1. INTRODUCTION AND LITERATURE REVIEW
In modern society, people use mobile devices for daily activities such as banking, booking, shopping, and working. The Ericsson Mobility Report indicates that the number of smart phone subscriptions worldwide is currently more than 7.9 billion, whereas the number of cellular Internet of Things devices in 2018 was only 1 billion; this number is expected to continue to increase with an annual growth rate of 27% through 2024 (Ericsson Mobility Report, 2018). As a result of the rapid growth in the number of mobile users, the competition among mobile phone service providers has drastically increased. Companies employ a wide range of marketing strategies to retain their current customers and increase their number of new customers. To provide customer service and technical support, call centers are used. The call center operations of network service providers have become increasingly complicated due to the variety of customer needs and the growing demand for mobile services. To satisfy customer needs, call centers must answer customer questions and resolve customer issues in a timely manner. Thus, accurately forecasting the number of calls is important for efficient workforce planning. Steckley et al. (2009) described effective forecasting techniques for arriving calls, and the forecasting accuracy was found to be the main factor influencing call center operations. Barrow (2016) studied time series forecasting methods for effective workforce management, using the seasonal moving average (SMA) for the initial systematic evaluation and artificial neural networks (ANNs) for forecasting intraday call arrivals. Xu et al. (2016) presented a twosector model (with upper and lower submodels) to forecast the numbers of calls in small and mediumsized areas. Singular value decomposition and an event pulse model were used to forecast intraday incoming calls. Combined forecasting is one of the most important and effective approaches for call prediction. Laouafi et al. (2017) presented a new combined forecasting methodology for shortterm electricity demand based on an Australian dataset and proposed an online forecasting system with high forecasting accuracy. In addition, (Wang et al., 2018) assessed combined forecasting models and proposed a new neuralnetworkbased linear ensemble framework (NNsLEF) for time series forecasting.
Because there is no single best forecasting method for all situations, researchers have proposed various forecast modeling frameworks to support effective and accurate forecasting methods. Holimchayachotikul and Phanruangrong (2010) presented a conceptual framework for efficient demand forecast modeling for the supply chain in the food product export industry; they used a time series forecasting model and a dataminingbased learning process to improve the forecasting system. Negash et al. (2016) proposed a conceptual framework for selecting an appropriate model for forecasting reservoir production. Four forecasting models (AR, ARI, ARMA, and ARIMA) were compared for the primary driving mechanisms, and six forecasting models (ARX, ARIX, ARMAX, ARIMAX, BJ, and BJI) were compared for the secondary driving mechanisms. Later (Luo et al., 2019) proposed a hybrid streamflow forecasting framework to achieve improved forecasting accuracy. This framework included factor analysis, time series decomposition, data regression, and error suppression. Zhou et al. (2019) proposed a geosensor data forecasting tensor framework for significant societal events; they used this strategic framework to improve the forecasting accuracy. The geosensor data were collected from sensors, and tensor decomposition was applied to forecast the upcoming time series. Khaliq et al. (2019) developed a conceptual framework for forecasting the parking decisions of car drivers in a city center; they used a mixed multinomial logit model to analyze the choices of car drivers. Recently Bedi and Toshniwal (2019) proposed a methodological electrical demand forecasting framework and used ANNs, recurrent neural networks, and support vector regression to evaluate the corresponding models. Additionally Jung et al. (2020) proposed a new conceptual framework for intelligent disaster management systems in South Korea and developed a big data analysis algorithm for decision making. From the literature there are no papers propose the forecasting framework on the special event, which is one factor that effect the forecasting number.
Mobile expo events are held as part of an important strategy for increasing the number of customers served by a given company. During such an event period, the number of incoming calls to a call center for that company will change, as will the call pattern. The current forecasting methods may not be suitable for such events; therefore, an appropriate method is needed. This paper proposes a framework for selecting the most appropriate forecasting method to be used during mobile expo events. This framework can help improve the accuracy of forecasting, workforce staffing and scheduling. The remainder of this paper is organized as follows. In Section 2, we describe the case study addressed in this manuscript. The framework and data analysis are presented in Section 3. In Section 4, we introduce different time series forecasting methods. The results of the study are presented and discussed in Section 5, and the conclusions are presented in Section 6.
2. CASE STUDY
