At the Order Fulfillment Centre of a Major Mail-Order Firm

question 100

Essay

At the order fulfillment centre of a major mail-order firm, customer orders, already packaged for shipment, arrive at the sorting machine to be sorted for loading onto the appropriate truck for the parcel's address. The arrival rate at the sorting machine is at the rate of 140 per hour following a Poisson distribution. The machine sorts at the constant rate of 150 per hour.
a. What is the utilization rate of the system?
b. What is the average number of packages waiting to be sorted?
c. What is the average number of packages in the sorting system?
d. How long must the average package wait until it gets sorted?

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Definitions:

Allocative Efficiency

A state of the economy in which production represents consumer preferences; every good or service is distributed to yield the highest aggregate utility.

Willingness To Pay

The maximum amount a consumer is prepared to spend to acquire a good or service.

Acceptable Price

The price at which consumers feel they are getting good value for the products or services purchased.

Allocative Efficiency

A state of resource distribution where it is impossible to make any one individual better off without making someone else worse off, maximizing social welfare.