A fast food restaurant is interested in looking at their staffing for the lunch rush, running from 10 am to 2 pm. People arrive one at a time, and inter arrival times (times between two successive arrivals) are exponentially distributed with the mean of 1 minute. Once people arrive, the first stop is with one of the servers at the order/payment counter. These two operations are sequential, first order-taking then payment, by the same server for a given customer. It is found that a proportion of customers pay by credit cards, while the rest of customers pay by cash. The ordering and payment times follow certain probability distributions. The next stop is to pick up the food ordered. The pickup time follows a certain probability distribution.

Then, each customer goes to the dining room, which has 30 seats (people are willing to sit anywhere). It is found that customers can be classified into two types (type A and type B), and their dining times follow different probability distributions. After that, a customer leaves. Queuing at each of the three service stations (order/pay, pickup food, and dining room) is allowed, with FIFO discipline.

Staffing is the main issue facing the restaurant. Currently, there are a certain number of servers (employees) in total, throughout the 4-hour period, some at the order/pay station and the others at the pickup food station. It is noted that the main performance measure for the restaurant is the average total time that customers stay in the restaurant. Both the probability distributions and the other parameters are shown in sheet Q2 in the attached Excel document.

1. Develop a discrete event simulation in Arena for the restaurant. Based on the current staffing, run the simulation for 10 replications, and present the average total time that customers stay in the restaurant for each replication.
2. Suppose the goal for the restaurant is to minimize the average total time that customers stay in the restaurant. How to assign the servers to minimize the average total time? Present the simulation results (with 10 replications) for different staffing scenarios that you try.

	Distribution	Parameter
Ordering time	Triangular	Min	1.3
		Mostly Likely	1.9
		Max	4.3
Payment time by credit cards	Uniform	Min	0.3
		Max	1.7
Payment time by cash	Normal	Mean	1.6
		Standard Deviation	0.3
Pickup time	Normal	Mean	2.7
		Standard Deviation	0.6
Dining time for type A customers	Triangular	Min	7.5
		Mostly Likely	14.2
		Max	28.1
Dining time for type B customers	Uniform	Min	15.7
		Max	42.9
Proportion of customers paying by credit cards	0.46
Proportion of type A customers	0.7
Current total number of servers	8
Current number of servers at the pickup food station	2