The 11th Asia Pacific Industrial Engineering and Management Systems Conference The 14th Asia Pacific Regional Meeting of International Foundation for Production Research Melaka, 7 – 10 December 2010
Modelling, Simulation, and Analysis of a Service System A Case Study through Arena Tool Amad-Uddin † 1, and Bilal Iftikhar 2 COMSATS Institute of Information Technology, Wah Cantt, Pakistan1 Drilling Engineer, HTHP Wells, POL, Pakistan 2
[email protected] or
[email protected] [email protected] or
[email protected] Tabinda Aziz3 Mirpur University of Science & Technology, Mirpur Azad Kashmir, Pakistan3
[email protected] Muhammad Aamir Saeed4 COMSATS Institute of Information Technology, Wah Cantt, Pakistan 4
[email protected] Abstract - A human cannot manage and improve a system what a human cannot study and predict a performance of a system. A system in itself is the total composition of all resources, activities, entities and various other factors. All of its constituents by varying in small details alter the nature of the entire system. This paper models, simulate, and analyse an airline ticket counter (ATC) service system (SS) through ARENA software. The influencing factors such as the service time, inter-arrival time, shifts timing, activities, and events etc are considered for the management of aforementioned service system. After modelling and simulation, the output analysis of computer modelling & simulation covers anova, bar plots, histogram results and manual mathematical calculations such as variance-mean by developing relationships among the available resources in a service system. Finally, a case study is summarized by pointing out and looking at the critical factors that can affect a service system and need to be managed and controlled in appropriate manner for the service system performance at 95% confidence interval. This paper also sets an example that how working of any real life SS can be managed and predicted with minimal assumptions once it is theoretically planned and organized before its practical implementation and hence resulting in cost and time savings. Keywords: Modelling & Simulation, Airline Ticket Counter (ATC), Service System (SS), Results & Analysis
1. INTRODUCTION A system comprises of a number of resources and involves number of activities whether it is social aspect or technical aspect of a life. Service Systems (SS) are the effective cause in a service economy, and effective system design is essential for service organizations such as retailers, distributors, and healthcare providers etc (Syam, 2008). SS is a composite of agents, technology, environment, and organization units of agents, functioning in space-time and cyberspace for a given period of time (Stanicek and Winkler, 2010). Today, number of organizations have taken charge of their service systems and effectively manage their queues to provide excellence service, one which meets or
________________________________________ † : 0092-(0)334-5450951
exceeds customer expectations (Cakebread, 2010). Even despite variations in the number of arrivals, events, and timespent-per-customer in a system, it is possible to calculate measures which characterize customers’ experiences waiting for service and help a system manager minimize investment in labor or capital equipment (Cakebread, 2010). Many service systems, there are two key components for arrival process i.e. a cyclic element and a random element. This paper majorly focuses the random element case study in a Airline Ticket Counter (ATC) system. The random element represents the intrinsic variability of the system even in the absence of trends (Kao and Chang 1988). Typical examples of such systems include patient arrivals to hospitals (Lewis
The 11th Asia Pacific Industrial Engineering and Management Systems Conference The 14th Asia Pacific Regional Meeting of International Foundation for Production Research Melaka, 7 – 10 December 2010 1972), aircraft arrivals at air terminals (Galliher and wheeler 1958, Koopman 1972).
2. STRUCTURE OF A CASE STUDY An ATC SS, a case study, is briefly described here. An ATC has two customer queues. One queue is for regular customers (RCs) and the other for frequent flyer customers (FFCs). The RCs are served by four agents and occasionally the counter manager whilst the FFCs are served by one agent. Approximately two out of ten customers have frequent flyer memberships. Customers arrive with an exponential inter-arrival time of seven minutes from 8 am to 4 pm and from 4 pm to closing at midnight. During the second shift from 4 pm to closing, all customers use the first counter with four agents, and the counter manager will not be available. During the first shift, if an arriving frequent flyer customer (FFC) observes that the regular customer (RC) queue has two or fewer people while the frequent flyer agent is busy, the customer will enter the RC queue. When there are five or more customers waiting in the RC queue, the customer manager will join the agents serving RCs until the queue size drops back to 2 or less. The agent serving the FFCs will only serve a RC under the condition that there is no frequent membership customer in the queue and the counter manager is serving RCs. Service time of RCs is normally distributed with a mean of 10 minutes and a standard deviation of 2 minutes. Service time of FFCs is also normally distributed with a mean of 7 minutes and a standard deviation of 2 minutes. All agents can take breaks during the normal working hours. The FFC counter has to be manned at all the time between 8am to 4pm. Any agent working for the RC service can temporarily work for the FFC service. The RC counter must have at least three agents available at all the time between 8 am to 4 pm and at least two agents available at all time between 4 pm to closing. An agent takes a break every 2 hours approximately. A break can start after 9:30 am and will not take place after 11.30 pm. Each break is about 10 minutes uniformly distributed between 5 to 15 minutes.
