a. Customers queue at the express aisle of a supermarket checkout at the rate of 16 perhour. Employees can serve one customer every three minutes. Assuming the numberof anivals follows a Poisson distribution:i. Calculate the average number of customers in the waiting line.ii. Calculate the average time a customer spends in the waiting line.b. An investment firm is considering whether to invest in the mining sector, property, orfixed interest in the coming year. The research division has provided modelling undervarious scenarios and estimated the expected profit for each choice depending onwhether economic growth is moderate, low, or in recession. It has also estimated theprobability for each economic growth scenario, as summarised in the table below:Economic growthModerateLowRecessionProfit for each Mining10055-25choice (Smillions)462515PropertyFixed202020Probability 0.20.350.45i Calculate the expected profit for each choice and state which investment the firmshould choose to maximise the expected profit.ii. The regret table for the problem isEconomic growthModerate LowRecession0045Regret for each Miningchoice (Smillions)305Property 54Fixed80350Probability 0.20.350.45Calculate the expected regret for each choice and state which investment the firmshould choose to minimise the expected regret. Is it the same alternative that waschosen in part (i)?

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Answered: a. Customers queue at the express aisle…

Practical Management Science

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Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

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Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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6. The Security & Trust Bank employs 4 tellers to serve its customers. Customers arrive according to a Poisson process at a mean rate of 2 per minute. However, business is growing and management projects that the mean arrival rate will be 3 per minute a year from now. The transaction time between the teller and customer has an exponential distribution with a mean of 1 minute. Management has established the following guidelines for a satisfactory level of service to customers. The average number of customers waiting in line to begin service should not exceed 1. At least 90 percent of the time, the number of customers waiting in line should not exceed 3. a)Use the Excel sheet to determine how many tellers will be needed a year from now to completely satisfy these guidelines.
The Hair Port is a hair-styling salon at Riverside Mall. Four stylists are always available to serve customers on a first-come, first-served basis. Customers arrive at an average rate of four per hour (Poisson distributed), and the stylists spendan average of 45 minutes (exponentially distributed) oneach customer.a. Determine the average number of customers in thesalon, the average time a customer must wait, and theaverage number waiting to be served.b. The salon manager is considering adding a fifth stylist.Would this have a significant impact on waiting time?
A supermarket manager notices that there are 20 customers at the checkouts andalso knows that arrivals to the checkout at that time of day are at a rate of abouttwo per minute. About how long are customers spending in the checkout process(queueing and being served) on average?
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During the early morning hours, customers arrive at a branch post office at an average rate of 45 per hour (Poisson), while clerks can handle transactions in an average time (exponential) of 4 minutes each. Find: (a) The average number of customers waiting for service if 5 clerks are used. (b) The minimum number of clerks needed to keep the average waiting time in the system to under 5 minutes. (c) If clerk cost is $40 per hour and customer waiting time represents a “cost” of $30 per hour, how many clerks can be justified on a cost basis? Please show work.
Please do not give solution in image formate thanku. A new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that people will arrive at the desk at a rate of 20 per hour. It takes an average of 2 minutes to answer a question. It is assumed that the arrivals follow a Poisson distribution and answer times are exponentially distributed. Required: (g) Assume that the information desk employee earns $10 per hour. The cost of waiting time, in terms of customer unhappiness with the mall, is $12 per hour of time spent waiting in line. Find the total expected costs over an 8-hour day.
At a fashion retailer, there are 3 cashiers providing checkout service simultaneously. On average, customers arrive at the checkout area every 6 minutes. It has been estimated that the arrival process is a Poisson process. The average checkout time for each customer is 12 minutes, with its standard deviation equal to 17 minutes. Suppose that customers form a single line. What is the average length of the line (i.e., average number of customers in the waiting line)? Note: 1. Keep 2 decimal places for your final answer. Either use Excel for your calculation, or keep at least 4 decimal places for your intermediate numbers. 2. The Poisson arrival process has exponentially distributed inter-arrival times.
The arrival rate of patients at a hospital counter follows Poisson distribution with a mean of 25 per hour. The service rate of the treatment to patients also follows Poisson distribution with a mean of 45 per hour.a) What is the probability of having 0 patients in the system (P 0 )?
5. The DMV Licensing office has a single line for customers waiting for the next available clerk. There are two clerks who work at the same rate. On average customers arrive every 8 minutes and the average service rate is 5 per hour for each of the two clerks. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. d.) Because the state has received less than expected tax receipts, the DMV is thinking of cutting one position. Is this a good idea? Why?
Pasquist Water Company (PWC) operates a 24-hour facil-ity designed to efficiently fill water-hauling tanker trucks.Trucks arrive randomly to the facility and wait in line to ac-cess a wellhead pump. Since trucks vary in size and the filling operation is manually performed by the truck driver, the timeto fill a truck is also random.a. If the manager of PWC uses the multiple-server modelto calculate the operating characteristics of the facility’swaiting line, list three assumptions she must make regard-ing the behavior of waiting trucks and the truck arrivalprocess.b. Suppose an average of 336 trucks arrive each day, thereare four wellhead pumps, and each pump can serve anaverage of four trucks per hour.▪ What is the probability that exactly 10 trucks will arrivebetween 1:00 p.m. and 2:00 p.m. on any given day?▪ How likely is it that once a truck is in position at a well-head, the filling time will be less than 15 minutes?c. Contrast and comment on the performance differencesbetween:▪…
A single server queuing system has an average service time of 10 minutes per customer, which is exponentially distributed. The manager is thinking of converting to a system with a constant service time of 10 minutes. The average arrival rate will remain the same. The effect will be to: Select one: a. increase utilization. b. decrease utilization. c. not have any effect since the service time is unchanged. d. increase the average waiting time. e. decrease the average waiting time.
Josh’s Hot Dogs is a one-person hot dog stand, and normally gets about 14 customers per hour. Assuming that Josh can serve one customer in about 3 minutes. What impact does this have on the queuing characteristics? Specifically, the following questions:a. Mean number of customer in the queue b. Mean number of customer in the system: c. Mean waiting time in the queue:d. Mean waiting time in the system:e. Utilization factor for the system:f. Probability of more than 1 customer in the system at any given time.g. Do you think he has an acceptable queuing system?

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