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

question 15

Essay

At the order fulfillment center 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:

Privacy Need

The intrinsic human requirement for personal space and confidentiality, affecting emotional and psychological well-being.

Neurotic Needs

Refers to ten interpersonal needs identified by Karen Horney that can become problematic if they dominate one's behavior, such as the need for approval or power.

Irrational Solutions

Refers to ineffective or unrealistic responses to problems or situations, often stemming from cognitive distortions or emotional biases.

Clusters

Groups or sets of similar items, events, or individuals, aggregated together based on shared characteristics.