the relationships amongst the customers and the unit agents need to be defined as ARENA uses the specific options available in tools bar for modelling and simulation. Therefore, Table 1 shows the assumptions that are set up to interpret and transform the real setup of the SS into a model. Table 1: The requirements for transforming real SS into a model S.No 1. 2. 3.
Model Requirements Entities Attributes Activities
4.
Events
5.
Resources
6. 7.
Queues State Variables
8.
Starting & Stopping Probabilities
9.
Real System Components Customers that move around Time of Arrival, Priority of customers Availability of specific tickets and benefits to specific customers Arrival of customers, Departure of customers, and Timings of shifts Five agents including counter manager (for RCs), and only one agent available (for FFCs) with certain conditions. Two queues available Number of customers waiting in the two queues, and number of agents busy during the service. Start & close time of first and second shift. Two out of every ten customers have FFCs, means probability of 0.8 for RC and 0.2 for FFC.
3. MODELLING & SIMULATION In the considered SS, the criteria for the classification of the system are based on the frequency of their flights. The customers that fly frequently have been awarded the status of the frequent flyers and in that capacity they are obviously given the priority over the other customers. The other customers are the RCs, they are without the benefits and privileges that the FFCs are provided but obviously they have the right to timely service and that is acknowledged by the customer service facility. The model developed in arena, based on the data as discussed in Table 1, is shown in Figure 1.
2.1 Assumptions Few assumptions are considered here to imitate the real system. Consider the system as a terminating one for each of the 16-hour day. All customers arrived before midnight have to be served and no customer will turn up after midnight. This means that the agents may not be busy immediately at the beginning of the day and may not finish exactly at the end of the day. To model the considered SS in the ARENA software,
Figure 1: Model of a case study in arena The AR and BR are the random names which describe the first and second shifts for agents’ availability
The 11th Asia Pacific Industrial Engineering and Management Systems Conference The 14th Asia Pacific Regional Meeting of International Foundation for Production Research Melaka, 7 – 10 December 2010 respectively. The total working of the customer facility is 16 hours. Since there are two shifts for the counter therefore the system broken down into two parts. Each shift has a total working time of 480 minutes. When the model is simulated, the following distinguish results can be observed in Figures 2 & 3.
Programming To build the ATC SS model, basic programing is also involved in ARENA software. Here, programing mapping is only described without going into hardware details. Each block represents certain information regarding the queues and the values are set in each block by looking at the ATC SS conditions. If or If-Else programming techniques are generally used in these blocks. Figure 5 represents the programing set for 1st shift and Figure 6 shows the programing set for 2nd shift. The confidence interval and half width can be adjusted by using the outputs module shown in Figure 5.
Figure 2: Model’s simulation revealing 1st shift run In Figure 2, RC queue is busy for first shift and a man standing idle (red-dotted) represents break time. The second shift is idle so the agents are idle (shown by pink colour pattern). Secondly, it is also noted that when there is no load of customers on RC agents, FFC agent is also available free. But as soon as the customers load increases the FFC queue also gets busy as shown in Figure 3 which was a part of our case study that if regular customer finds FFC queue free then he can move there. The red square box describes the entity i.e. customer served. Figure 5: Logic diagram for 1st shift
Figure 3: FFC agent serving when all RC agents are busy The second shift model simulation clearly indicates in Figure 4 the idle state of first shift, hence model is precisely working according to the ATC system requirements.
