Question

Phoenix Boutique Hotel Group (PBHG) was founded in 2007 by Bree Bristowe. Having worked for several luxury resorts, Bristowe decided to pursue her dream of owning and operating a boutique hotel. Her hotel, which she called PHX, was located in an area that included several high-end resorts and business hotels. PHX filled a niche market for “modern travelers looking for excellent service and contemporary design without the frills.” Since opening PHX, Bristowe has invested, purchased, or renovated three other small hotels in the Phoenix metropolitan area: Canyon Inn PHX, PHX B&B, and The PHX Bungalows.

One of the customer service enhancements Bristowe has implemented is a centralized, toll-free reservation system. Although many customers book specific hotels online, the phone reservation system enables PBHG to find the best reservation match at all properties. It has been an excellent option for those customers who have preferences regarding the type of room, amenity options, and the best price across the four hotel locations.

Currently, three agents are on staff for the 6 a.m. to 2 p.m. call shift. The time between calls during this shift is represented in Table 1. The time to process reservation requests during this shift is in Table 2.

Table 1: Incoming Call Distribution

Time Between Calls (Minutes)	Probability
1	0.13
2	0.23
3	0.27
4	0.19
5	0.15
6	0.09

Table 2: Service Time Distribution

Time to Process Customer Inquiries (Minutes)	Probability
1	0.19
2	0.17
3	0.16
4	0.15
5	0.11
6	0.08
7	0.03

Bristowe wants to ensure customers are not on hold for longer than 2 minutes. She is debating hiring additional staff for this shift based on the available data. Additionally, Bristowe and PBHG will soon be featured in a national travel magazine with a circulation of over a million subscriptions. Bristowe is worried that the current operators may not be able to handle the increase in reservations. The projected increase for call distribution is represented in Table 3.

Table 3: Incoming Call Distribution

Time Between Calls (Minutes)	Probability
1	0.26
2	0.27
3	0.24
4	0.14
5	0.11
6	0.06

Bristowe has asked for your advice in evaluating the current phone reservation system. Create a simulation model to investigate her concerns. Make recommendations about the reservation agents.

Answer 1

From given information, we got

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