Concept explainers
a)
To determine: The number of jobs present in the shop.
Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.
b)
To determine: The time taken to finish the order.
Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.
c)
To determine: The probability of starting the work within two days after the arrival.
Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.
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Chapter 12 Solutions
Practical Management Science
- True or False? The average number of customers in queue plus the number of servers equals the average number of customers in the system. The main cause of delay at Logan Airport was overbooking, and building a new runway solved the delay problem. If a company hopes to increase the capacity of a process, the company needs to try to shorten the process’s cycle time. Little’s Law only applies to an M/M/1 queue, which is a special case of a G/G/C queue. If a queuing system has deterministic arrival rate λ and service rate μ, and λ < μ, then Lq = 0 in this queue.arrow_forwardFind a Doctor is a small startup that helps people find a physician who best meets their needs (location, insurance accepted, etc.). During a “slow” time for it, it has 8 staff members taking calls from customers. On average, one call arrives every 5 minutes (with a standard deviation of 5 minutes). Each staff member spends on average 18 minutes with each customer (with a standard deviation of 27.00 minutes). How long does one of their customers spend, on average, waiting on hold before he or she can start speaking to a representative?arrow_forwardA summer camp that offers one-week programs faces the challenges of long queues asparents try to check in their children each Saturday morning. If they were to add morestaff to assist with the check-in process, then which of the following will occur?i. The average time parents wait decreases.ii. The maximum time the parents wait decreases.iii. The average number of parents waiting to check in their child decreases. a. Just Ib. Just IIc. Just IIId. I and IIe. I and IIIf. II and IIIg. I, II, and IIIarrow_forward
- The Solomon, Smith, and Samson law firm produces manylegal documents that must be word processed for clients andthe firm. Requests average eight pages of documents perhour, and they arrive according to a Poisson distribution. Thesecretary can word process 10 pages per hour on average ac-cording to an exponential distribution.a. What is the average utilization rate of the secretary?b. What is the probability that more than four pages are wait-ing or being word processed?c. What is the average number of pages waiting to be wordprocessed?arrow_forwardA chemical plant stores spare parts for maintenance in a large warehouse. Throughout the working day, maintenance personnel go to the warehouse to pick up supplies needed for their jobs. The warehouse receives a request for supplies, on average, every 2 minutes (Poisson distributed). The average request requires 1.7 minutes to fill (exponential service times). Maintenance employees are paid $20 per hour, and warehouse employees are paid $12 per hour. The warehouse is open 8 hours each day. What is the optimal number of warehouse employees to hire? (Hint: Time spent by maintenance workers waiting in line for supplies should be considered an expense.) What is the total cost per hour (waiting plus warehouse employee labor cost) of your solution?arrow_forwardThe Bijou Theater shows vintage movies. Customers arrive at the theater line at the rate of 100 per hour. The ticket seller averages 30 seconds per customer, which includes placing validation stamps on customers’ parking lot receipts and punching their frequent watcher cards. (Because of these added services, many customers don’t get in until after the feature has started.) (Use the Excel spreadsheet Queue Models.) What is the average customer time in the system? What would be the effect on customer time in the system of having a second ticket taker doing nothing but validations and card punching, thereby cutting the average service time to 20 seconds? Note: Round your answer to 3 decimal places. What would be the customer time in the system if instead of the change in part (b), a second window was opened with each server doing all three tasks? Note: Do not round intermediate calculations. Round your answer to 3 decimal places. Would system waiting time which is obtained…arrow_forward
- please answer within 30 minutes.arrow_forward[Queuing Theory - Operation Research] RBMC Industry manufactures a special printing according to customer specifications with respect to the number of sheets the machine can produce per hour. With this, there is a $50 increase in the production rate x. A shop owner is considering buying one of these machines. From his past experiences, the owner estimates that the arrival rate is three per hour and each order averages 500 sheets. Contracts signed by the owner, and the customer says that there will be a penalty of 10$ per late order per hour. It is assumed that the actual production time is exponential. (a) Formulate the cost model as a function of the production rate x. (b) Determine the optimal production rate the owner should specify in his purchase of the machine from RBMC. Hint: Get the derivative of the cost function.arrow_forwardFor each of the following queuing systems, indicate if it isa single- or multiple-server model, the queue discipline,and if its calling population is infinite or finite:a. Hair salonb. Bankc. Laundromatd. Doctor’s officee. Adviser’s officef. Airport runwayg. Service stationh. Copy centeri. Team trainerj. Mainframe computerarrow_forward
- Eliminating the queue of work dramatically quickens the time it takes a part to flow through the system. What are the disadvantages of removing those queues?arrow_forwardPLS HELP!!!arrow_forwardA graphics reproduction firm has four units of equipment that are automatic but occasionally become inoperative because of the need for supplies, maintenance, or repair. Each unit requires service roughly twice each hour, or, more precisely, each unit of equipment runs an average of 30 minutes before needing service. Service times vary widely, ranging from a simple service (such as pressing a restart switch or repositioning paper) to more involved equipment disassembly. The average service time, however, is five minutes. Equipment downtime results in a loss of $20 per hour. The one equipment attendant is paid $6 per hour.Using finite queuing analysis, answer the following questions: a. What is the average number of units in line? b. What is the average number of units still in operation? c. What is the average number of units being serviced?d. The fi- rm is considering adding another attendant at the same $6 rate. Should the firm do it?arrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,