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

question 114

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 125 per hour.
(a) What is the average number of packages waiting to be sorted?
(b) What is the average number of packages in the sorting system?
(c) How long must the average package wait until it gets sorted?
(d) What would L_q and W_q be if the service rate were exponential, not constant?

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Definitions:

Counterconditioning

A behavior therapy technique that involves replacing an unwanted response to a stimulus with a desired response.

Shaping

A method of positive reinforcement in operant conditioning that rewards closer and closer approximations of the desired behavior.

Negative Punishment

A behavior modification technique where a desirable stimulus is removed following a behavior, with the intention of decreasing that behavior.

Positive Punishment

Adding an undesirable stimulus to decrease a behavior, such as giving extra chores to reduce instances of lying.