OPSM $301$ Waiting Lines Team Assignment $2024$

Use the queueing spreadsheet we used in class to answer the following questions. In your report, make

sure that in addition to your answers to the questions, you indicate in each question how you used the

spreadsheet $($which tab, which parameters you took$).$ You may include screenshots from the

spreadsheet to show your use.

You are an analyst at a hotel. The hotel lobby deals with check$-$in and check$-$out requests. The

concierge desk handles other requests by guests.

Data were collected for both customer arrival patterns and service times for the $9$:$00-5$:$00$ time period.

The average numbers of customer arrivals for the lobby and concierge desk are provided in the Table

below. The average time it takes to serve customers in the lobby is three minutes for both the lobby

and the concierge desk. Inter$-$arrival times and service times come from an exponential distribution.

An overall goal for the hotel is that customers should not have to wait more than an average of two

minutes in the line.

Average number of customers

Find the staffing requirements $($in terms of number of servers$)$ for the lobby for each time

period that satisfies the hotel's overall goal. Similarly find the staffing requirements $($in terms

of number of servers$)$ required for the concierge desk.

Based on your analysis in question $1,$ propose a fixed number of servers for all time periods for

the lobby as well as the concierge desk. What is the service level goal in terms of the wait in

line that can be satisfied under your proposed number of servers? How would you

explain$/$justify your proposal to management? What additional data $($if any$)$ would you need

for your justification?

Now suppose that you decide to combine the lobby and concierge service into one, so that

servers can handle both lobby and concierge requests. Reconsider the arrival rates in the Table

and the service goal of no more than $2$ minutes wait in line. Assume service times remain the

same. Compare the number of servers you need for the combined lobby$-$concierge desk with

those you found in Question $1.$ What do you observe? Explain.

You want to consider the additional benefit of reducing service time variability via automation.

Consider the setting in question $3.$ Assume now that service times have no variability. For the

time interval $13$:$00-14$:$00$ compare the number of servers needed to those found under

question $3$ for this time period.