12ed1.00An overhead crane of ABC Ltd. moves jobs from one machine to another and must be usedevery time a machine requires loading or unloading. The demand for service is random. Datataken by recording the elapsed time between service calls followed an exponential distributionhaving a mean of a call every 24 minutes. In a similar manner, the actual service time of loadingor unloading took an average of 8 minutes. What is the average number of units in the system inthe steady state?a) 0.6Select one:O 1. c02. aO 3. bO 4. db) 0.9c) 0.5d) 0.7

From the above information, Arrival rate, λ =60 ÷24 =2.5 calls every hour Service rate, μ=60÷8 =7.5…

Answered: An overhead crane of ABC Ltd. moves…

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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Provide instead: 3 Positive and 3 negative outcomes for forecasting 3 Positive and 3 negative outcomes for queuing model
The owner of an automobile repair shop studied the waiting times for customers who arrive at the shop for an oil change. The following data with waiting times in minutes were collected over a one-month period. 2 5 22 6 5 0-4 5-9 10-14 (a) Develop a frequency distribution using classes of 0-4, 5-9, 10-14, 15-19, and 20-24. Class 15-19 20-24 Total 5 6 7 15 21 0-4 5-9 10-14 15-19 20-24 Class Total 0-4 5-9 10-14 Class 15-19 0-4 20-24 5-9 (b) Develop a relative frequency distribution using the classes in part (a). If required, round your answers to two decimal places. Relative Frequency 11 4 9 6 Class 16 10-14 15-19 12 21 8 20-24 9 10 Frequency 2 % 10 3 2 3 20 .1 .50 (c) Develop a cumulative frequency distribution using the classes in part (a) .15 .1 .15 1 M ✔ ✔ ✔ S (d) Develop a cumulative relative frequency distribution using the classes in part (a). If required, round your answers to two decimal places. 10 ✔ ✓ ✔ ✔ ✔ Cumulative Frequency Cumulative Relative Frequency X X (e) What…
Assume that during minute t (the current minute isminute 1), the following sequence of events occurs: (1) Atthe beginning of the minute, xt customers arrive at the cashregister; (2) the store manager decides how many cashregisters should be operated during the current minute;(3) if s cash registers are operated and i customers arepresent (including the current minute’s arrivals), c(s, i)customers complete service; and (4) the next minute begins.A cost of 10¢ is assessed for each minute a customerspends waiting to check out (this time includes checkouttime). Assume that it costs c(s) cents to operate s cashregisters for 1 minute. Formulate a dynamic programmingrecursion that minimizes the sum of holding and servicecosts during the next 60 minutes. Assume that before thefirst minute’s arrivals, no customers are present and thatholding cost is assessed at the end of each minute.
Please do not give solution in image formate thanku. The manager of the Safeway store (close to Santa Clara University) is considering improving the customer service level by reducing customers’ average waiting time for checkout. Based on the past year’s data, he knows that customers try to check out every 2 minutes, on average, and the standard deviation of the interarrival time is also 2 minutes. It takes on average 3 minutes to finish the checkout process. The standard deviation of the processing times is 3 minutes. The manager’s goal is to make sure the customers’ average waiting time is less than 0.5 minute. How many checkout cashiers should the manager use?
Suppose the waiting time at a certain checkout counter is bi-modal. With probability 0.85, the waiting time follows an exponential distribution with a mean waiting time of four minutes. With probability 0.15, the waiting time equals 20 minutes. a) Compute the mean and median waiting time at the checkout counter. b) Compute the variance of the waiting time at the checkout counter. c) Compute the probability that an individual customer waits longer than 5 minutes at the checkout counter.
With which decisions related to FMS design or control can the following methodsassist? Also, briefly describe how each method would be used.a. Queuing theory
5. A small town with one hospital has two ambulances to supply ambulance service. Requests forambulances during non-holiday weekends average .45 per hour and tend to be Poisson-distributed.Travel and assistance time averages two hours per call and follows an exponential distribution.Find:a. System utilizationb. The average number of customers waitingc. The average time customers wait for an ambulanced. The probability that both ambulances will be busy when a call comes in
Zilibwino Bank had received a number of complaints on the length of time(queuing time) customers took to make deposit and withdraw money. The manager responded by increasing the bank teller staff by 10 percent. Complaints on queuing time quickly decreased, but then complaints on the cost of staffsuddenly increased. Oddly enough, when staff costs were analyzed, the manager found that the average cost of staff had actually decreased relative to what it was before the increase in staff. What are some possible explanations for the complaints, and what actions might the manager contemplate?
The common measures of a queuing system's performance include: O probability that the service facility will be idle, average queue length, and probability that the waiting time will exceed a specified duration. average time each customer spends in the system, probability that the service system will be idle, and average time each customer spends in the queue. average queue length, maximum time a customer may spend in the queue, and the utilization factor for the system. average time each customer spends in the system, maximum queue length, and probability of a specific number of customers in the system. maximum queue length, maximum time a customer may spend in the queue, and average queue length.
Need help with question B. The fomula is Lmax = In K/ In P
A worker at the State Unemployment Office isresponsible for processing a company’s forms when it opensfor business. The worker can process an average of 4 formsper week. In 2002, an average of 1.8 companies per weeksubmitted forms for processing, and the worker had abacklog of .45 week. In 2003, an average of 3.9 companiesper week submitted forms for processing, and the workerhad a 5-week backlog. The poor worker was fired and suedto get his job back. The court said that since the amount ofwork submitted to the worker had approximately doubled,the worker’s backlog should have also doubled. Since his backlog increased by more than a factor of 10, he must havebeen slacking off, so the state was justified in firing him.Use queuing theory to defend the worker (based on an actualcase!).
1. A single cashier handles customers that arrive at a bakery. About 34.8 customers come into the bakery per hour. It takes 73 seconds to serve each customer (standard time). 2. What is the utilization of the cashier?What is the probability there are no customers in line or at the cashier? 3. What is the probability there are less than 2 customers waiting? Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.

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