Two New Checkout Scanning Systems Are Under Consideration by a Retail

question 33

Essay

Two new checkout scanning systems are under consideration by a retail store. Arrivals to the checkout stand follow the Poisson distribution with $\lambda$ = 2 per minute. The cost for waiting is $18 per hour. The first system has an exponential service rate of 5 per minute and costs $10 per hour to operate. The second system has an exponential service rate of 8 per minute and costs $20 per hour to operate. Which system should be chosen?

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Definitions:

State of Nature

A term used in decision theory referring to the actual but possibly unknown status of the world, which affects the outcomes of decisions.

Opportunity Loss

The cost of the next best alternative foregone as a result of making a decision.

Actual Profit

The realised gain from business operations or investments, after all costs and expenses have been deducted.

Payoff Table

A tabular representation of the possible outcomes or payoffs in a decision-making problem, against various decisions under different states of nature.