The call center company investigated in this study operates a mobile communication call center in Thailand. At present, a forecasting method based on multiplicative decomposition is used to forecast the number of incoming calls. However, with this method, the number of calls during a mobile expo event is not balanced among agents; on some days, too many agents are on call, and on other days, not enough agents are present. This problem affects customer satisfaction and customer loyalty. Company reports provide information on the call volume and average handling time, and this information is used to calculate the number of agents needed and develop biweekly schedules for the workforce. The studied call center is open 24 hours a day, and incoming calls are received throughout the day. Customer questions are divided into 4 types: (i) billing, (ii) downloading content from the internet, (iii) general information, and (iv) information on promotions. The company has received complaints from customers due to the long wait times for calls during mobile expo events. This paper studies the incoming calls during mobile expo events and during nonevent periods. Mobile expo events occur three times a year in Thailand: in (i) week 6, (ii) week 19, and (iii) week 40. Each event lasts for four days, from Thursday until Sunday. The mobile company, a telecommunication service provider and an IT product developer participate in these events.
3. FRAMEWORK AND METHODOLOGY
This section introduces the steps of the proposed framework for forecasting incoming calls during mobile expo events, as illustrated in Figure 1. There are four steps in this process, as follows.
3.1 Data Types
3.1.1 Historical Call Arrival Records
The historical number of incoming calls is used to select the forecasting model(s) used. An accurate forecasting model can help determine the optimal number of agents. The records of arriving calls include both mobile expo event and nonevent calls from 20152017 and the corresponding data. The nonevent calls include incoming calls from customers asking questions about billing, downloading content from the internet, general information and information on promotions throughout the study period. The event calls include customer calls received during mobile expo events. Incoming call volumes are aggregated daily.
3.1.2 Data analysis
We study the incoming call types, including those in the periods when a mobile expo event was occurring and those in the periods when there was no mobile expo event. A nonevent call is defined as an incoming call received in the absence of a mobile expo event. In one year, there are three mobile expo events, which occur in week 6, week 19, and week 40. The study period for each mobile expo event comprises 49 days, consisting of (i) the 3 weeks before the mobile expo event (day 1day 21), (ii) the nonevent days in the mobile expo week (day 22day 24), (iii) the mobile expo event period (day 25day 28) and (iv) the 3 weeks after the mobile expo event (day 29day 49). Table 1 summarizes the study periods and the corresponding calendar weeks. Figures 24 show the incoming calls during mobile expos 13 over 3 years. Notably, the incoming calls during a mobile expo period peaked on the first day of the event and declined on each subsequent day during each event over these three years. Clearly, mobile expo campaigns and events affect the total number of incoming calls at a call center.
3.1.3 Definition of Data Types
To prepare the data to be used to determine the best the forecasting model in the next step, Figure 5 shows the data types for incoming calls. The incoming calls are classified into three types: nonevent period calls, mobile expo event period calls, and mixedperiod calls.
3.2 Time Series Forecasting Methods with Different Data Types
3.2.1 Verification of Time Series Methods
In this study, two time series methods, namely, multiplicative decomposition and the multiplicative HoltWinters method, are applied for three data types: nonevent, event and mixedperiod data. The sets of time series are defined as shown in equations (1) – (3).
where N_{1…t} denotes a set of time series values during a nonevent period 1, …, t and N_{i} represents the value of this time series on day i. The length of such a nonevent time series is denoted by TN.
where M_{1…t} denotes a set of time series values during a mobile expo event period 1, …, t and M_{i} represents the value of this time series on day i. The length of such a mobile expo event time series is denoted by TM.
where X_{1…mix} denotes a set of time series values during a mixed nonevent and mobile expo event period. Three separate time series compose this mixed period: (i) N_{1…bef} represents the time series spanning the three weeks prior to the mobile expo event, (ii) N_{1…dm} represents the time series spanning the nonevent during mobile expo event week, (ii) N_{1…aft} represents the time series spanning the three weeks after the mobile expo event, and (iii) M_{i…t} represents the time series spanning the mobile expo event itself. The length of such a mixedperiod time series is denoted by TX.
Given these definitions of the sets of time series values for each data type, the forecasting models are applied as shown in equations (4) – (9), where equations (4) and (5) correspond to a nonevent period, equations (6) and (7) correspond to an event period, and equations (8) and (9) correspond to a mixed period.
3.2.2 Comparison of the Forecasting Error
To evaluate the forecasting models in equations (4) – (9), the forecasting error is calculated using equation (10).
where the MAPE is the mean percentage error,

