Arrival Interval Distribution Random Number Lower Limit Probability 0.11 0.21 0.22 0.2 0.16 0.1 Service Time Distribution 0 11 32 54 74 90 Random Number Lower Limit Probability 0.2 0.19 0.18 0.17 0.13 0.1 0.03 0 20 39 57 74 87 97 Customer Number Random Number 1 2 3 4 5 6 7 8 9 10 46 22 70 13 8 54 89 9 2 85 Range Upper Limit Arrival Gap Minute 10 31 53 73 89 99 1 2 3 4 5 6 Range Upper Limit Service Time (minutes) 19 38 56 73 86 96 99 1 2 3 4 5 6 7 Arrival Gap Random Number 79 67 46 22 83 82 58 90 40 64 Service Time Arrive Time Summary for This Trial Run A max 11 12 13 14 15 7 78 69 71 51 89 72 23 90 33 Service Start Service End Time in System Summary for This Trial Run Average: maximums Time on Hold Time Server Idle Percent Utilization Simulation Case Study: Phoenix Boutique Hotel Group 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) 1 2 3 4 5 6 Probability 0.11 0.21 0.22 0.20 0.16 0.10 Table 2: Service Time Distribution Time to Process Customer Inquiries (Minutes) 1 2 3 4 5 6 7 Probability 0.20 0.19 0.18 0.17 0.13 0.10 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) 1 2 3 4 5 6 Probability 0.24 0.25 0.23 0.13 0.10 0.05 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. 2 Arrival Interval Distribution Random Number Lower Limit Probability 0.11 0.21 0.22 0.2 0.16 0.1 Service Time Distribution 0 11 32 54 74 90 Random Number Lower Limit Probability 0.2 0.19 0.18 0.17 0.13 0.1 0.03 0 20 39 57 74 87 97 Customer Number Random Number Range Upper Limit Arrival Gap Minute 10 31 53 73 89 99 1 2 3 4 5 6 Range Upper Limit Service Time (minutes) 19 38 56 73 86 96 99 1 2 3 4 5 6 7 Arrival Gap Random Number Service Time Summary for T 1 2 3 4 5 6 7 8 9 10 73 78 29 2 46 39 98 29 60 42 4 5 2 1 3 3 6 2 4 3 10 11 77 94 52 74 57 79 24 7 1 2 5 6 3 5 4 5 2 1 11 12 13 14 15 27 42 80 96 88 2 3 5 6 5 28 74 73 90 3 2 5 4 6 1 Average interarrival time 1/ 3.39 = 3.39 Arrival rate = 1/ Arrival rate = 0.2949852507 Arrival rate = 0.2950/min 17.6991150442 Arrival rate = 17.69 customers per hour Average service time 3.26 Service rate = 1/ 0.3067484663 18.4049079755 service rate = 18.40 customers per hour Arrive Time Service Start Service End Time in System Time on Hold Time Server Idle Summary for This Trial Run Average: maximums 4 4 7.26 3.26 0 9 9 12.26 3.26 0 11 11 14.26 3.26 0 12 12 15.26 3.26 0 15 15 18.26 3.26 0 18 18.26 21.52 3.52 0.26 24 21.52 24.78 0.78 -2.48 26 24.78 28.04 2.04 -1.22 30 28.04 31.3 1.3 -1.96 33 31.3 34.56 1.56 -1.7 0 0 0 0 0 0 0 0 0 0 35 38 43 49 54 34.56 37.82 41.08 44.34 47.6 37.82 41.08 44.34 47.6 50.86 2.82 3.08 1.34 -1.4 -3.14 -0.44 -0.18 -1.92 -4.66 -6.4 0 0 0 0 0 Percent Utilization 0 0 0 0 0 7.3863636364 -317.9487179487 -59.8039215686 -150.7692307692 -108.9743589744 -15.6028368794 -5.8441558442 -143.2835820896 332.8571428571 203.821656051 Recommendations on the reservation agents Simulation technique allows the business to test new ideas before they make any complex decisions. From the simulated data found on the excel spreadsheet, it is important to ensure that the workers optimize their time as much as they can and at the same time ensure that the customers are served effectively. From the information, the average arrival rate is 3.45 while the service rate is 2.85. The rule of thumb state that, in a queueing process, when the arrival rate is greater than the service rate, there will be a probability of a queue forming, this will amount to a waiting time for the clients. According to PBHG, there is a queue forming as a result of the increased number of customers and the difference between the service time and the arrival time, for this reason, customers tend to spend more time in waiting causing inconveniences to the clients. Apart from that, other customers may opt to go for other substitute services which they believe to be better than that of PBGH. By having the workers working in shifts, this only reduces the burden on the workers proving the service rather than improving the customer service. Thus adopting a new technique to manage the queue and reducing the service and waiting time of the clients will be highly recommended. From the simulation results, adding more service providers will be logical and profitable in ensuring all the customers are attended to on time. Introducing a multi-server system will ensure that once a customer finds the server occupied, they can opt to go to a different server this will reduce the queue thus reducing the waiting time hence efficiency