Operations Management
17th Edition
ISBN: 9781259142208
Author: CACHON, Gérard, Terwiesch, Christian
Publisher: Mcgraw-hill Education,
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Question
Chapter 16, Problem 3PA
Summary Introduction
To determine: How long the client should wait to receive the product.
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[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.
The 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?
(Please do not give solution in image format thanku)
A single Automated Teller Machine (ATM) is located on the ground floor of a popular shopping mall. Service time at this machine is exponentially distributed. On average, the ATM machine can serve a customer in 3 minutes. Customer arrivals at the machine are Poisson distributed, with an average of 15 customers an hour. Relevant formulas to analyze this M/M/1 model are available in your textbook.
What percent of the time is this machine idle?
25%
0%
75%
50%
100%
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- Janson's Department Store in Stark, Ohio, maintains a successful catalog sales department in which a clerk takes orders by telephone. If the clerk is occupied on one line, incoming phone calls to the catalog department are answered automatically by a recording machine and asked to wait. As soon as the clerk is free, the party who has waited the longest is transferred and serviced first. Calls come in at a rate of about 10 per hour. The clerk can take an order in an average of 4.0 minutes. Calls tend to follow a Poisson distribution, and service times tend to be negative exponential. The cost of the clerk is $8 per hour, but because of lost goodwill and sales, Janson's loses about $25 per hour of customer time spent waiting for the clerk to take an order. a) The average time that catalog customers must wait before their calls are transferred to the order clerk = minutes (round your response to two decimal places). b) The average number of callers waiting to place an…arrow_forwardPlease do not give solution in image format thanku Dan himself came to your store and wanted to know how long customers were waiting in line (this is very important to Dan!). Report the time customers wait in your queue if you have 2 cashiers open, 55 customers come into the store per hour and your cashiers take 1.9 minutes per customer to ring them up.arrow_forwardThe Shady Farm Milk Company can process milk at a fixed rate of 7500 gallons/hour.The company’s clients request 100,000 gallons of milk over the course of one day. Thisdemand is spread out uniformly from 8 a.m. to 6 p.m. The company starts producing at8 a.m. and continues to work until all of the demand has been satisfied. At noon, howmany gallons of milk are in the queue to be processed?arrow_forward
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