A_{i} is the actual number of calls on day i,

F_{i} is the forecasted number of calls on day i, and

T is the length of the time period (T=TN, TM, TX).
3.2.3 Results
We select the better of the twotime series forecasting methods based on the lower MAPE.
3.3 Models for Forecasting Incoming Calls
3.3.1 Definition of Forecasting Models
Based on the results of the time series forecasting methods, we create two separate models for forecasting incoming calls to the call center during mobile expo events. The model assumptions are presented below.
3.3.2 Combined and Individual Forecasting
The 1^{st} model, which is used for combined forecasting, is defined in equation (11). Let ${f}_{i{t}_{i}}$ denote a forecast of the first model, where t is the day of the time period, and let w_{i} represent the weight of the forecasting method for call type i, where i=1, …, NUM. In this case, y_{1} can be expressed by equation (11).
where ${f}_{1{t}_{1},\hspace{0.17em}\mathrm{...},\hspace{0.17em}{F}_{NUM{t}_{NUM}}}$ are the best forecasts for variable y1. The second forecasting model, as shown in equation (12), is an individual forecasting model. Let ${f}_{i{t}_{i}}$ denote a forecast of the 2^{nd} model, where t_{i} represents the day of the time period and i is the daily index (i=1, 2, 3, ..., NUM).
.3.3.3 Driving Models
The result of the above steps is two forecasting models: the 1^{st} model for combined forecasting and the 2^{nd} model for individual forecasting.
3.4 Forecasting Future Incoming Calls
3.4.1 Define the Model based on the Forecasting Error
The forecasting models in equation (11) and equation (12) are run with two forecasting methods: multiplicative decomposition and the multiplicative HoltWinters method. Then, we compare the forecasting error of the obtained results using equation (10).
3.4.2 Classification by period
In this step, we identify the best forecasts and the best models during the three analyzed periods in each year.
3.4.3 Analysis of Results
The results of the model with the lowest forecasting error are analyzed. For comparison, analyses are performed for workforce planning during the three mobile expo event periods and for different numbers of customers interested in the mobile expo event.
4. TIME SERIES FORECASTING METHODS
In this paper, the multiplicative decomposition and multiplicative HoltWinters methods are applied. The details of each model are described as follows.
4.1 Multiplicative decomposition model
In equation (13), the number of calls is forecast based on the overall trendcycle information, a seasonal component and an irregular component, as represented in the time series data set (Hyndman and Athanasopoulos, 2014;Heizer and Render, 2011).
where

