Operations Management
Operations Management
13th Edition
ISBN: 9781259667473
Author: William J Stevenson
Publisher: McGraw-Hill Education
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Chapter 18, Problem 2P

a)

Summary Introduction

To determine: Average number of customers waiting in line (Lq).

Queuing theory: It is a mathematical study of queues or waiting lines. Using queuing model, length of a queue and waiting time can be determined.  In operations management, queuing theory is used for decision making about the resources required to offer services.

b)

Summary Introduction

To determine: Average time customers spend in the system (hours).

c)

Summary Introduction

To determine: The average number of customers in the system (Ls).

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12-17 Automobiles arrive at the drive-through window at a post office at the rate of four every 10 minutes. The average service time is 2 minutes. The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed. a. What is the average time a car is in the system? b. What is the average number of cars in the system? c. What is the average time cars spend waiting to receive service? d. What is the average number of cars in line behind the customer receiving service? e. What is the probability that there are no cars at the window? f. What percentage of the time is the postal clerk busy? g. What is the probability that there are exactly two cars in the system?
A vending machine dispenses hot chocolate or coffee. Service time is 30 seconds per cup and isconstant. Customers arrive at a mean rate of 80 per hour, and this rate is Poisson-distributed. Determine the following:a. The average number of customers waiting in lineb. The average time customers spend in the systemc. The average number in the system
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