Figure 6: Logic diagram for 2nd shift
Simulation Results It should be noted that the outputs modules have been defined in the model, therefore in the end of final replication’s result, an output report generates that shows the average, half width, minimum, and maximum values of each resource for 10 replications (shown in Figure 7 on next page). Figure 4: The model simulation for 2nd shift run
The 11th Asia Pacific Industrial Engineering and Management Systems Conference The 14th Asia Pacific Regional Meeting of International Foundation for Production Research Melaka, 7 – 10 December 2010
Figure 7: Simulation results for 10 replications
4. RESULTS & ANALYSIS The output results of a model after simulation are analysed and discussed in this section. The bar chart, the busy interval tables, the confidence intervals and the histograms all denote the resources (agents) working and the idle periods in between them. The confidence intervals have been set to 95% probability according to the given criterion. The results are analysed in following sequence; Setting Confidence Interval of 95% on each resource output Bar Charts/Plots Tables Histograms ANOVA (hypothesis test, A Performance Measure test) 95% Confidence Interval Results A confidence interval of 0.95 has been set to account for the readings that acquired on the lumped observations showing average, minimum & maximum working capacity of resources. In ARENA software, 95% confidence interval sets the results very near to the real life values, means more precise results can be obtained at this interval. In Figure 8, the working capacity of each resource can be seen in each queue serving the customers. The maximum value indicting the maximum capacity of a resource to serve the customer and similar is the case for minimum value. The standard deviation is also observed. Figure 9 (on next page) evaluates the customers serving capacity in each queue individually.
Figure 8: Agents working capacity readings at 95% confidence interval
The 11th Asia Pacific Industrial Engineering and Management Systems Conference The 14th Asia Pacific Regional Meeting of International Foundation for Production Research Melaka, 7 – 10 December 2010
Figure 9: RCs and FFCs queues serving capacity at 95% confidence interval Bar Charts The bar plots in the ARENA software describes the busy rate of each agent available in the both queues and the busy rate of each queue. These plots are set in order to note the time taken by each resource to serve the customers. The bar plots are shown in Figure 10 for AR1, BR1 and for queues. Tables In order to observe the changes in between each replication (i.e. more than one replication during simulation run gives more accurate results which later in manual calculation helps in estimating the exact value) for each resource in terms of completion of job duration, idle and busy, and break-time states, tables from analysis toolbar are used. The table result for AR1 agent is shown in Figure 11. The result is shown up to time of 299 minutes due to windows restriction but actually the result goes up to 480 minutes which is showing busy and idle conditions with 1 and 0 respectively in each replication.
Figure 10: The busy rate bar charts
Figure 11: For available resource AR1: status in 10 replications & 1st shift
The 11th Asia Pacific Industrial Engineering and Management Systems Conference The 14th Asia Pacific Regional Meeting of International Foundation for Production Research Melaka, 7 – 10 December 2010
Figure 12: For available resource BR1: status in 10 replications & 2nd shift
For sake of confirmation whether model works properly or not, readings of BR1 resource (agent in 2nd shift) is analysed when 1st shift model is simulated which in Figure 12 clearly indicates that it remains idle because it is designed for 2nd shift which starts working after 480th minute. Histograms Histograms are the graphical way of displaying the output of one parameter along the other. Histograms usually interpret the results in terms of relative and cumulative frequencies. The histograms are effective in their ability to display an output in well-defined steps or signals as time proceeds onwards. In Figure 13, histograms of few agents available in the 1st and 2nd shifts are shown. The absolute, relative and cumulative frequencies are shown and it should be noted that process ends with cumulative frequency of 1. The cell width etc. is taken as default values.
ANOVA A hypothesis test can be performed on the basis of mean analysis of 10 replications for each resource available in the system’s queue by using the Bonferroni in One-Way ANOVA and it is analysed in Figure 14 on next page. A collection of specific problems and techniques, called analysis of variance (ANOVA), is a standard part of any statistics. It should be noted that the null hypothesis i.e. H0 is that all the means across the different models are the same; if we do not reject this, there is no evidence of any difference on the performance measure that the different models make. But if reject H0 then it means that there is some difference somewhere among the means. In the developed model, results are showing that reject H0 (can be seen in Figure 13), It means that there is some difference in the means of each resources.
