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

question 81

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 100 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?
e.What would L_q and W_q be if the service rate were exponential,not constant?

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Definitions:

Contribution Margin

The amount by which a product's sales revenue exceeds its variable costs, contributing towards covering fixed costs and generating profit.

Gross Margin

The difference between sales revenue and the cost of goods sold, representing the core profitability of a company's products.

Variable Cost

Costs that vary directly with the level of production or business activity, including expenses such as raw materials and labor.

Machine Hours

The total operating time of machinery used in the production process during a specific period.