T_{t} is the trendcycle component at period t,

S_{t} is the seasonal component at period t,

E_{t} is the irregular component at period t, and

t is time period
For the trendcycle component, T_{t} is calculated as a moving average that is centered at t. The estimated trend also depends on the seasonality of the time series. In this paper, the moving average is determined daily, and the data on mobile expo event calls are obtained from three periods of 4 days each per year. Suppose that a time series of mobile expo event calls starts on the 1^{st} day (t = 1), and we average the number of calls received per day up through the 4^{th} day (t = 4). This average corresponds to a time of t = 2.5 (the halfway point between the 1^{st} day and the 4^{th} day). The next process is called centering, which can be achieved by averaging the moving averages (Hyndman and Athanasopoulos, 2014). The trend at time t, $\widehat{T}$, can be estimated as the centered average, as shown in equation (14).
where m = 2k+1 and k is a time in period t. For mobile expo events, each seasonal index is divided over 4 days. A detrended series can be calculated by determining $\frac{{y}_{t}}{{\widehat{T}}_{t}}$. Then, the estimated seasonal component for each period is the average of the detrended values for that period. These seasonal indexes are then adjusted over 4 days. The values obtained are denoted by ${\widehat{S}}_{t}$. Next, the remaining component in equation (13) is calculated by dividing by the estimated seasonal and trendcycle components, as shown in equation (15).
4.2 Multiplicative HoltWinters Model
The forecast value F_{t+m/t} shown in equation (16) is calculated from a level component L_{t}, a trend component T_{t} and a seasonal component S_{t} (Charles and Chase, 2013). This model involves three smoothing parameters: a parameter for the level component (α), a parameter for the trend component (β), and a parameter for the seasonal component (γ). These parameters are optimized by minimizing the forecasting error, as shown in equation (20). The values of the three parameters α, β and γ are chosen between 0.1 and 0.9 to minimize the MAPE (E). The actual call data (A_{t}) from 20152017 include data for incoming calls during mobile expo event and nonevent periods.
where
where