in the provision of service in the business. However, before implementation, the use of Monte Carlo simulation will be highly recommended for the decision making since it will be easy to assess the risk that will be associated in hiring more workers. In addition, it will be easy to track the potential output that is associated with the new method that has been implemented this will create and give additional strategies for PBGH in managing their time and the quality of service they provide to their customers. In addition, the output will increase as a result of an analysis using the simulation technique the associated profitability in cutting on the time spent on their customers. By increasing the number of servers in the business, PBGH will be able to serve more customers. This will be able to ensure that the revenues of the company are increased as a result of the improved service after obtaining the results from the simulation model. Increase in output is a decision arrived after implementing the strategies for increasing the servers due to analysis of the business from the simulation method. Further, there will be a reduction in the risk of capital outlay. This will ensure that the needs of customers that are demanding and the dynamic market conditions are manipulated in order to afford the practice in both the customer relations and the economic processes that arise. Recommendations In this scenario the average arrival rate is 3.39 while the service rate is 3.26. In queuing process, when the arrival rate is greater than the service rate, there will be a probability of a queue forming (waiting time). Due to increased waiting time, other customers may choose to go for other services. If workers are allotted shifts then it reduces the burden on the workers proving the service but doesn't improve the customer service. Adding service providers will be profitable. It will make sure that all customers are attended to on desired time period. Introducing a multi-server system will guarantee that once a customer finds the server occupied, they can opt to go to a different server this will reduce the queue. This reduces the waiting time overall and thereby the efficiency of service. But it is important to make use of Monte Carlo simulation in order to know and control the risk associated with hiring more workers. C.prob Minutes Probability from c.prob to Between 0.22 0 22 1 0.24 22 46 2 0.17 46 63 3 0.15 63 78 4 0.13 78 91 5 0.09 91 100 6 Customer Random Delay Number before 1 19 2 75 3 54 4 15 5 21 6 28 7 38 8 51 9 62 10 95 11 96 12 12 13 76 14 76 15 86 16 30 17 77 18 30 19 54 20 69 Arrival Time 1 5 2 1 1 2 2 3 3 6 6 1 4 4 5 2 4 2 3 4 Prob. C.prob from 0.15 0.2 0.37 0.2 0.08 0 15 35 72 92 c.prob to 15 35 72 92 100 Agent Starts service at 1 6 8 9 10 16 17 20 23 24 25 31 32 34 36 38 39 41 44 47 Random Time to complete Service Number service Over at 1 0 2 6 43 6 12 24 4 12 91 8 17 44 6 16 0 2 18 46 6 23 45 6 26 98 10 33 80 8 32 9 2 31 90 8 39 85 8 40 68 6 40 99 10 46 46 6 44 11 2 41 50 6 47 56 6 50 93 10 3 12 12 17 16 18 23 26 33 32 27 39 40 40 46 44 41 47 50 57 Minutes to help customer 2 4 6 8 10 Waiting Time Time in Service store Agent Idle 0 6 0 6 4 4 3 8 7 6 0 2 1 6 3 6 3 10 9 8 7 2 0 8 7 8 6 6 4 10 8 6 5 2 0 6 3 6 3 10 1 3 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 Arrival Interval Distribution Random Number Lower Limit Probability 0.11 0.21 0.22 0.2 0.16 0.1 Service Time Distribution 0 11 32 54 74 90 Random Number Lower Limit Probability 0.2 0.19 0.18 0.17 0.13 0.1 0.03 0 20 39 57 74 87 97 Customer Number Random Number 1 2 3 4 5 6 7 8 9 10 88 85 52 53 89 96 42 68 11 63 Range Upper Limit Arrival Gap Minute 10 31 53 73 89 99 1 2 3 4 5 6 Range Upper Limit Service Time (minutes) 19 38 56 73 86 96 99 1 2 3 4 5 6 7 Arrival Gap Random Number 5 1 6 4 2 3 6 4 3 2 Service Time Arrive Time Summary for This Trial Run A max 24 2 5 5 6 22 12 94 1 2 16 89 4 18 59 21 93 1 2 27 19 2 31 10 34 25 3 20 5 36 11 12 13 14 15 57 55 59 49 44 3 3 2 4 2 57 64 61 35 12 2 4 4 1 2 39 42 44 48 50 Service Start Service End Time in System Time on Hold Time Server Idle Percent Utilization Summary for This Trial Run Average: 2.6666666667 0.4666666667 1.2666666667 98.2666666667 maximums 5 2 5 100 5 7 2 0 5 95 11 5 1 7 0 99 12 13 1 0 1 99 16 18 2 0 3 97 18 22 4 0 0 100 22 22 1 1 99 0 27 29 2 0 5 95 31 2 0 2 98 33 34 37 3 0 1 99 37 41 5 1 0 99 41 42 46 48 50 41 46 48 49 52 2 4 4 1 2 2 0 2 0 0 0 1 0 0 1 98 99 98 100 99