Question: A small grocery store has a single checkout line. On a typical day customers arrive at the checkout on an average of one every 8
A small grocery store has a single checkout line. On a typical day customers arrive at the checkout on an average of one every 8 minutes (lets assume exponential interarrival times). The cashier takes an average of 6 minutes (lets also assume the service time has exponential distribution) to process a single customer. We assume that the service time is randomly distributed, and the customers arrive randomly. The store's owner believes that the amount of time that a customer has to wait hurts his business; he estimates that waiting time costs him $20 per customer-hour in lost business (i.e. Let's say 3 customers wait for one hour, the store incurs a cost of $20*3*1 = $60). In order to speed up service, the owner is considering hiring a teenager to bag the groceries at $6 per hour. With the addition of the bagger, the cashier will be able to process a customer in an average of 4.5 minutes. What is the wait time cost in no-bagger and with-bagger scenarios. Should the bagger be hired?
HINT: Build a simulation model in Simio. You can run a simulation for lets say 12 hours with 10 replications. No warm-up time needed. Costs are incurred from customer waiting time and the bagger cost, if utilized, as all other costs will be the same comparing the two scenarios. Realize that we are asking for a per hour cost comparison, that is why the total run time is not that significant. Run both scenarios, figure out average wait time per customers under each scenario. Your wait time cost can be computed by multiplying the cost per hour (i.e. $20/hr) with the average wait time per customer in hours and arrival rate (i.e. on average 7.5 customers arrive to the store in an hour and experience the computed average wait).
a.
No bagger wait time cost: Less than $30; With bagger wait time cost: Less than $20; Store should hire the bagger.
b.
No bagger wait time cost: More than $40; With bagger wait time cost: More than $30; Store should hire the bagger.
c.
No bagger wait time cost: More than $40; With bagger wait time cost: Less than $20; Store should hire the bagger.
d.
No bagger wait time cost: Less than $20; With bagger wait time cost: Less than $20; Store should NOT hire the bagger.
e.
No bagger wait time cost: Less than $40; With bagger wait time cost: More than $30; Store should NOT hire the bagger.
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