Ben’s Beard Barn (BBB) is a high-end men’s salon specializing in the grooming of beards and mustaches. BBB customers, most of whom are busy professionals, don’t like to wait for their facial hair care. BBB’s process is organized as follows, with each step taking place in a different room and luxurious waiting areas between each station (containing comfy chairs, wide-screen TVs, and beer coolers):

• Reception: customers are greeted, and payment is exchanged (reception takes 3 minutes, there is one receptionist)
• Washing: customers have their beards washed, conditioned and dried (this step takes 15 minutes, there are four washers)
• Trimming: customers’ beards are trimmed according to their preferences (this step takes 20 minutes, there are five trimmers)
• Conditioning/Coloration: customers have their beards conditioned and dyed (this step takes 50 minutes, there are nine coloration experts)

As part of an advertising campaign, BBB is giving away a free craft beer each time a customer waits more than fifteen minutes between stations (for example, a customer would receive two beers for a 31-minute wait). Each craft beer costs BBB $5. Assume that patrons will wait any length of time, so long as they get their free beers as promised. On a typical day, 100 customers arrive, evenly distributed over a ten-hour day. There is one receptionist, four washers, five trimmers and nine coloration specialists.

Questions:

1. Create a process map for BBB 
2. Determine the capacity of each process step, calculate utilization of each process step, and identify the bottleneck 
3. For the bottlenecked process step (only), determine the values of the three key queueing parameters (λ, μ, and C) 
4. Using your online calculator, analyze the bottlenecked process (only):
   1. How many chairs must BBB have in the waiting area? 
   2. How long will customers have to wait on average? 
   3. Over the course of a day, how much will BBB spend on beer? 
5. Advertising increases demand by 20%. BBB needs to add staff and can pay $180/day per person for temporary labor. How many staff should BBB add in order to serve their customers at the least cost? Should your calculations. 
6. How might you improve BBB’s bottlenecked process, without spending money (assume that they are not spending money on advertising and do not have a 20% demand increase):
   a. What process changes would you make?
   b. How much would BBB save in reduced beer consumption just prior to the bottlenecked process?