Question

The market at the UTSC farm opens every Saturday morning. They offer fresh
organic produce that mostly comes from the farm itself. The counter opens at 9am. However,
customers start lining up at 8:30am. Customers show up at a rate of 30/hr until 9:30am
and then at a rate of 15/hr until 10:30. The counter can serve at a rate of 20/hr, and the
counter works till all customers are served.
A. Draw a graph of the number of customers waiting in the line. Start the graph at 8:30am
and show the number of waiting customers until the line is empty again. Also explain your graph and why you placed your points wherever you did.

B. Using the inventory build-up diagram, calculate the average number of customers in
line.
C. How long on average does a person stay in the line? (Hint: Little’s Law. 2nd Hint:
Make sure you calculate the throughput rate correctly.)

Answer 1

Answer A=

The graph is as below=

In the figure, the customer arrival is 15 customers from 830 am to 9.00 am, after 9 AM the customer arrival increases up to 20 customers per hour till 930AM. Then it continues to decline till 1115AM

Answer B= In order to determine the average number of customers in line, we have to first calculate the area under the curve. This is calculated by adding the areas of two triangles and two trapezoids.

The area under the curve= 15*0.5/2 + (15+20)*0.5/2 + (20+15)*1/2 + 15*0.75/2 = 35.625

Once area is determined , now this has to be divided by total time which is 1125-830=2.75 hour

Total number of customers in line = 35.625/2.75=12.95 customers

Answer C= Throughput rate = Actual output rate = 45 customers / 2.75 hrs = 16.36 customers/hr.

As per Little’s Law:

Average Flow time = Average Inventory/Throughput rate

Average Flow time = = 12.95/16.36 = 0.79 hr =

Average Flow time =0.79*60= 47.5 minutes.