A Crew of Mechanics at the Highway Department Garage Repair

question 133

Essay

A crew of mechanics at the Highway Department garage repair vehicles that break down at an average of λ = 7.5 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of μ = 10 vehicles per day with a repair time distribution that approximates an exponential distribution.
a. What is the utilization rate for this service system?
b. What is the average time before the facility can return a breakdown to service?
c. How much of that time is spent waiting for service?
d. How many vehicles are likely to be in the system at any one time?

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Definitions:

Operations Management

The field that deals with designing, overseeing, and controlling the process of production and redesigning business operations in the production of goods and services.

Learning Rate

A measure of how quickly a person or system improves performance or gains knowledge over time through experience or training.

Skilled Labour

Workers who have specialized training, expertise, or qualifications in a particular field or task, often requiring formal education or apprenticeship.

Learning Rate

A concept in machine learning and various disciplines that dictates the speed at which a model or a learner adapts to a problem, often influencing training duration and efficiency.