Figure 13: AR1, AR2, AR3, BR1, BR3 histograms
The 11th Asia Pacific Industrial Engineering and Management Systems Conference The 14th Asia Pacific Regional Meeting of International Foundation for Production Research Melaka, 7 – 10 December 2010 FFCs Queue Table 2: Observations in FFCs queue at each replication After simulation run Replications Observations n=10 xi 1 14 2 18 3 14 4 13 5 11 6 15 7 14 8 8 9 17 10 19 Apply the confidence interval of 0.95 & a half width of 0.0 Mean:
1 xi n Where n i.e. the number of replications is 10 and therefore x = 14.3 x
Variance:
S 2 ( x)
1 ( xi x )2 n 1
(1)
(2)
S2(x) = (1/9) [ (14 - 14.3)2 + (18 - 14.3)2... (19 – 14.3)2] S2(x) = {(0.09 + 13.69 + 0.09 + 1.69 + 10.89 + 0.49 + 0.09 + 39.69 + 7.29 + 22.09)}/9 S2(x) = 10.67 Variance Mean:
Figure 14. Anova test for output modules
Therefore
( x) n S 2 ( x ) 1.067
S2 x S2
(3)
The Half width of the Confidence Interval C.I.
h tn1,1 /2 S 2 ( x ) 5. MANUAL CALCULATIONS After analysing the output results in different plots w.r.t time and cumulative frequency, covering statistical data which describing the usage/working capacity of resources available in the ATC SS, it is also necessary to analyse the other main part of the model and that is how many customers are served by ATC’s queues in a day. To analyse the results, basic statistical data technique i.e. variance-standard deviation method is used.
(4)
h=t9,0.975 √1.067 Therefore from the statistical table corresponding to this value; h=2.26 √1.067 = 2.3344 In terms of Probability the term Confidence Interval implies, (5) P( x h x h) 1 Now we construct a Confidence Interval on mean;
x h, x h
μ=[14.3 – 2.3344 , 14.3 + 2.3344] μ=[ 11.9656 , 16.6344] Hence it is stated with a high confidence 0.95 that the true expected number of observations (customers) per day for
The 11th Asia Pacific Industrial Engineering and Management Systems Conference The 14th Asia Pacific Regional Meeting of International Foundation for Production Research Melaka, 7 – 10 December 2010 the ATC model at FFCs queue is between 11.9656 and 16.6344 i.e. 12 to 17 customers per day.
service system’s performance can be increased with 95% confidence interval and half-width interval.
RCs Queue
Table 4: Summary for the effective performance of a service system Necessary steps for any random element service system’s Efficient Performance
Table 3: Observations in RCs Queue at each replication After simulation run Replications Observations n=10 xi 1 47 2 49 3 39 4 47 5 44 6 45 7 46 8 48 9 48 10 47
1 x xi which in turn gives us a value of 46. n 1 2 S ( x) ( xi x )2 which gives us value of n 1 S2(x) = 8.22 S2 x = S2(x)/n which implies 0.822
h tn1,1 /2 S 2 ( x ) h=t9,0.975√0.822 h=2.049 Therefore this implies that
x h, x h
μ=[46 – 2.049, 46 + 2.049] μ= [43.95,48.049] Hence it can be stated with a high confidence 0.95 that the true expected number of observations per day for the ATC model at RCs queue is between 43.95 and 48.04 i.e. 44 to 49 customers per day. Thus, the ATC SS can be summarized by looking at the model’s performance and at its critical factors. The case study shows that which are the critical factors that play vital role in the management of any SS. The Table 4 shows the critical factors in any random element service systems that have to be managed if the system’s performance is to evaluate before its implementation in the real life. In order to save the time and cost (i.e. overstaffing cost) in the management of such SS, it is better to model the real system, analyse its performance and highlight the major factors that can affect the system’s performance. Thus, table 2 summarizes the key factors that can affect any service system and by managing these factors properly,
For Modelling & Simulation S.No
Critical factors to control in Model
At 95% Confidence Interval
At Half Width
For Real-life Service System Critical factors to control in real System Customer’s strength Time taken by customer & customer’s satisfaction Special services for special customers Arrival, departure, & timings of shifts Counter agents with their busy & break time schedule
1
Entities
√
√
2
Attributes
√
×
3
Activities
×
×
4
Events
√
×
5
Resources
√
√
√
×
Start and End time of 1st & 2nd Shift
√
√
-
6 7
Start & End Time of an Event Output Modules
6. CONCLUSIONS The practical physical problems in real service systems can be carried out efficiently in arena software. The imitation of real industry manufacturing processes and daily life works such as assembling operations, banking process, and car parking processes can be easily analysed with slight variations and assumptions. Animation can be done which brings the model to a very close look of real system and the movement of each part and resource effect can be analysed. The 95% confidence interval can be set on every key performance measure. A key performance measure such as average busy rate or mean can be set to analyse any service system performance. For more accurate and fine results, the number of replications can be increased. In short with the help of arena software, the practical systems regarding industrial, daily life, and manufacturing environment can be analysed by designing a model and thereafter simulating it to analyse the system’s performance before implementing it practically in real life which results in cost and time savings.
