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understanding management

Quantitative Techniques In Management 4th Edition N D VOHRA - Solutions

6. Describe a single-server waiting line model. Give an example from real life, for each of the following queuing models:(i) First-come-first-served,(ii) Last-come-first-served,(iii) Random pick service,(iv) Customers stay only if served instantly.
5. What is a queuing problem? What are the basic characteristics ofa queuing system?
4. Analyse the following queuing systems by describing their various system properties:(a) Hospital Emergency Room,(b) Traffic Light,(c) Computer System at a University.
3. What is queuing theory? In what types of problem situations can it be applied successfully? Discuss giving examples.
2. Give a general structure of the queuing system and explain. Illustrate some queuing situations.
1. What is queuing theory? What type of questions are sought to be answered in analysing a queuing system?
29. Parallel service stations implies multiple servers providing same service. Mark the statement as T (True) or F (False).
28. In a multiple server model, the arrival rate of customers may be larger than the service rate of an individual server but it should be smaller than the combined service rate of all K service facilities. Mark the statement as T (True) or F (False).
27. The Poisson-exponential multiple server model is based on the assumption, among others, that multiple queues are formed. Mark the statement as T (True) or F (False).
26. The distribution of waiting time is not related to queue discipline used in selecting the waiting customers for service. Mark the statement as T (True) or F (False).
25. In both single server and multi-server models, rho is defined as the ratio of lambda to mu. Mark the statement as T (True) or F (False).
24. Equal degree of change in the service rate on higher and lower sides produces skewed effect in terms of changes in various parameters. Mark the statement as T (True) or F (False).
23. In the Poisson-exponential single server model with finite source population, there is a strong dependency relationship between the arrivals. Mark the statement as T (True) or F (False).
22. It is necessary that at the optimal level of service, the cost of waiting equals cost of servicing. Mark the statement as T (True) or F (False).
21. The expected length of system, Ls, should be equal to the expected length of queue plus one. Mark the statement as T (True) or F (False).
20. For a single server model, Lq' >Ls> Lq and Ws > Wq. Mark the statement as T (True) or F (False).
19. In a Poisson-exponential single server queuing model, the probability of having at least n customers in the system at a random point of time is equal to pn (1 - p). Mark the statement as T (True) or F (False).
18. In a single server queuing situation, steady state is reached after a sufficiently long period of time if the service rate is greater than the arrival rate. Mark the statement as T (True) or F (False). Mark the statement as T (True) or F (False).
17. In the Poisson-exponential single server model, the system is not workable if the arrival and service rates are equal. Mark the statement as T (True) or F (False). Mark the statement as T (True) or F (False).
16. The arrival rate in the Poisson distribution is equal to the mean of the exponential inter-arrival time. Mark the statement as T (True) or F (False).
15. An arrival rate of 10 customers per hour according to Poisson process implies an average inter-arrival time of six minutes. Mark the statement as T (True) or F (False).
14. If the arrivals occur according to a Poisson distribution, the inter-arrival times would be exponentially distributed. Mark the statement as T (True) or F (False).
13. The term Poisson-exponential in the context of a queuing model indicates that the arrival rate of customers is Poisson distributed while the service rate is distributed exponentially. Mark the statement as T (True) or F (False).
12. In a deterministic queuing model, the arrival rate must not exceed the service rate, but in a probabilistic model it can. Mark the statement as T (True) or F (False).
11. A queuing model where customer arrivals are at known intervals and the service time is also certain, is a deterministic model. Mark the statement as T (True) or F (False).
10. Jockeying is exercised by the customers in shifting to the "fast" moving queues in an attempt to save the waiting time. Mark the statement as T (True) or F (False).
9. An expectation of a long waiting time, particularly when there are limits on the time and extent of storage capacity available, an arriving customer may balk. Mark the statement as T (True) or F (False).
8. If a waiting customer becomes impatient, it may decide to renege. Mark the statement as T (True) or F (False).
7. The only way the customers are serviced in queuing situations is the first-come-first-served basis. Mark the statement as T (True) or F (False).
6. Multiple servers may be in series or in parallel. Mark the statement as T (True) or F (False).
5. The service rate and service time are reciprocals of each other. Mark the statement as T (True) or F (False).
4. Arrival of patients with appointment to a dentist can be described as arrival by Poisson process. Mark the statement as T (True) or F (False).
3. Arrival of passengers from aeroplanes at an airport is an example of individual arrivals of customers. Mark the statement as T (True) or F (False).
2. A study of queuing theory helps the manager to establish an optimal level of service. Mark the statement as T (True) or F (False).
