The 4M company has a lathe as the centerpiece of the plant's work. The jobs arrive according to a Poisson process with an average rate of 2 per day. The processing time of each job is exponentially distributed with an average of 1/ 4 day. Since the jobs are large, if they are not in process they are stored in a warehouse some distance from the machine. However, to save time in bringing them in, the production manager proposes to add space for 3 in-process jobs in addition to the one on the lathe (the rest will continue to be stored). With this proposal, what proportion of the time will the space next to the lathe be adequate for the waiting jobs? Calculate your answer using the formulas available.

The 4M company has a lathe as the centerpiece of the plant's work. The jobs arrive according to a Poisson process with an average rate of 2 per day. The processing time of each job is exponentially distributed with an average of 1/ 4 day. Since the jobs are large, if they are not in process they are stored in a warehouse some distance from the machine. However, to save time in bringing them in, the production manager proposes to add space for 3 in-process jobs in addition to the one on the lathe (the rest will continue to be stored). With this proposal, what proportion of the time will the space next to the lathe be adequate for the waiting jobs? Calculate your answer using the formulas available.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 9P

See similar textbooks

Similar questions

Joan has a small design and tailoring shop making custom outfits for women. She has two employees. Each employee only begins working on a dress when a customer order has been received and then she makes the dress from beginning to end. The average production time of a dress is 1.8 days, with a standard deviation of 2.1 days. Historically, Joan has been receiving orders with interarrival times of one day on average. The interarrival times of orders have a coefficient of variation of one. (Carry at least 4 decimal places in all intermediate calculations. Round your final answer to 2 decimal places.) What is the expected waiting time, in days, between when an order is received and when production begins on the dress? A. 9.12 days B. 6.50 days C. 1.23 days D.3.41 days
You operate a process with three workstations; the cycle times are given below. A regular batch is 52 units and your production line runs 5 hours per day. Calculate how many hours lead time is required to ship a batch, assuming there are no orders ahead in the queue and there is no inventory to fill the order. Workstation 1 has a cycle time of 2 minutes per unit Workstation 2 has a cycle time of 3 minutes per unit Workstation 3 has a cycle time of 3 minutes per unit Select one: a. 1560.00 b. 8.00 c. 1560.00 d. 90.00 e. 2340.00
An ice cream stand has a single window and one employee to serve customers. During their busy season, 30 customers arrive each hour on average. It takes 1.5 minutes on average to serve a customer. What is the utilization of the employee?
A small call center normally has four employees answering calls while open. On average, seven calls arrive every four minutes. Under normal operating conditions, each employee on average handles each call in 3.3 minutes. But today, one employee has the flu, so the center needs to operate with three employees during this time. The manager is nervous that it may be supply-constrained and so she directs her employees to hurry up their processing of calls today. What is the maximum average processing time for each call that they need to achieve today so that they have a stable queue? Note: Round your answer to 2 decimal places. Answer is complete but not entirely correct. Maximum average processing time 4,73 minutes
To keep track of the queue and meet deadlines, two things are required: meticulous scheduling and planning.
RideShare offers short-term rentals of vehicles that are kept in small lots in urbanneighborhoods with plenty of potential customers. With one lot, it has eight cars. Theinterarrival time of potential demand for this lot from its base of customers is 40 minutes.The average rental period is five hours. If a customer checks availability of vehicles in thislot online and finds that they are all rented for the desired time, the customer skips rentingand finds alternative arrangements. However, because customers pay a monthly fee tosubscribe to this service, RideShare does not want customers to be disappointed too often.a. What is the offered load?b. What is the implied utilization?c. What is the capacity of the process (rentals per hour)?d. What is the probability that all eight cars are rented at the same time?e. How many customers are served every hour?f. What is the utilization of the cars?g. How many cars should it have in this lot to ensure that it serves at least 90 percent ofdemand?
A veterinary office with three processes (examination, greeting, and checkout) has two types of customers (boarding and medical). A veterinary office has a demand of 2 boarding customers per hour and 5 medical customers per hour. Boarding customers visit the greeting and checkout processes while medical customers visit all three processes. What is the total demand at the checkout process each hour? customers per hour
You have started a new business with your friends while you are still a student. You have special clientele.. they like snakes as pets…Hence you start a tea/snake shop (you will serve tea and snakes for entertaining your clients). You decide to hire one server in the beginning. You expect about 15 customers per hour (mean value with Poission distributed arrivals) arriving in the morning hours. The server will take about 4 minutes to serve a customer (mean time). For this situation (Situation A) Find: a. Arrival and service rates b. Find system utilization c. Percentage of time server is idle d. What is wrong with the picture? e. What can you do to help the situation? f. Once you correct the situation (adopt one of the possible solutions), find probability of 5 customers in the system. g. Find the expected number of customers waiting to be served. h. What is the service and weight times (system wait time)? i. Solve the above problem assuming M/M/1 queue discipline. You are now become…
A local café has a single cash register, with a single assistant to work it, and three servers working to fill the customer orders. Customers arrive with exponential interarrivaltime an average of one every 2 minutes. The time to place their order and pay at theregister is normally distributed with mean 90 seconds and standard deviation 20 seconds. Each customer’s order is then passed to one of the servers who take on average5 minutes with standard deviation 1.5 minutes, also normally distributed, to fill the order.d. What is the expected time from a customer’s arrival to the order being passed on tothe servers (including any queueing time)?
A local café has a single cash register, with a single assistant to work it, and three servers working to fill the customer orders. Customers arrive with exponential interarrivaltime an average of one every 2 minutes. The time to place their order and pay at theregister is normally distributed with mean 90 seconds and standard deviation 20 seconds. Each customer’s order is then passed to one of the servers who take on average5 minutes with standard deviation 1.5 minutes, also normally distributed, to fill the order.i. List as many ways you can think of that would decrease the average time acustomer spends waiting from placing their order to receiving their food.
A local café has a single cash register, with a single assistant to work it, and three servers working to fill the customer orders. Customers arrive with exponential interarrivaltime an average of one every 2 minutes. The time to place their order and pay at theregister is normally distributed with mean 90 seconds and standard deviation 20 seconds. Each customer’s order is then passed to one of the servers who take on average5 minutes with standard deviation 1.5 minutes, also normally distributed, to fill the order.a. Calculate the capacity of the register and the servers. What is the bottleneck inthis system?
An engineering i rm retains a technical specialist to assist four design engineers workingon a project. The help that the specialist gives engineers ranges widely in time consumption.The specialist has some answers available in memory, others require computation,and still others require signii cant search time. On the average, each request for assistancetakes the specialist one hour.The engineers require help from the specialist on the average of once each day. Becauseeach assistance takes about an hour, each engineer can work for seven hours, on the average,without assistance. One further point: Engineers needing help do not interrupt if thespecialist is already involved with another problem.Treat this as a i nite queuing problem and answer the following questions:a. How many engineers, on average, are waiting for the technical specialist for help?b. What is the average time that an engineer has to wait for the specialist?c. What is the probability that an engineer will have to wait…