Examples of Process Analysis Problems

Retail Bank

1. Consider the following two-stage process at a retail bank with a single receptionist. Upon arriving, customers typically wait 2 minutes before talking to the receptionist, with whom they usually spend 3 minutes. Customers are then directed to one of six bankers, for whom there is usually no wait.
(a) What is the cycle time of the two-stage process? 
(b) What is the capacity of the two-stage process?
2. The Belly Total Fitness health club offers a “no commitments” membership: Customers pay on a month-by-month basis and can cancel their membership at any time. At the time of cancellation, they are refunded the prorated fee for any remaining days in their monthly membership. Every month an average of 80 new members sign-up for the plan. Only 30% of those joining on any given month keep their memberships for a whole year. 
(a) Of the total number of active club members, on average how many keep their memberships for exactly one year? 
(b) The average number of active club members on any given day is 420. The club estimates that of these, the average number of customers who keep their memberships for one year or longer is 291. Consider the members who will drop-out before their first year. On average, how long (in months) do these members stay in the program? 
3. A neck and back masseuse has a kiosk at the local mall. Customers arrive at the kiosk on average every 6 minutes. The average duration of a massage is 5 minutes. Assume that both customer interarrival times and massage times are exponentially distributed. 
(a) What is the throughput of the kiosk’s operation? 
(b) What is the capacity of the kiosk’s operation? 
(c) How long on average does a customer spend at the kiosk from the time she arrives? 
4. Customers arrive on average every 30 minutes to The Grease Monkey, an auto repair shop with only one mechanic. The inter-arrival times are exponentially distributed. Repair times are variable with a mean of 25 minutes and a standard deviation of 20 minutes. The mechanic works on one vehicle at a time from beginning to end and takes in any waiting vehicles on a first-come first-served basis. The shop consists of a small garage and an adjacent parking lot. The garage itself has room for only one vehicle at a time, so waiting vehicles are kept in the parking lot where there are always plenty of spaces available. Assume customers never balk or renege. 
(a) How long (in minutes) do vehicles wait on average exclusively in the adjacent parking lot? final answer 
(b) What is the average number of vehicles one would expect to find exclusively in the garage? (In other words, at any given time, what is the probability of finding a vehicle in the garage?)