The 11th Asia Pacific Industrial Engineering and Management Systems Conference The 14th Asia Pacific Regional Meeting of International Foundation for Production Research Melaka, 7 – 10 December 2010
ACKNOWLEDGMENT This style file and sample file are adopted from APIEMS2009 format developed based on ASME style file of Harry H. Cheng, UCLA.
REFERENCES Cakebread, K. (2010) Get control of our service system: A practical introduction to queueing theory. http://www.codeproject.com/KB/recipes/QueueDemo.aspx. Access date: 16 July 2010 at 14.00. Galliher, H.P., Wheeler, R.C. (1980) Nonstationary queuing probabilities for landing congestion of Aircraft. Operation Research Vol. 6, 264-275. Kao, E.P.C., Chang, S.L. (1988) Modelling time dependent arrivals to service systems: A case in using a piece-wise polynomial rate function in a non-homogeneous poisson process. Management Science Vol. 34, No. 11, 1367-1379. Koopman, B.O. (1972) Air-Terminal queues under time dependent conditions. Operations Research, 10891114. Lewis, P.A.W. (1972) Recent Results in Statistical Analysis of Univariate Point Processes In Stochastic Point Processes, Wiley, New York, 1-54. Stanicek, Z., Winkler, M. (2010) Service systems through the prism of conceptual modelling. Service Science 2(1/2), 112 – 125. Syam, S.S. (2008) A multiple server locationallocation model for service system design. Computers and Operations Research Elsevier Science Ltd, 35(7): 2248-2265.
AUTHOR BIOGRAPHIES Mr. Amad-Uddin is a Lecturer at the Department of Mechanical Engineering, COMSATS Institute of Information Technology, Pakistan. He received a Postgraduate Degree from the School of Engineering, Design & Technology at University of Bradford, UK in 2008 and Graduate Degree from UET Peshawar, PK in 2007. His teaching and research interests include manufacturing planning & control systems (MPCs), modelling & simulation of control systems, dynamic systems, mechanical vibrations, thermodynamics and solid mechanics. He can be reached at
[email protected] or
[email protected] Mr. Bilal Iftikhar received a Postgraduate Degree in Mechanical Engineering from the School of Engineering, Design & Technology at University of Bradford, UK in 2008 and Graduate Degree from EME, NUST, PK in 2007. He served at educational and research sector as a lecturer in COMSATS about a year and currently, he is working as a drilling engineer at Pakistan Oilfields Limited; his work focuses on Oil and Gas Wells’ design and Down Hole equipment optimisation and operational monitoring and supervision. He is available at
[email protected],
[email protected] Miss. Tabinda Aiz is an Assistant Professor at the Department of Mechanical Engineering, Mirpur University of Science & Technology, Mirpur Azad Kashmir, Pakistan. She received a Postgraduate Degree from the School of Engineering, Design & Technology at University of Bradford, UK in 2008 and Graduate Degree from UET Lahore, PK in 2007. Her teaching and research interests include design optimization, machine design, manufacturing systems and solid mechanics. She can be reached at
[email protected] Mr. M. Aamir Saeed is a lecturer at the Department of Management Sciences, COMSATS Institute of Information Technology, Wah Cantt, Pakistan. He received his MS in TQM from Institute of Quality and Technology Management at University of the Punjab, Lahore, Pakistan in 2006 and did Master of Information & Operational Management from University of the Punjab, Lahore, PK in 2004. His teaching and research interests include issues effecting organizational productivity and product or service quality, decision analysis, project management and product design.