1. In queuing theory, customers might include humans, machines, automobiles, and so on. Mark the statement as T (True) or F (False).
A company currently has two tool cribs, each having a single clerk, in its manufacturing area. One tool crib handles only the tools for the heavy machinery, while the second one handles all other tools. It is observed that for each tool crib the arrivals follow a Poisson distribution with a mean of
A bank has two tellers working on savings accounts. The first teller handles withdrawals only while the second teller handles depositors only. It has been found that the service time distributions of both depositors and withdrawals are exponential with a mean service time of 3 minutes per
Customers arrive at the rate of twenty per hour and the present serving arrangements can cope with thirty per hour for an eight-hour day.Using the queuing formulae provided, you are required to calculate and state:(a) the average time in the queue;(b) the implied value of customers' time if the
The Tooth-Care Hospital provides free dental service to the patients on every Saturday morning. There are three dentists on duty, who are equally qualified and experienced. It takes, on an average, 20 minutes for a patient to get treatment, and the actual time taken is known to vary approximately
On an average, 4 patients per hour require the service of an emergency clinic. Also, on an average, a patient requires 10 minutes of active attention. The clinic can handle only one emergency at a time. Suppose that it costs the clinic Rs 300 per patient treated to obtain an average servicing time
A factory operates for 8 hours everyday and has 240 working days in the year. It buys a large number of small machines which can be serviced by its maintenance engineer at a cost of Rs 4 per hour for the labour and spare parts. The machines can, alternatively, be serviced by the supplier at an
(a) A typist at an office receives, on an average, 22 letters per day of typing. The typist works 8 hours a day and it takes on an average 20 minutes to type a letter. The company has determined that the cost of a letter waiting to be mailed (opportunity cost) is 80 paise per hour and the equipment
A warehouse has only one loading dock manned by a three person crew. Trucks arrive at the loading dock at an average rate of 4 trucks per hour and the arrivals are Poisson distributed. The loading of a truck takes 10 minutes on an average and the loading time can be assumed to be exponentially
The average time between successive arrivals to a repair shop, which works 8 hours a day, is 30 minutes. The shop has one mechanic who can repair the incoming vehicles at an average rate of 3 per hour. The mechanic is paid at Rs 14 per hour while the cost of waiting time, in terms of customer
The rate of arrival of customers at a public telephone follows Poisson distribution, with an average time of ten minutes between one customer and the next. The duration of a phone call is assumed to follow exponential distribution with a mean time of three minutes.(i) What is the probability that a
Assume that at a bank teller window the customers arrive in their cars at the average rate of twenty per hour according to a Poisson distribution. Assume also that the bank teller spends an average of two minutes per customer to complete a service, and the service time is exponentially distributed.
A TV repairman finds that the time spent on his job has an exponential distribution with mean 30 minutes. If he repairs sets in the order in which they come and if the arrival of sets is approximately Poisson with an average rate of 10 per 8-hour day, what is his expected idle time each day? How
Customers arrive at the First Class Ticket counter of a Theatre at a rate of 12 per hour. There is one clerk serving the customers at a rate of 30 per hour.(i) What is the probability that there is no customer in counter (i.e. that the system is idle)?(ii) What is the probability that there are
The Taj Service Station has five mechanics each of whom can service a scooter in 2 hours on an average. The scooters are registered at a single counter and then sent for servicing to different mechanics.Scooters arrive at the service station at an average rate of 2 scooters per hour.Assuming that
Past records indicate that of the five machines that a factory owns, breakdowns occur at random and the average time between the breakdowns is 2 days. Assuming that the repairing capacity of the workman is one machine a day and the repairing time is distributed exponentially, determine the
A repairman is to be hired by a company to repair machines that break down following a Poisson process, with an average rate of four per hour. The cost of non-productive machine time is Rs 90 per hour. The company has the option of choosing either a fast or a slow repairman. The fast repairman
The thick curve shows that the total cost declines upto a point and then rises. The service level corresponding to the minimum point on it is the optimal service level.Let us analytically consider the manager's problem. Suppose that the service mechanics are paid at Rs 8 per hour and the storeroom
The Taj Service Station has a central store where service mechanics arrive to take spare parts for the jobs they work upon. The mechanics wait in queue if necessary and are served on a first-comefirst-served basis. The store is manned by one attendant who can attend 8 mechanics in an hour on an
Arrivals at a telephone booth are considered to be Poisson, with an average time of 10 minutes between one arrival and the next. The length of a phone call is assumed to be distributed exponentially, with mean 3 minutes. Find:(i) the probability that an arrival finds that four persons are waiting
A tailor specialises in ladies' dresses. The number of customers approaching the tailor appear to be Poisson distributed with a mean of 6 customers per hour. The tailor attends the customers on a first-come-first-served basis and the customers wait if the need be. The tailor can attend the
The manager of a bank observes that, on the average, 18 customers are served by a cashier in an hour. Assuming that the service time has an exponential distribution, what is the probability that (a) a customer shall be free within 3 minutes, (b) a customer shall be serviced in more than 12 minutes?
