18. All airplane passengers at the Lake City Regional Airport must pass through a securityscreening area before proceeding to the boarding area. The airport has three screening sta-tions available, and the facility manager must decide how many to have open at any par-ticular time. The service rate for processing passengers at each screening station is 3passengers per minute. On Monday morning the arrival rate is 5.4 passengers per minute.Problems535Assume that processing times at each screening station follow an exponential distributionand that arrivals follow a Poisson distribution.a. Suppose two of the three screening stations are open on Monday morning. Computethe operating characteristics for the screening facility.b.Because of space considerations, the facility manager's goal is to limit the averagenumber of passengers waiting in line to 10 or fewer. Will the two-screening-stationsystem be able to meet the manager's goal?C. What is the average time required for a passenger to pass through security screening?

Given data: Service rate μ= 3 passengers per minuteArrival rate λ = 5.4 passengers per minute

Answered: 18. All airplane passengers at the Lake…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

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

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B. Draw and explain the flow charts of the Arrival Event and Service Completion Event.
Customer Interarrival | Service [Time of Time Number Time Arrival 22 74 22 89 105 3 21 34 4 26 38 5 80 23 6 81 26 7 78 90 20 26 32 37 10 13 88 11 28 38 12 18 73 13 29 93 14 19 25 15 20 93 16 23 17 78 37 18 20 51 19 109 28 20 78 85 You're given a table of ice-cream shop customers. 20 customers have arrived starting from 22. second of the opening. Interarrival times and service times are given in seconds.
The state operates a weigh station for trucks traveling on the highway. Every truck must pull off the highway, enter the weigh station, and undergo state inspection procedures before counting on. Trucks arrive at this station at a poisson rate of seven per hour. The time to inspect/weigh a truck varies, having an exponential probability density with a mean of 7 minutes.A. How many trucks are detained at the station on the average? B. How long can a truck expect to be detained?C. How many trucks are lined up in front of the station on the average?D. How long on the average does a truck driver have to wait in line for the truck to beinspected?
11. Leo manages a receiving station for rice. Farmers deliver their loads of rice from 7 am to 7 pm. Leo can process them at a rate of 4.5 tons an hour, and on a heavy day, a total of 96 tons can be expected. The station has room to hold only 15 tons of rice in inventory prior to processing. Once this space is filled, the farmers’ trucks must wait to dump their contents. What is the throughput (flow) rate after 7 pm (in tons/hr)?
The Y-ME central railroad station has 5 screening stations. At peak times, 175 customers arrive per hour. The average time to screen a passenger is 1.6 minutes. a. What is the rate per hour at which customers are screened? b. What is the average waiting time until beginning screening? They are concerned about the area where people line up and wait to begin screening. c. What is the average number of passengers waiting to begin screening? They want to reduce the average number of passengers in queue to fewer than 5. d. If they were able to reduce service time to 1.5 minutes, could they achieve the goal of fewer than 5 passengers waiting? Carry out to the necessary calculations to answer this question.
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?
Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 2.2 customers arrive each hour. One design consultant is available to answer customer questions and make product recommendations. The consultant averages 10 minutes with each customer. (a) Compute the operating characteristics of the customer waiting line, assuming Poisson arrivals and exponential service times. (Round your answers to four decimal places. Report time in hours.) λ Wa { é L = P q = || W = W = h h (b) Service goals dictate that an arriving customer should not wait for service more than an average of 5 minutes. Is this goal being met? (Round your answer to one decimal place.) W (in minutes) = What action do you recommend? (Select all that apply.) Increase the hours of operation. Increase the mean service rate. Hire another consultant. Decrease the mean service rate. There is no need to change the current operating parameters. min, which is greater ✓than…
True or False? In a waiting line system, the average system time Wₛ must be longer than the average waiting time Wq
Picture
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?
Suggest THREE (3) methods that an operations manager can adapt to enhance their customers' waiting experience rather than simply reducing the waiting time.
2

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