A restaurant is interested in looking at their staf?ng for the lunch rush, running from 10 AM to 2 PM. People arrive as walk-ins, by car, or on a (roughly) scheduled bus, as follows:
· Walk-ins—one at a time, inter arrivals are exponential with mean 3 minutes; the ?rst walk-in occurs EXPO(3) minutes past 10 AM.
· By car—with one, two, three, or four people to a car with respective probabilities 0.2, 0.3, 0.3, and 0.2; inter arrivals distributed as exponential with mean 5 minutes; the ?rst car arrives EXPO(5) minutes past 10 AM.
· A single bus arrives every day sometime between 11 AM and 1 PM (arrival time distributed uniformly over this period). The number of people on the bus varies from day to day, but it appears to follow a Poisson distribution with a mean of30 people.
Once people arrive, either alone or in a group from any source, they operate in-dependently regardless of their source. The ?rst stop is with one of the servers at the order/payment counter, where ordering takes TRIA(1, 2, 4) minutes and payment then takes TRIA(1, 2, 3) minutes; these two operations are sequential, ?rst order-taking then payment, by the same server for a given customer. The next stop is to pick up the food ordered, which takes an amount of time distributed uniformly between 30 seconds and2 minutes. Then each customer goes to the dining room, which has 30 seats (people are willing to sit anywhere, not necessarily with their group), and partakes of the sublime victuals, taking an enjoyable TRIA (11, 20, 31) minutes. After that, the customer walks ful?lled to the door and leaves. Queueing at each of the three “service” stations (order/ pay, pickup food, and dining room) is allowed, with FIFO discipline. There is a travel time of EXPO(30) seconds from each station to all but the exit door—entry to order/pay, order/pay to pickup food, and pickup food to dining. After eating, people move more slowly, so the travel time from the dining room to the exit is EXPO(1) minute.
The servers at both order/pay and pickup food have a single break that they “share” on a rotating basis. More speci?cally, at 10:50 AM, 11:50 AM, 12:50PM, and 1:50 PM, one server from each station goes on a 10-minute break; if the person due to go on break at a station is busy at break time, he or she ?nishes serving the customer but still has to be back at the top of the hour (so the break could be a little shorter than 10 minutes).
Staf?ng is the main issue facing the restaurant. Currently, there are six servers at the order/pay station and two at the pickup food station throughout the 4-hour period. Since they know that the bus arrives sometime during the middle 2 hours, they’re considering a variable staf?ng plan that, for the ?rst and last hour would have three at order/pay andone at pickup food, and for the middle 2 hours would have nine at order/pay and three at pickup food (note that the total number of person-hours on the payroll is the same, 32, under either the current staf?ng plan or the alternate plan, so the payroll cost is the same).
1) Build an Arena simulation model for this restaurant.
2) Run your simulation model, find out a) the average and maximum length of each queue, b) the average and maximum time in each queue, and the total number of customers completely served and out the door. Make plots of the queues to get into order/pay, pickup food, and the dining room.
3) What is your advice on the staffing and operation of the restaurant?