On an average, 5 customers reach a barber's shop every hour. Determine the probability that exactly 2 customers will reach in a 30-minute period, assuming that the arrivals follow Poisson distribution
Easton Electronics Co produces 2,000 TV sets in a year for which it needs an equal number of tubes of a certain type. Each tube costs Rs 10 and the cost to hold a tube in stock for a year is Rs 2.40.Besides, the cost of placing an order is Rs 150, which is not related to its size.Now, if an order
Using the following data, obtain the EOQ and the total variable cost associated with the policy of ordering quantities of that size.
A hardware store procures and sells hardware items. Information on an item is given here:The item can be purchased according to the following schedule:You are required to determine the best order size. Expected annual sales Ordering cost Holding cost = 8,000 units Rs 180 per order = 10% of the
Using the EOQ model, an inventory manager has established the economic order quantity in respect of an item with annual usage of 24,000 units on the average, to be equal to 4800 units, with a mean usage of 80 units per day. The lead time is known to be 5 working days. It is also known that the cost
An examination of past records gives the following distributions of lead time and daily demand.Determine the distribution of demand during the lead time. Hence, compute the mean and variance of demand during lead time. Lead Time Distribution Lead Time (Days) Frequency Demand Distribution Demand
DB pie operates a conventional stock control system based on re-order levels and economic order quantities. The various control levels were set originally based on estimates which did not allow for any uncertainty and this has caused difficulties because, in practice, lead times, demands and other
Given here is the distribution of the actual demand of an inventory item of the Cutex Manufacturing Company, over a long period of time.The average lead time (with negligible variation) is 10 days.Assuming that the distribution adequately represents the system, (a) determine the safety stock
The demand for an item during the order period is known to be normally distributed with mean = 600 units and standard deviation = 50 units. What service level can the firm expect to offer (i) when it has 80 units of safety stock, and (ii) when it provides for average demand only? (iii) Also
The Chi-Square Manufacturing Company has adopted the periodic review system for its inventory management. For an item PS-700, the review period is 25 days during which the demand for this item is known to be normally distributed with an average of 1,450 units and standard deviation equal to 150
A TV dealer finds that the cost of holding a TV in stock for a week is Rs 30 and the cost of unit shortage is Rs 70. For a particular model of TV, the probability distribution is as follows:How many units per week should the dealer order? Weekly Sales 0 1 2 3 4 5 6 Probability 0.05 0.10 0.20 0.25
Perform ABC analysis using the following data: Item Units Unit price (Rs) Item Units Unit price (Rs) 700 5.00 7 6,000 0.20 234 56 2,400 3.00 8 300 3.50 150 10.00 9 30 8.00 60 22.00 10 2,900 0.40 3,800 1.50 11 1,150 7.10 4,000 0.50 12 410 6.20
A manufacturing company has determined from an analysis of its accounting and production data for a certain part that (i) its demand is 9,000 units per annum and is uniformly distributed over the year, (ii) its cost price is Rs 2 per unit, (iii) its ordering cost is Rs 40 per order, (iv) the
Yogesh keeps his inventory in special containers. Each container occupies 10 sq ft of store space. Only 5,000 sq ft of the storage space is available. The annual demand for the inventory item is 9,000 containers, priced at Rs 8 per container. The ordering cost is estimated at Rs 40 per order, and
A wholesaler supplies 30 stuffed dolls each day to various shops. Dolls are purchased from the manufacturer in lots of 120 each at Rs 1,200 per lot. Every order incurs a handling charge of Rs 60 plus a freight charge of Rs 250 per lot. Multiple and fractional lots can also be ordered, and all
The purchasing manager of a distillery company is considering three sources of supply for oak barrels. The first supplier offers any quantity of barrels at Rs 150 each. The second supplier offers barrels in lots of 150 or more at Rs 125 per barrel. The third supplier offers barrels in lots of 250
A company uses 8,000 units of a product as raw material, costing Rs 10 per unit. The administrative cost per purchase is Rs 40. The holding costs are 28% of the average inventory. The company is following an optimal purchase policy and places orders according to the EOQ. It has been offered a
An aircraft uses high tensile bolts at an approximately constant rate of 50,000 numbers per year. The bolts cost Rs 20 each and the purchase department estimated the cost at Rs 200 to place an order.The opportunity cost on working capital is 20% per year. No shortages are allowed.(i) How frequently
A manufacturing company needs 2,500 units of a particular component every year. The company buys it at the rate of Rs 30 per unit. The order-processing cost for this part is estimated at Rs 15 and the cost of carrying a part in stock comes to about Rs 4 per year.The company can manufacture this
