Agan Interior Design provides home and office decorating assistance to its custo
ID: 449660 • Letter: A
Question
Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 3.5 customers arrive each hour. One design consultant is available to answer customer questions and make product recommendations. The consultant averages 10 minutes with each customer. Agan’s management would like to evaluate two alternatives:
Use one consultant with an average service time of 10 minutes per customer.
Expand to two consultants, each of whom has an average service time of 12 minutes per customer.
If the consultants are paid $17 per hour and the customer waiting time is valued at $30 per hour for waiting time prior to service, should Agan expand to the two-consultant system?
Yes
Explain. If required, round your answers to two decimal places.
The total cost for the first scenario where thre is one consultant with an average service time of 10 minutes per customer is $____ . The total cost for the second scenario where thre are two consultants with an average service time of 12 minutes per customer is $_____ .
Explanation / Answer
For one consultant
Average arrivate rate (A)=3.5
Average service rate (U)= 60/10 =6 per hour
Lets find W, Wq,L,Lq for these queues
L= A/(U-A) =3.5/(6-3.5)=3.5/2.5=1.4
Lq= LA/U= 1.4 X3.5/6=0.817
W= L/A=1.4/3.5 =0.4 hr
Wq= Lq/A= 0.817/3.5=0.23 hr
Total cost per hour = (0.4)17+(0.23)30=13.7
if Two consultants are used. We will assume two separate lines will be formed for each of the consultant
New arrival rate (A1)=3.5/2= 1.75
Average service rate (U1)=60/12=5 per hour
L= A1/(U1-A1) =1.75/(5-1.75)=0.538
Lq= LA1/U1= 0.538 X1.75/5=0.188
W= L/A1=0.538/1.75 =0.31hr
Wq= Lq/A1= 0.188/1.75=0.11hr
Total cost per hour = 2(0.31)17+(0.11)30=13.84
Since hourly cost is less by using single consultant, Agan should not expand to the two-consultant mode