14-10. The Schmedley Discount Dep. Store has approx. 300 customers shopping in i

ID: 2956072 • Letter: 1

Question

14-10. The Schmedley Discount Dep. Store has approx. 300 customers shopping in its store between 9a.m. and 5p.m. on Saturdays,
In deciding, how many csash registers to keep open each Saturday, Schmedley's manager considers two factors: customer
waiting time and the associated waiting cost and the service costs of employing additional checkout clerks. Checkout clerks are paid
an average of $8 per hour. When only one is on duty, the waiting timer per customer is about 10 minutes or 1/6 hour, when two cloerks
are on duty, the average checkout time is 6 minutes per person; 4 minutes when three clerks are working; and 3 minutes when four clerks are
are on duty. Schmedley's management has conducted customer satisfaction surveys and has been able to estimate that the store
suffers approximately $10 in lost sales and goodwill for every hour of customer time spent waiting in checkout lines. Using the information
provided determine the optimal number of clerks to have on duty each Saturday to minimize the store's total expected cost.

Explanation / Answer

1 clerk

2clerk

3 clerk

4 clerk

Service cost per day

1 clerk x 8 per clerk x 8 hours per day = $64 per day

2 clerk x 8 per clerk x 8 hours per day = $128 per day

3 clerk x 8 per clerk x 8 hours per day = $192 per day

4 clerk x 8 per clerk x 8 hours per day = $256 per day

Average wait time per customer

10 min per cost

Or 1/6 wait per cost

6 min per cost

Or 1/10 wait per cost

4 min per cost

Or 1/15 wait per cost

3min per cost

Or 1/20 wait per cost

Wait cost per day

1/6 wait per cost x

$10 per wait hr x 300 cost per daay= $ 500 per day

1/10 wait per cost x

$10 per wait hr x 300 cost per daay= $ 300 per day

1/15 wait per cost x

$10 per wait hr x 300 cost per daay= $ 200 per day

1/20 wait per cost x

$10 per wait hr x 300 cost per daay= $ 150 per day

Total cost per (servcice +wait cost

$64 per day+500 per day=$ 564 per day

$128 per day+300 per day=$ 428 per day

$192 per day+200 per day=$ 392 per day

$256 per day+150 per day=$ 406 per day

optimal number of clerks=3