2 3 The Schmedley Discount Department Store has approximately 4 300 customers shopping in its store 5 between 9 a.m. and 5 p.m. on Saturdays. In deciding 6 how many cash registers to keep open each Saturday, 7 Schmedley's manager considers two factors: customer 8 waiting time and the associated waiting cost) 9 and the service costs of employing additional checkout 10 clerks. Checkout clerks are paid an average of 11 $ 7 12 per hour. When only one is on duty, the waiting 13 time per customer is about 14 15 minutes 15 when two clerks are on duty, the average checkout 16 time is 9 minutes per person; 17 7 minutes when three clerks are working; and 18 6 minutes when four clerks are on duty. 19 Schmedley's management has conducted customer 20 satisfaction surveys and has been able to estimate 21 that the store suffers approximately $ 11 23 in lost sales and goodwill for every hour of customer 24 time spent waiting in checkout lines. Using the information 25 provided, determine the optimal number 26 of clerks to have on duty each Saturday to minimize 27 the store's total expected cost. 28 Note: You need to create a waiting line cost analysis table, see 22 A13 X fx =IF(B7>=B8,"The service rate must be greater than the arrival rate","'"') F G . 1 J K L M A R D E 4 The arrival RATE and service RATE both must be rates and use the same time unit. Given a 5 time such as 10 minutes, convert it to a rate such as 6 per hour. 6 Data Results 7 Arrival rate (2) Average server utilization(p) #DIV/0! 8 Service rate (1) Average number of customers in the queuel4 #DIV/0! 9 9 Number of servers 1 Average number of customers in the system(#DIV/0! 10 Server cost $/time) Average waiting time in the queue(w.) #DIV/0! 11 Waiting cost ($/time) Average time in the system(W) #DIV/0! 12 Probability (% of time) system is empty (Po) #DIV/0! 13 The service rate must be greater than the arr Cost - based on waiting #DIV/0! 14 Cost - based on system #DIV/0! 15 16 17 Probabilities 18 Number Probabili Cumulative Probability 19 O #DIV/0! #DIV/0! 20 1 #DIV/0! #DIV/0! 21 2 #DIV/0! 22 3 #DIV/0! #DIV/0! 23 4 #DIV/0! #DIV/0! 24 5 #DIV/0! #DIV/0! 25 6 #DIV/0! #DIV/0! 26 7 #DIV/0! #DIV/0! 27 8 #DIV/0! #DIV/0! 28 9 #DIV/0! #DIV/0! 29 101 #DIV/0! #DIV/0! 30 11 #DIV/0! #DIV/0! 31 12 #DIV/0! #DIV/0! 32 13/ #DIV/0! #DIV/0! 33 14 #DIV/0! #DIV/0! 34 15 #DIV/0! #DIV/0! 35 16 #DIV/0! #DIV/0! 36 17 #DIV/0! #DIV/0! 37 18 #DIV/0! #DIV/0! 38 19 #DIV/0! #DIV/0! 39 20 #DIV/0! #DIV/0! 10 #DIV/0