Practical Management Science
Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
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Chapter 12, Problem 46P
Summary Introduction

To determine: The number of postal windows that should be opened to minimize the hourly costs.

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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Model:

Practical Management Science, Chapter 12, Problem 46P , additional homework tip  1

Practical Management Science, Chapter 12, Problem 46P , additional homework tip  2

Practical Management Science, Chapter 12, Problem 46P , additional homework tip  3

Formulae to determine the model:

Practical Management Science, Chapter 12, Problem 46P , additional homework tip  4

Practical Management Science, Chapter 12, Problem 46P , additional homework tip  5

Practical Management Science, Chapter 12, Problem 46P , additional homework tip  6

Practical Management Science, Chapter 12, Problem 46P , additional homework tip  7

Three postal windows should be opened in order to minimize the hourly costs

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An average of 90 patrons per hour arrive at a hotel lobby(interarrival times are exponential), waiting to check in. At present, there are 5 clerks, and patrons are waiting in a singleline for the first available clerk. The average time for a clerkto service a patron is 3 minutes (exponentially distributed).Clerks earn $10 per hour, and the hotel assesses a waitingtime cost of $20 for each hour that a patron waits in line.a Compute the expected cost per hour of the currentsystem.b The hotel is considering replacing one clerk with an Automatic Clerk Machine (ACM). Management esti-mates that 20% of all patrons will use an ACM. An ACM takes an average of 1 minute to service a patron.It costs $48 per day (1 day 8 hours) to operate anACM. Should the hotel install the ACM? Assume thatall customers who are willing to use the ACM wait in asingle queue.
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