L_{t} is the level component,

S_{t} is the seasonal component,

T_{t} is the trend component,

F_{m} is the forecast m periods ahead,

Y is the observation,

S is the seasonal period,

t is the time,

mis the number of time periods (i.e., 1, 2, …, m periods),

α is a levelrelated parameter,

β is a sloperelated parameter, and

γ is a smoothing constant related to the seasonal factor.
The corresponding objective function is as follows:
Subject to
5. EMPIRICAL EVALUATION
In this section, the results of evaluation are presented. The details are as follows.
5.1 Conceptual Steps
5.1.1 Data Types for Forecasting
The first step of the framework involves defining the data types. The details of each data type are displayed in Table 2. The day and week numbers are provided for all three data types.
5.1.2 Time series forecasting methods with different data types
The second step involves selecting the relevant time series forecasting methods. The method with the lowest forecasting error is used to calculate the results of the two models. Table 3 presents a comparison of the two time series methods (multiplicative decomposition and the multiplicative HoltWinters method) based on the MAPE. Among the nonevent periods, the results for MondayWednesday in week 19 can be better predicted by multiplicative decomposition with the trend equation y_{t} = 9988 240t. For the mobile expo event and mixed periods, the results are better predicted using the multiplicative HoltWinters approach.
5.1.3 Models for Forecasting Incoming Calls
In this step, the results of the forecasting models are presented. Figure 6 illustrates the internal structures of the two models, which use (1) nonevent + mobile expo event periods and (2) mixed periods. These models are compared to identify the one with better performance.
For model (1), the assumptions adopted for analysis based on the combined approach are given by equation (11). Let ${f}_{a{t}_{a}},\hspace{0.17em}{f}_{b{t}_{b}},\hspace{0.17em}{f}_{c{t}_{c}}\hspace{0.17em}\text{and}\hspace{0.17em}{f}_{d{t}_{d}}$ denote the numbers of incoming calls forecast by model (1), where i = a, b, c, d. Here, a corresponds to the nonevent period in the same week as a mobile expo event, with t_{a} = 1, 2, 3; b corresponds to the nonevent period spanning the 3 weeks before a mobile expo event, with t_{b} =1, 2, 3, …, 21; c corresponds to the nonevent period spanning the 3 weeks after a mobile expo event, with t_{c} = 1, 2, 3, …, 21; and d corresponds to the mobile expo event period itself, with t_{d} = 1, 2, 3, 4. y_{model}_{1} can be expressed as shown in equation (23).
where ${f}_{a{t}_{a}},\hspace{0.17em}{f}_{b{t}_{b}},\hspace{0.17em}{f}_{c{t}_{c}}\hspace{0.17em}\text{and}\hspace{0.17em}{f}_{d{t}_{d}}$ are the best forecasts for y_{model}_{1}.
Forecasting model (2), as shown in equation (12), is used for individual forecasting. Let ${f}_{i,{t}_{i}}$ denote a forecast for a mixed period, where t_{i} represents the period spanning the 3 weeks before a mobile expo, every day of the mobile expo week, and the 3 weeks after the mobile expo. In this case, i is a daily index (i = 1, 2, 3, …, 49). ${y}_{mode{l}_{2}}$ can be expressed as shown in equation (24).
5.1.4 Forecasting Future Incoming Calls
Finally, Table 4 compares the performance of the two models, namely, the (1) nonevent period + mobile expo event period mode and (2) the mixedperiod model, based on the MAPE. For the 2^{nd} mobile expo event period, better results are obtained with the nonevent period + mobile expo event period model. For the 1^{st} and 3^{rd} mobile expo event periods, better results are obtained based on the mixedperiod model. The minimum MAPEs are 7.82%, 13.37%, and 8.28% for the first, second, and third events, respectively.
The results can be classified by time period. For the first event period, Figure 7 shows the incoming calls forecast based on the mixedperiod model (2) using the multiplicative HoltWinters method (α, β, γ: 0.48, 0.1, 0.1). The forecast number of calls is high on the first day of the mobile expo event, at 12,159 calls, and low on the Sunday of the same week, at 6,375 calls. Thus, during a mobile expo event, the call volume is highest on the first day and sequentially decreases each subsequent day.
For the second event period, Figure 8 presents the incoming calls forecast based on model (1). There are four distinct periods, as shown in Figure 8a, Figure 8b, Figure 8c, and Figure 8d. For each period, we can assess the trend and seasonality of the incoming calls. Figure 8a illustrates the number of actual calls and the number of calls forecast using multiplicative decomposition during the nonevent period (MondayWednesday) during the week of the event. The number of forecast incoming calls increases from Monday to Wednesday. The number of calls forecast using the multiplicative HoltWinters method (α, β, γ: 0.6, 0.2, 0.2) for the nonevent period spanning the 3 weeks (MondaySunday) before the mobile expo event is shown in Figure 8b. The number of forecast incoming calls peaks on Monday in week 18 and on Friday in weeks 16 and 17. Conversely, the lowest numbers of incoming calls are predicted for Monday in week 16 and Sunday in weeks 17 and 18. Figure 8c shows the incoming calls forecast for the nonevent period spanning the 3 weeks (MondaySunday) after the expo event using the multiplicative HoltWinters method (α, β, γ: 0.7, 0.1, 0.1). The lowest volumes of incoming calls are forecast to fall on the same day (Sunday) in each of these three weeks. The number of forecast incoming calls is highest on Monday (9,182 calls) in week 20 and on Tuesday in weeks 21 and 22 (8,397 calls and 7,639 calls, respectively). Figure 8d presents the number of calls during the mobile expo itself (ThursdaySunday) in week 19 as forecast using the multiplicative HoltWinters method (α, β, γ: 0.9, 0.2, 0.2). The forecast number of incoming calls is highest on Thursday, at 14,653 calls. Then, this number decreases to 14,025 calls, 13,272 calls, and 12,835 calls on Friday, Saturday, and Sunday, respectively.
For the last event period, Figure 9 presents the number of incoming calls forecast using the multiplicative HoltWinters method (α, β, γ: 0.2, 0.1, 0.1) based on model (2). The incoming calls show both trend and seasonal patterns. The numbers of calls forecast during the mobile expo event are higher than those during other periods. During the mobile expo period, customer calls peak on Thursday and decline sequentially on subsequent days. The day with the highest number of incoming calls varies during the nonevent periods, falling on Monday in weeks 37 and 38, on Tuesday in weeks 42 and 43, and on Wednesday in weeks 39 and 41. However, the number of incoming calls is lowest on Sunday every week.
By synthesizing these results, we find that the numbers of calls differ among the three mobile expo event periods. Model (2) is more appropriate for the first and third mobile expo event periods, and model (1) is better for the second mobile expo event period. The multiplicative HoltWinters method can be used for forecasting in all periods other than the nonevent period during the week of the expo event. In addition, the numbers of incoming calls during the mobile expo event period itself are similar among the three events. Specifically, the number of calls peaks on the first day of a mobile expo event and then declines through the last day. During the nonevent periods, the peak day for calls varies each week. In contrast, the lowest number of calls always occurs on the final day of the week. We have compared the forecasting method currently used by the studied call center company and the method based on the new framework proposed in this study in terms of the threetimeperiod MAPE, as shown in Tables 3 and 4. The results show that the new approach yields a higher forecasting accuracy than the presently used method in all three periods.
5.2 The Validation of the Proposed Method
5.2.1 Comparison with the Existing Forecasting Method
To ensure the proposed method is appropriate for the case study, the validation process is performed by testing with the arrival calls of year 2018 and compared the forecast error with the existing method, Holt’s two Parameter and SARIMA as shown in Table 5.
From Table 5, the forecasting error obtained by the proposed method are extremely lower than the other methods in all event periods. It is clearly that the proposed method provides the best result than those of them.
5.2.2 Forecasting on Different Scenario
The proposed framework is tested on the different scenario, Songkran festival event (Thailand tradition new year). For Songkran event period, the dataset of this period is drawn from 12 15 April and Nonevent period is the other days on April (20162018). We conduct four steps of the proposed framework as follows.

