typist is not free. The typist completes the typing jobs in an average time of 15 minutes, the times taken being
10. Customers arrive at a one-window drive according to a Poisson distribution with mean of 10 minutes and service time per customer is exponential with mean of 6 minutes. The space in front of the window can accommodate only three vehicles including the serviced one. Other vehicles have to wait
9. Customers for a local bakery arrive randomly following a Poisson process. The single salesman can attend customers at an average rate of 12 customers per hour, the service time being distributed exponentially. The mean arrival rate of the customers is 20 per hour.Is the above queuing system
8. A company distributes its products by trucks loaded at its only loading station. Both, company's trucks and contractor's trucks are used for this purpose. It was found that on an average, every five minutes, one truck arrived and the average loading time was three minutes. 50% of the trucks
7. The mechanic at CarPoint is able to install new mufflers at an average of three per hour while customers needing this service arrive at an average rate of2 per hour. Assuming that the conditions for a single-server infinite population model are all satisfied, calculate the following:(a) The
6. A foreign bank is considering opening a drive-in window for customer service. Management estimates that customers will arrive for service at the rate of 12 per hour. The teller, whom it is considering to staff the window, can serve customers at the rate of one every three minutes. Assuming
5. A TV repairman finds that the time spent on his jobs has an exponential distribution with a mean 30 minutes. If he repairs sets on the first-come-first-served basis and if the arrival of sets is with an average rate of 10 per 8-hour day, what is repairman's expected idle time each day? Also
4. (a) For a single server queuing model, the average service time is 3 minutes and service is idle for 25% of the time. The inter-arrival time of customers for such a system will be:(i) 12 minutes (ii) 4.5 minutes (iii) 4 minutes (iv) indeterminate(b) For a single server queuing model, the average
3. On a national highway, automobiles arrive for toll tax payment at an average rate of 3 in 5 minutes, according to the Poisson probability law. The attendant receives the tax in an average time of one minute per customer. The service (collecting the tax) time is exponentially distributed. You are
2. The secretary of the Excellent Corporation receives letters for typing, the arrival of which follows the Poisson law with an average arrival rate ;\, = 3 letters/hour.(a) Find the probability that she will receive no more than 2 letters in an hour, at least one letter in an hour.(b) Determine
1. At a certain petrol pump, customers arrive in a Poisson process with an average time of five minutes between successive arrivals. The time taken at the petrol pump to serve customers follows exponential distribution with an average of two minutes. You are required to obtain the following:(a)
12. Give the role of queuing theory in decision-making and discuss its application.
11. Write the expressions for (a) expected length of the queue, and (b) expected waiting time of customers in the queue, in the single server model (i) with infinite input population, and (ii) with finite input population.
10. What is traffic intensity? If traffic intensity ofa system is given to be 0.76, what per cent of time the system would be idle? Can the traffic intensity be more than 1?
9. Distinguish between deterministic and probabilistic queuing models. Discuss some probabilistic queuing models with examples.
8. Explain the basic queuing process. State the meaning of queue discipline and give its role in queuing problem.
7. What do you understand by queuing structure? Explain (a) first-come-first-served, (b) last-come-firstserved, and (c) service-in-random-order basis of customer handling.
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