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?

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?

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 27P

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A 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?
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A 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?
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