Question

Capacity Retailer 1 - A local retailer is considering installing self-service checkout lanes into the current system. All the self-service lanes will be used for 20 items or less, and the new self-service kiosks can accept debit cards, credit cards or cash. Based on a study completed over the past 200 days from the current operations, he has recorded the following data for the peak hourly demand for purchases of 20 items or less. The data appears in the following table. The retailer hopes to achieve two customer related service goals. 3 First, he is interested in determining the number of self-service lanes necessary to meet the estimated peak hourly demand 95% of the time. Second, he is interested in determining the capacity required to accommodate 125 percent of the estimated average demand plus a 15 percent allowance for growth. Assuming that self-service kiosk can service 25 customers per hour, estimate the number of kiosks required for each of the two options. Are there any other issues to be considered? *** Note: you can copy and paste the table below into your answer area Number of Customers Probability Number of Days Average was Observed 10 Cumulative Probability 40 55 16 30 85 125 24 145 50 175 40 200 20 245 10

Answer 1

Answer:

Number of customers	Number of days average was observed	Probability	Cumulative Probability
40	10	0.05	0.05
55	16	0.08	0.13
85	30	0.15	0.28
125	24	0.12	0.40
145	50	0.25	0.65
175	40	0.20	0.85
200	20	0.10	0.95
245	10	0.05	1.00

Option 1)

No of Kiosks required to meet the demand 95% of the time = 8 Kiosks

Option 2)

No of Kiosks required to meet 125% of average demand + 15% of growth =  8 Kiosks

Are there any other issues that need to be considered?

Yes. Another important thing that needs to be considered is the waiting time of customers. As a customer arrives and get served at a kiosk, some other customers will wait in the queue. If the queue becomes long, the waiting will increase which will affect the customer satisfaction for the service. Another important factor that will be required to consider is how many customers can be accomodated in the queue. Because a larger queue will require larger space for customers. Otherwise, there will be congestion during peak hours and customers will be further dissatisfied if there is not enough space for waiting in queue for a Kiosk.

CALCULATIONS:

Number of customers	Number of days average was observed	Probability	Cumulative Probability
40	10	=10/200 = 0.05	0.05
55	16	=16/200 =0.08	= 0.05 + 0.08 =0.13
85	30	=30/200 =0.15	=0.13+0.15 =0.28
125	24	=24/200 =0.12	=0.28+0.12 =0.40
145	50	=50/200 =0.25	=0.40 +0.25 = 0.65
175	40	=40/200 =0.20	=0.65 + 0.20 =0.85
200	20	=20/200 =0.10	=0.85 + 0.10 =0.95
245	10	=10/200 =0.05	=0.95 + 0.05 =1.00

First case

From above table, 95% of the time, demand is less than or equal to 200 customers per hour.

So, to meet the the estimated peak hourly demand 95% of the time, the kiosks should be able to serve st least 200 customers.

Therefore,

No of Kiosks required to meet the demand 95% of the time = 200/25 = 8 Kiosks

Second case

Estimated average demand

= 0.05*40 + 0.08*55 + 0.15*85 + 0.12*125 + 0.25*145 + 0.20*175 + 0.10*200 + 0.05*245

=137.65 customers per hour

For second option, 125% of average demand = 1.25*137.65 =172.1

Growth allowance = 0.15*172.1 = 25.89

Total demand = 172.1 + 25.89 = 198 customers per hour

No of Kiosks required = 198/25 = 7.92 $\approx$ 8 kiosks