Logistics Modelling
Problem 1
People arrive at a barbershop at the rate of one every 4.5 minutes. The shop can hold up to four people waiting to be served in the FIFO manner for a haircut. If the shop is full, 30% of the potential customers leave and come back in a time uniformly distributed between 40 minutes and 80 minutes. The others leave and do not return. One barber gives a haircut in a time uniformly distributed between 6 minutes and 10 minutes; the second talks a lot and takes a time uniformly distributed between 8 minutes and 16 minutes. If both barbers are idle, a customer prefers the first barber. (Model customers trying to reenter the shop as if they are new customers.) The system is simulated until 300 customers have received a haircut.
Using SIMUL8, perform 100 independent runs to determine the average number of customers in the shop at any one time. Give your answer together with its low and high 95% range as indicated in "Results Manager". Describe as clearly as possible in
about 500 to 700 words how you build your model and determine the average number of customers in the shop at a time. Screenshots and computer outputs should be provided in your description, and a screenshot of your simulation model must be provided. You do not need to submit the SIMUL8 file used to solve the problem. Use the number v as your initial random seed.
Problem 2
A bank with 4 tellers opens its doors at 9am and closes its doors at 5pm, but operates until all customers in the bank by 5pm have been served. Assume that the interarrival times of customers are independent and identically distributed that is exponential with a mean of 1 minute, and that service times of customers are independent and identically distributed that is exponential with a mean of 4.5 minutes.
Each teller has a separate queue. An arriving customer joins the shortest queue, choosing an arbitrary shortest queue in case of ties. Queue discipline is FIFO. Now, suppose that the bank's lobby is large enough to hold only 25 customers in the queues (total). If a customer arrives to find that there are already a total of 25 customers in the queues, he or she just goes away and the business is lost; this is called balking and is clearly unfortunate.
Problem Situation: The bank's management is concerned with operating costs as well as the quality of service currently being provided to customers, and is thinking of changing the number of tellers. Changing the number of tellers by one saves/costs the bank £8,000 per year, while management does not want a customer to wait too long in a queue and also customers leaving without being served, hence affecting the quality of service and incurring loss of goodwill.
a) Conceptual Model. Develop a conceptual model for the problem, by describing the objectives, inputs, outputs, content (including a logic flow diagram), assumptions and simplications of the model, in approximately 400 to 600 words.
b) Computer Model. Build a computer simulation model in SIMUL8 to model the system. A screenshot of your simulation model should be provided in your report.
Run the model independently 100 times to find
i. The average waiting time in each queue in the current system;
ii. Average number of customers who balked in the current system; and
from the "Results Manager" in SIMUL8. Give your answers together with their low and high 95% range as indicated in "Results Manager". Use the number v as your initial random seed.
c) Report to Manager. Write a report of approximately 1500 to 1800 words to the system manager, explaining your recommendations to the problem situation described above. Include the reasoning behind your choice and the comparative advantages and disadvantages of your choice. Include graphs/tables to illustrate and explain your recommendations. Remember that this report is for a business manager and should hence be of high quality and not overly-technical.