1. First step, the data is separated into three data types: Nonevent period, Songkran event period, and Mixed period.

2. The time series forecasting methods are applied to forecast different data types and the results of MAPE are displayed in Table 6. The Multiplicative HoltWinters provides the minimum MAPE then this method is used for forecasting three data types.

3. The forecast incoming call of two models, (1) Nonevent + Songkran festival event periods and (2) Mixed periods are performed.

4. In the final step, the model which has the lowest MAPE is selected. In Table 7 the MAPE of model (1) is lower than model (2). It can be concluded that the proposed method can be applied to forecast the incoming call in the other special event period.
5.3 Comparison with the Similar Works
In this section, we compared the forecasting framework concept among the proposed method and the recent selected relevant framework in four aspects: (i) Define data types; (ii) Forecasting selection; (iii) Forecasting driving models; and (iv) Forecasting classify by period as shown in Table 8.
From Table 8, we found no one fits all aspects of framework concept accept our proposed method. Then we can claim that the proposed framework for forecasting incoming call during mobile expo events is a novelty concept in methodological approach.
6. CONCLUSIONS
This paper presents an empirical study of a proposed framework for forecasting the number of incoming calls to a call center during mobile expo event periods. It is applied to estimate the numbers of incoming calls in three mobile expo event periods and to select the best forecasting model. Two models, a nonevent period + mobile expo event period model and a mixedperiod model, are defined. Between the combined forecasting approach of model (1) and individual forecasting approach of model (2), the results illustrate that model (2) provides the better results for the first and the third mobile event periods and model (1) provides the better results for the second event period. This framework allows the heterogeneous features of time series data from different periods to be disentangled to forecast incoming calls with higher accuracy. Consequently, decision makers can use this framework for forecasting to support workforce planning during a mobile expo event.
In the future, additional features can be included to enhance this framework, such as developing a new forecasting algorithm that can detect the call pattern earlier. This would allow the most appropriate forecasting model to be applied in a more timely manner. Furthermore, the forecasting methods proposed in this study can serve as the basis for the construction of a tool for simulation and optimization. The ability to leverage Internet of Things applications based on call center data will be an important tool for enhancing forecasting and workforce planning.