Question

Can someone please show me how to solve this using excel?

During the busy lunch period at Café, customers arrive at the rate of 240 customers/hour. Studies have indicated that 20% of the customers order their lunch from the Grill, and 40% of customers get lunch from the Deli (the remaining 40% just get self-service items). All customers pay for their food at the cash register. On average, the grill-chef takes 45 seconds to serve a customer, the deli-chef takes 20 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. What is the average throughput time (including both waiting and service time) at the Grill? The Deli? The Register?

b. How long does the average customer spend being served at Café (don’t count the time walking from one spot to another or getting self-service items)?

c. As manager of Café, 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)?

Answer 1

Answer:-

Average throughput time (TPT) =(1/µ) / (1-ρ)

ʎgrill =0.2*240=48 customer/hr

(1/µ)grill =45 seconds

µgrill = 3600/45=80 customers/hr

ρgrill= ʎgrill / µgrill =48/80=0.6

TPT grill = 45/(1-0.6) =112.5 sec/customer

ʎdeli =0.4*240=96customer/hr

(1/µ)deli=20 seconds

µdeli = 3600/20=180 customers/hr

ρdeli= ʎdeli / µdeli =96/180=0.53

TPT deli = 20/(1-0.53) =42.55 sec/customer

ʎreg=1*240=240customer/hr

(1/µ)reg=12 seconds

µreg = 3600/12=300 customers/hr

ρreg= ʎreg/ µreg=240/300=0.8

TPT reg = 12/(1-0.8) =60 sec/customer

Answer b:- Grill customer = 112.5+60=172.5seconds

Deli customers =42.55+60=102.55 seconds

Self serving customer =60 seconds

Average customer will spend the time = 172.5*0.2+ 102.55*0.4 +60*0.4 =99.52 seconds

Average customer will spend the time = 99.52 seconds