Operations Management
17th Edition
ISBN: 9781259142208
Author: CACHON, Gérard, Terwiesch, Christian
Publisher: Mcgraw-hill Education,
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Chapter 16, Problem 17PA
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To determine: The maximum average processing time for each call.
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Podunk University Operations Research Departmenthas two phone lines. An average of 30 people per hour tryto call the OR Department, and the average length of aphone call is 1 minute. If a person attempts to call whenboth lines are busy, he or she hangs up and is lost to thesystem. Assume that the time between people attempting tocall and service times is exponential.a What fraction of the time will both lines be free?What fraction of the time will both lines be busy? Whatfraction of the time will exactly one line be free?b On the average, how many lines will be busy?c On the average, how many callers will hang up eachhour?
A graphics reproduction i rm has four units of equipment that are automatic but occasionallybecome inoperative because of the need for supplies, maintenance, or repair. Eachunit requires service roughly twice each hour, or, more precisely, each unit of equipmentruns an average of 30 minutes before needing service. Service times vary widely, rangingfrom a simple service (such as pressing a restart switch or repositioning paper) to moreinvolved equipment disassembly. The average service time, however, is i ve minutes.Equipment downtime results in a loss of $20 per hour. The one equipment attendant ispaid $6 per hour.Using i nite 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 i rm is considering adding another attendant at the same $6 rate. Should the i rmdo it?
The magnetic resonance imaging (MRI) unit of St Francis hospital has 2 MRI machines and sees two kinds of patients, "regular" patients and "contrast" patients. The regular patients don't need any special preparation before imaging but the contrast patients receive an injection of "dye" that enables the physicians to see the images more clearly. Regular patients require 15 minutes in an MRI machine whereas contrast patients take on average 25 minutes in an MRI machine. Over an 8-hour day, the MRI unit receives an average of 25 regular patients and 5 contrast patients. (a) What is the implied utilization (as a %) of the MRI unit? % (b) What are the actual and maximum flow rates through the MRI (patients per day)? regular contrast Actual flow rates Max flow rates.
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- The magnetic resonance imaging (MRI) unit of St Francis hospital has 2 MRI machines and sees two kinds of patients, “regular” patients and “contrast” patients. The regular patients don’t need any special preparation before imaging but the contrast patients receive an injection of “dye” that enables the physicians to see the images more clearly. Regular patients require 15 minutes in an MRI machine whereas contrast patients take on average 25 minutes in an MRI machine. Over an 8-hour day, the MRI unit receives an average of 25 regular patients and 5 contrast patients. Convert the demand and capacity into "hours of work per day" to answer the following questions: (a) What is the implied utilization (as a %) of the MRI unit? % (Round your answer to whole number) Hint: First calculate the demand in hours of work per day: If there are 5 Contrast patients per day and each Contrast patient takes 25 minutes to 'process', how many 'minutes of work' are demanded every day from…arrow_forwardA copier store has four pieces of automatic equipment, but sometimes they are down because they need supplies, maintenance or repair. Each unit requires about two services every hour or, to be exact, each piece of equipment runs an average of 30 minutes before needing service. Service times vary greatly, from a simple service (such as pressing the reset switch or replenishing the paper) to disassembling the equipment in question. However, the average service time is five minutes. The time the equipment is down generates a loss of $60 per hour. The single employee who services the equipment earns $18 per hour. Using finite population analysis, answer the following questions: a. What is the average number of units idling? b. What is the average number of units still operating? c. What is the average number of units being serviced? d. The company is considering adding another manager at the same wage of $18 per hour. should it do so?arrow_forwardThe Shady Farm Milk Company can process milk at a fixed rate of 6,200 gallons/hour. The company’s clients request 104,000 gallons of milk over the course of one day. This demand is spread out uniformly from 8 a.m. to 6 p.m. The company starts producing at 8 a.m. and continues to work until all of the demand has been satisfied. How long does an average unit milk have to wait between its arrival at the dairy until it is processed?arrow_forward
- Consider doctor’s office: Physician’s have 30 min appointment slots starting at 8 AM to 6 PM Physicians spend 90 min (1.5 hrs.) each day on electronic medical records and 30 min on claims processing/questions related to medical insurance Typically, physicians have 75 percent appointments booked in advance, which leads to frequent cancellations. One out of 6 patients do not show up Even though appointment slots are 30 min, physicians spend on average 23 minutes with patient. Out of those 23 min, say 5 min could be done by nurse How much of physician’s work is value addedarrow_forwardIn general, pooling available safety capacity to serve all customers improves the performance of a service process, as inventory pooling also improved service level. However, if arrivals differ significantly in terms of processing requirements and waiting costs, it may be better to ________ and process them separately, because it will ________ variability in processing time within each class. **segregate; increase **segregate; reduce **pool; reduce **pool; increase Reducing variability in interarrival and processing time is a key to the performance improvement in a process. Which one of the following is NOT an appropriate lever to reduce the variability? **In manufacturing, choose more reliable supplier with consistent delivery time. **In service operations, use reservation or appointments to reduce variability in interarrival times. **Standardize work procedure, lower worker turnover rate to reduce the variability in processing times. **Increase the level of customization to offer a…arrow_forwardThe Delacroix Inn in Alexandria is a small, exclusive hotel with 20 rooms. Guests can call housekeeping from 8:00 A.M. to midnight for any of their service needs. Housekeeping keeps one person on duty during this time to respond to guest calls. Each room averages 0.7 call per day to housekeeping (Poisson distributed), and a guest request requires an average of 30 minutes (exponentially distributed) for the staff person to respond to and take care of. Determine the portion of time the staff person is busy and how long a guest must wait for his or her request to be addressed. Does the housekeeping system seem adequate?arrow_forward
- Suppose that documents are transmitted by a facsimile machine. Assume that the documents arrive at random, 75% of which is of the fixed form with constant transmission (service) time 40 seconds, whereas the rest are exponentially distributed with the mean 2 minutes. 1. How many documents per hour can be transmitted with mean waiting time no greater than 30 seconds? 2. If the number of documents per hour is the same as (1), and if all documents are of the fixed form, how much is the mean waiting time? Please answer both 1 and 2 with a complete step and formula used.arrow_forwardMax Stamp approves study abroad documents for the university. Students must wait inline with their forms outside Max’s office. One student at a time is allowed in his officeand Max takes precisely 15 minutes to evaluate each student’s set of documents. Onaverage, two students per hour go to his office and they spend, on average, 160 minutestrying to get their forms approved (time waiting in queue plus time in Max’s office having him evaluate their documents). On average, how many students are waiting outsideof Max’s office?arrow_forwardKitty Wonderland (KW) makes toys for cats. KW’s managers have recently learned that they can calculate the average waiting time for an order from the time an order is received and the time it is manufactured. They have asked for your help and have provided the following information. Expected number of orders for the product: 2,000 Manufacturing time per order: 4 hours Annual machine capacity in hours: 10,000 After learning about the average waiting time, KW’s managers are confused. They do not understand why, if annual machine capacity is greater than the average number of orders for the product, there would be any waiting time at all. Briefly answer the following questions Calculate the average waiting time per order. The managers have asked for your suggestions on what they can do to minimize or eliminate waiting time. How would you respond? Management is expecting sales to increase. Will average waiting time increase or decrease? Explain briefly.arrow_forward
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