The manager of a large group of employees must decidewhether she needs another photocopying machine. Thecost of a machine is $40 per eight-hour day regardlessof whether the machine is in use. On average, fourpeople need to use the copying machine per hour. Eachperson uses the copier for an average of 10 minutes.Interarrival times and copying times are exponentiallydistributed. Employees are paid $8 per hour, and weassume that a waiting cost is incurred when a worker iswaiting in line or is using the copying machine. Howmany copying machines should be rented?

The manager of a large group of employees must decidewhether she needs another photocopying machine. Thecost of a machine is $40 per eight-hour day regardlessof whether the machine is in use. On average, fourpeople need to use the copying machine per hour. Eachperson uses the copier for an average of 10 minutes.Interarrival times and copying times are exponentiallydistributed. Employees are paid $8 per hour, and weassume that a waiting cost is incurred when a worker iswaiting in line or is using the copying machine. Howmany copying machines should be rented?

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 21P

See similar textbooks

Similar questions

The Decision Sciences Department is trying todetermine whether to rent a slow or a fast copier. Thedepartment believes that an employee’s time is worth $15per hour. The slow copier rents for $4 per hour and it takesan employee an average of 10 minutes to complete copying(exponentially distributed). The fast copier rents for $15 perhour and it takes an employee an average of 6 minutes tocomplete copying. An average of 4 employees per hour needto use the copying machine (interarrival times areexponential). Which machine should the department rent?
The Decision Sciences Department is tyring to determine whether to rent a slow or fast copier. The department believes that an employee's time is worth $15/hour. The slow copier rents for $4/hr, and it takes an employee an average of 10 minutes to complete copying. The fast copier rents for $15/hr, and it takes an employee an average of 6 minutes to complete copying. On average, four employees per hour need to use the copying machine. (Assume the copying times and interarrival times to the copying machine are exponentially distributed.) Which machine should the department rent to minimize expected total cost per hour? Please note this class revolves around Microsoft Excel so the answer I need needs to show the formulas in Excel, along with any corresponding graphs, etc. Thank you in advance!
The Decision Sciences Department is trying todetermine whether to rent a slow or a fast copier. Thedepartment believes that an employee’s time is worth$15 per hour. The slow copier rents for $4 per hour,and it takes an employee an average of 10 minutes tocomplete copying. The fast copier rents for $15 per hour,and it takes an employee an average of six minutes tocomplete copying. On average, four employees per hourneed to use the copying machine. (Assume the copyingtimes and interarrival times to the copying machineare exponentially distributed.) Which machine shouldthe department rent to minimize expected total cost perhour?
Consider the problem of assigning multiple jdentical machines to an individual operator for the following situations: the loading and unloading time is 5 minutes, the independent operator activity time is 2 minutes, the independent machine activity time is 15 minutes. (a) How many machines should be assigned so that the operator will not be idle? What is the machine idle time in this case? (b) How many machines should be assigned so that machines will not be idle? What is the operator idle time in this case?
Based on Jacobs (1954). The Carter Caterer Company must have the following number of clean napkins available at the beginning of each of the next four days: day 1, 1500; day 2, 1200; day 3, 1800; day 4, 600. After being used, a napkin can be cleaned by one of two methods: fast service or slow service. Fast service costs 50 cents per napkin, and a napkin cleaned via fast service is available for use the day after it is last used. Slow service costs 30 cents per napkin, and these napkins can be reused two days after they are last used. New napkins can be purchased for a cost of 95 cents per napkin. Determine how to minimize the cost of meeting the demand for napkins during the next four days. (Note: There are at least two possible modeling approaches, one network and one nonnetwork. See if you can model it each way.)
A small shoe manufacturer makes two styles of shoes: oxfords and loafers. Two machines are used in the process: a cutting machine and a sewing machine. Each type of shoe requires 15 min per pair on the cutting machine. Oxfords require 10 min of sewing per pair, and loafers require 20 min of sewing per pair. Because the manufacturer can hire only one operator for each machine, each process is available for just 8 hours a day. Set up a system of linear inequalities that describes the number of pairs of each style of shoes that the manufacturer can produce within required working hours.
The Decision Sciences Department is trying to determine whether to rent a slow or a fast copier. The department believes that an employee’s time is worth $15 per hour. The slow copier rents for $4 per hour, and it takes an employee an average of 10 minutes to complete copying. The fast copier rents for $15 per hour, and it takes an employee an average of six minutes to complete copying. On average, four employees per hour need to use the copying machine. (Assume the copying times and interarrival times to the copying machine are exponentially distributed.) Which machine shouldthe department rent to minimize expected total cost per hour?
A small bank is trying to determine how many tellers toemploy. The total cost of employing a teller is $100 perday, and a teller can serve an average of 60 customersper day. On average, 50 customers arrive per day at thebank, and both service times and interarrival times areexponentially distributed. If the delay cost per customerday is $100, how many tellers should the bank hire?
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?
as the staff director of a new hospital, you are planning to hire cardiologists rehabilitation and infectious diseased specialists. according to recent data, each cardiology case averages $ 12,000 in revenue, each physical rehabilitation case $19,000, and each infectious diseased case, $14,000. you judge that each specialist you employed will expand the hospital caseload by about 10 patients per week. You already have 3 cardiologists and rehabilitation specialists bring in one government researched per year, while each infectious diseased specialist brings in three. Your board of directors would like your weekly revenue to be as large as possible. How many of each kind of specialist should you hire? a. State the LP in standard form, defining all variables? b. Solve the LP with the online solver and attach it. In a complete sentence, state your solution to the problem, How many of each kind of specialist should you hire? c. let's say you completely misjudged the number of patients each…
CPU-on-Demand (CPUD) offers real-time high-performance computing services. CPUD owns 1 supercomputer that can be accessed through the Internet. Their customers send jobs that arrive, on average, every 4 hours. The standard deviation of the interarrival times is 4 hours. Executing each job takes, on average, 3 hours on the supercomputer and the standard deviation of the processing time is 3.6 hours. On average, how long will it take to complete a job (from the time it is submitted by the customer until the time it is completed)?
A small bank is trying to determine how many tellers toemploy. The total cost of employing a teller is $100 per day,and a teller can serve an average of 60 customers per day.An average of 50 customers per day arrive at the bank, andboth service times and interarrival times are exponential. Ifthe delay cost per customer-day is $100, how many tellersshould the bank hire?