The annual demand for a component Z is 2,08,000 units at a steady weekly rate of 4,000 units. An appropriate formula for calculating the economic batch quantity for production of a component which is being used (at a rate of s) and produced (at a rate of r per week) at the same time isThe initial
A dealer supplies you the following information with regard to a product dealt with by him:The dealer is considering the possibility of allowing some back-order (stockout) to occur. He has estimated that the annual cost of back-ordering will be 25% of the value of inventory.(a) What should be the
A dealer supplies you the following information pertaining to an item of inventory:(i) What will be the optimal number of units of the inventory item he should buy in one lot?(ii) What quantity he should allow to be back-ordered?(iii) What will be the cost-savings, if any, resulting from
The demand for an item is deterministic and constant over time at 600 units per year. The item costs Rs 50 per unit and the cost of placing an order is estimated to be Rs 5. The inventory carrying cost is 20% and the shortage cost is Re 1 per unit per month. Find the optimal ordering quantity if
You are given the following information in regard to an item: Annual usage Ordering cost = =20,000 units Rs 160 per order Carrying cost = 20% of the average inventory investment Unit cost = Rs 2 Lead time = 10 working days Total working days = 250 per annum
For a Fixed Order Quantity System, find out the various parameters for an item with the following data:Annual consumption - 10,000 units, cost of one unit - Re 1, set up cost - Rs 12 per production run, the inventory carrying cost-Re 0.24 per unit. Past lead times: 15 days, 25 days, 12 days, 14
Daily demand for a product AX-303 is normally distributed with mean = 60 units and a standard deviation of 6 units. The lead time is constant at 9 days (working). The cost of placing an order is Rs 20 and the annual holding costs are 20% of the unit price of Rs 10. A 95% service level is desired
A company uses a component for which the forecast of usage is known to be normally distributed with mean absolute deviation (MAD) = 40 units. The company management adopts a policy which limits the stockouts to be no more than one order cycle in a year. Required: (a) How much safety stock should be
CD Ltd sells an electric motor but finds that it runs out of stock on occasions and thus loses the contribution on missed sales. The following information is available:The company works a five-day week for 48 weeks a year, that is 240 days. The demand figures have been analysed for the last 27
Your company's experience of being out-of-stock in respect of a key item is as follows:Figures in brackets represent percentage of times the item was out of stock. Assume that the stockout costs are Rs 100 per unit. The carrying cost of inventory is Rs 50 per unit. Determine the optimal level of
1. Lead time is the time elapsing between placing an order and having the goods ready in stock for use. Mark the statement as T (True) or F (False).
2. The stock which is kept to meet the total demand during lead time is called safety stock.Mark the statement as T (True) or F (False).
3. The amount of safety stock required depends on the variations in the demand rate and the lead time.
4. Ordering cost is assumed to be independent of the order quantity.Mark the statement as T (True) or F (False).
5. The ordering cost per unit is variable while the holding cost per unit per time period is fixed.Mark the statement as T (True) or F (False).
6. Stockout cost is the easiest to estimate.Mark the statement as T (True) or F (False).
7. In periodic review system of inventory management, the stock is usually replenished at equal time intervals.Mark the statement as T (True) or F (False).
8. The Wilson formulation assumes, among other things, that the demand for the item is fixed and continuous over time.Mark the statement as T (True) or F (False).
9. When it is assumed that there are no variations in the demand rate and the lead time, the re-order level would be equal to the demand during lead time, and no safety stock is needed to be kept.Mark the statement as T (True) or F (False).
10. Inventory cycle is the time interval between the successive points of time when orders are placed.Mark the statement as T (True) or F (False).
11. In the classical inventory model, the ordering and the holding costs are equal at EOQ.Mark the statement as T (True) or F (False).
12. The relevant cost in the classical EOQ model is the sum of the ordering and holding costs.Mark the statement as T (True) or F (False).
13. With increases in the carrying cost, the optimal order quantity also increases.Mark the statement as T (True) or F (False).
14. The total cost curve in the price break model is discontinuous.Mark the statement as T (True) or F (False).
15. In case of multiple price breaks, once a feasible EOQ is determined, the total cost function is evaluated at the EOQ so determined and each of the points at which the breaks are available. The point at which the total cost is the minimum, gives the optimal order quantity.Mark the statement as T

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