Question

Waiting lines Customers walk in at random to a deli. The interarrival times are exponentially distributed with an average of 5 minutes. The deli prepares one order at a time. The order preparation times are exponentially distributed with an average of 3 minutes. 13. What kind of waiting line model is appropriate for the deli? 14. What is the utilization? 15. What is the total amount of time a customer would expect to spend at the deli (from walking in until walking out with a sandwich)? 16. If the deli conducted a process improvement exercise to standardize the sandwich making process (i.e., eliminate as much process variability as possible), would the answer to #15 be larger, smaller, or the same? Why? Customers arrive at a theater randomly (i.e., interarrival times are exponential) and wait in line at the box office until the next ticket salesperson is available. The time it takes for the customer to select their seat and pay is exponentially distributed with a mean of 2 minutes. On Mondays, 25 customers arrive per hour and one salesperson is scheduled to work. On Tuesdays, 35 customers arrive per hour and two salespeople are scheduled to work 17. What kind of waiting line model is appropriate for Monday? On average, how many customers do we expect to see waiting in line on a Monday? 18. What kind of waiting line model is appropriate for Tuesday? On average, how many customers do we expect to see at the ticket windows on a Tuesday? Yield management 19. Choose an industry that uses differential pricing and describe an example. 20·"The Daily Show with Trevor Noah" has a studio with space for an audience of 100. Tickets are free and the number of no shows varies with an average of 20 and standard deviation of 3. How many tickets should the show distribute for each taping, if they want to have a 15% chance of turning people away?

Answer 1

13. The waiting line model here is Single Server/Single Channel System or an M/M/1 queue model. There is one deli to serve many customers walking in.

14. Arrival time = 5 minutes

Arrival rate, a = 60 / Arrival time = 60/5 = 12/hour

Service rate, s = 60/3 = 20/hour

Utilization, p = a/s = 12/20 =60%

15. Total time in the system (Waiting + Getting the sandwich) = W = 1/ (s-a) = 1/ (20-12) = 1/8 hours or 1/8*60 = 7.5 minutes

16. The answer to number 15 will be lesser. The waiting time is directly proportional to the coefficient of variation of service time. With a standardized process, the coefficient would be reduced and hence waiting time would reduce.

Note - answered 1st 4 parts as per Q&A policy