Sample Case Study Paper on Operations Strategy

. Melanie is the manager of the Clean Machine car wash and

has gathered the following information. Customers arrive at a

rate of eight per hour according to a Poisson distribution. The

car washer can service an average of ten cars per hour with service times described by an exponential distribution. Melanie is concerned about the number of customers waiting in line. She has asked you to calculate the following system characteristics:

The average number of customers is 8 per hour. The car washer is able to service an average of 10 cars per hour.

Solution:

P= ƛ/µ= Average utilization of the system

p = ƛ/µ=8/10=0.8

 

  • The average number of customers in the system
Solution:

L= ƛ W= Average number of customers in the system

L= ƛ/µ-ƛ= 8/10-8= 2 customers

 

  • The average number of customers waiting inline
Solution:

The average number of customers in the system- Average system utilization

=2-0.8

= 1.2

LQ = Average number of customers waiting in line.

 

LQ=p L= 0.8* 1.2 customers

  1. Melanie realizes that how long the customer must wait is also very important. She is also concerned about customers’ balk-ing when the waiting line is too long. Using the arrival and service rates in Problem 1, she wants you to calculate the following
system characteristics:
  • The average time a customer spends in the system

 

Solution:

W=Average time spent waiting in the system, including service.

W=1/µ-ƛ= 1/10-2=0.5 hours

  • The average time a customer spends waiting inline
Solution:

WQ = Average time spent waiting in the line

WQ=pw=0.8*0.5=0.4 hours

(c) The probability of having more than three customers in
the system
Solution:

P3=cof having more than three customers in the system

P3= {(72/12)/3}3/3} = 2.6667(into four decimal places)

 

 

(d) The probability of having more than four customers in
the system
Solution:

P4= The probability of having more than four customers in

the system

p4= {(72/12)/4}4/4} = 1.2656 (into four decimal places.)