2. Café McColl (25 points) During the busy lunch period at Café McColl, customer

Question

2. Café McColl (25 points) During the busy lunch period at Café McColl, customers arrive at the rate of 200 customers/hour. Studies have indicated that 30% of the customers order their lunch from the Grill, and 50% of customers get lunch from the Deli (the remaining 20% just get self-service items). All customers pay for their food at the cash register. On average, the grill-chef takes 40 seconds to serve a customer, the deli-chef takes 30 seconds, and the register-clerk takes 12 seconds. (Assume that all service time and interarrival times are distributed exponentially, and that there is one employee at each of the three stations.) a. (10 points) What is the average throughput time (including both waiting and service time) at the Grill? The Deli? The Register? b. (5 points) How long does the average customer spend being served at Café McColl (don’t count the time walking from one spot to another or getting self-service items)? c. (10 points) As manager of Café McColl, you have been authorized by the state legislature (all salary increases must be approved by this body) to give a performance bonus to one of your employees. This bonus will cause the employee to work 10% faster. Which employee -- grill-chef, deli-chef, or register-clerk -- should receive this bonus (in addition to any calculations you perform, please give a one sentence justification for your choice)?

Explanation / Answer

a)

average throughput time at the Grill = Wq + 1/µ

Wq =Lq/

Lq = ^2 /µ(µ-)

= 60 customers/hour or 1 customer/minute

µ =1.5 customers/minute

Lq=1.33

Wq = 1.33

average throughput time at the Grill = 1.33 +.66

= 1.99 0r 2 minutes

average throughput time at the Deli = Wq + 1/µ

= 100 customers/hour or 1.67 customer/minute

µ =2 customers/minute

Lq=4.23

Wq = 2.53

average throughput time at the Deli = 2.53 +.5

= 3.03 minutes

average throughput time at the register = Wq + 1/µ

= 40 customers/hour or 0.67 customer/minute

µ =5 customers/minute

Lq=0.02

Wq = 0.03

average throughput time at the register = 0.03 +.2

= 0.23 minutes

b) average time spend by customer being served at Cafe Mcroll =(2 +3.03 +0,23)/3

= 1.75 minutes

c) Deli- chef should receive this bonus because it has maximum inflow of customer as well as it takes maximum time to serve the customer.

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