Workload-based manpower requirements determination using statistical time-series hierarchical modeling

Introduction

Past research [1][2][3][4][5][6][7][8][9] has discussed various approaches to calculating and determining manpower requirements, such as the ratio-based method, survey-based method, and hourly availabilitybased method. Although several non-workload-based manpower determination methods have been proposed, most organizations prefer workload-based methods, as they are considered the fairest, most scientifically sound, and justifiable approach to calculating staffing needs. Despite the numerous published articles proposing manpower calculation methods, none have developed workload-based methodologies-except for the most recent paper by Rahardja (2025) [10] . As a recap, Rahardja (2025) [10] presented a generic (naïve) manpower modeling equation. However, this model treated all input variables solely as fixed-effect variables. Since it did not distinguish between fixed and random effects, parameters and variables, or hierarchical and nonhierarchical modeling, it remains purely a mathematical model rather than a statistical one. Without the inclusion of any random variables, the model can only provide rough estimates of current manning requirements. It lacks the flexibility needed for deeper analyses-such as forecasting future manpower needs, performing model selection, controlling error rates, or refining accuracy. Ultimately, especially when budgets are tight, organizations seek reasonably assured and accurate projections of both current and future manning requirements. In contrast, Rahardja (2025) [10] also notes that the input variable 'Volume'-representing the volume of a task under an organization's mission function-can naturally be treated as a random variable. As 'Volume' varies over time, it can be modeled as coming from a distribution, thereby transforming the model into a statistical one. Once 'Volume' is treated as a random variable, the previously generic (naïve) mathematical model becomes a hierarchical statistical model. With this expanded statistical framework, we can project both current and future manning needs more effectively. Accordingly, this paper proposes a statistical methodology that employs time-series (TS) algorithms to enhance the workload-based, generic (naïve) model discussed in prior literature [10] .

In this enhancement, we hierarchize 'Volume' using TS algorithms. The remainder of the paper is organized as follows. Section 2 constructs the statistical methodology using a workload-based, time-series hierarchical manpower modeling equation to project required manning. Section 3 describes the data. Section 4 demonstrates the methodology on a dataset. Section 5 concludes the paper.

Methodology

The goal of this section is to develop a staffing methodology for determining manpower requirements. We build upon the workload-based manpower equation (1) in Rahardja (2025) [10] , applying hierarchical time-series (TS) modeling to the input variable Volume, which is treated as a random variable and depicted in Figure 1. The staffing methodology comprises two scenarios for projecting final full-time equivalent (FTE) manning requirements: Baseline (Estimations) and Endpoint (Forecasts). Typically, the Baseline scenario involves collecting initial or baseline FTE manning numbers from the organization's systems of record (SOR) data and field surveys. These figures may include the number of onboard personnel (ONBD), assigned personnel (ASSGN), and/or authorized positions (AUTH). The purpose of collecting multiple baseline figures is to obtain different perspectives for comparison with the Endpoint numbers-namely, the current and future required (REQD) staffing levels. The methodology for the Endpoint scenario follows a generalized approach discussed in Rahardja (2025) [10] , which is based on the workload-based manpower model described in Equation ( 1). As a recap, the outcome variable in Equation ( 1) estimates the number of FTE personnel required for the intended studied year. The input variables include yearly work Volume, average task Duration, the standard Work Year (e.g., 2080 hours/year) and Utilization Rate (UR).

Equation ( 1) is robust and can be applied across a broad range of scenarios. Each step in the process aims to balance timeliness with a reasonable level of assured accuracy, taking into account factors such as the rigor of the information or datasets collected, dataset partitioning, estimation methods, and available software.

The methodology and analysis are presented in both graphical and tabular formats in Figure 1 and Figure 2. Initially, the workload-based manpower model in Equation ( 1) serves as a simple, generalized model, where all input variables are treated as Fixed Effects [10] . In this approach, analyses are performed at a basic level. To implement it, yearly data for each input component is gathered, substituted into Equation ( 1), and solved for the required FTE workforce. This calculation can be performed for each study year as necessary. We refer to this preliminary, coarse analysis as the Phase 1 Study.

In Phase 1, Equation ( 1) is used to calculate the FTE requirements (REQD) for the current and past several years, serving as input patterns for Phase 2. At this stage, we ensure the consistency of each step and data source. If inconsistencies arise, we identify the root causes and mitigate or address the data risks. Additionally, we compare the authorized or assigned FTEs (AUTH or ASSGN) with the actual number of onboard FTEs (ONBD). Based on these findings, we provide recommendations in Phase 1.

In the refined analysis of Phase 2, the model can be extended to a more detailed level, depending on resource availability and feasibility. By treating volume as a Random-Effect variable through Hierarchical Modeling and using Time Series (TS) statistical algorithms [11][12][13][14][15][16] , the manpower model is enhanced (refer to Figure 1 and Figure 2). This allows forecasting FTE requirements (REQD) from the current studied year into future studied years, expanding the original model's capabilities. For demonstration purposes, in this particular dataset, suppose that for a Shuttle-Van company, a major (main) task within one of the company's Essential Mission Functions (EMF) was to transport all airline passengers shown in Figure 3-from each passenger's pick-up point to their drop-off point at the airport. The company aimed to determine both the current and future projected number of FTE drivers required to perform this EMF. Specifically, the drivers' main duties under this EMF are to manage, verify, and transport airline passengers to and from the airport and their destinations. A WS is conducted using a workload-based approach (i.e., manpower hierarchical modeling) to gather monthly passenger volume data (i.e., number of airline passengers) and the average duration of driver activities. This data is sourced from both the organization's system of record (SOR) and/or field surveys, covering all shuttle-van company locations. A review of this staffing projection WS should occur at the minimum every three years, or more frequently at the organization's discretion, based on variations in passenger volume. The scope of the WS is as follows: This example captures and analyzes airline passenger volume data from calendar years (CY) 1949 to 1960, with the objective of projecting current and future driver manning requirements for CY61-CY63.

The constraints are as follows Timeliness, accuracy, and funding are key constraints for any study, including this shuttle-van drivers WS. Therefore, an initial analysis is essential to assess the feasibility of the study and strike a balance among these constraints. Key assumptions for this example WS include:  Assumed passengers Volume is a Random Effect variable for the Hierarchical Modeling  Assumed the rest of input variables or components are Fixed Effect variables  Assumed average Durations was 3 hour/case for field's van driver, assumed per fields survey following previous example [10]  Assumed Work Year is 2080 hours/year following previous example [10]  Assumed utilization rate (UR) is 0.64 following previous example [10]  Utilized an average past 3y estimates & future 3y forecasts for current & future required staffing following the organization's discretion on updates

The data analysis process goes as follows:

Following the methodology discussed earlier, the Baseline Analysis is conducted. For illustration purposes, assume that, based on the company's current records, the total number of ONBD drivers is 10 FTEs (see Table 1 in the Results and Recommendations section), while the number of funded positions-i.e., the total authorized (AUTH) drivers-is 11 FTEs. In the Phase 2 Study, using available software (Excel, 2021) [13] , the overall projected endpoints were calculated to be 12 and 15 FTEs for the current and future states, respectively (see Figure 4). The right-hand side panel of Figure 4 shows the projected current and future requirements of 12 FTE and 15 FTE, respectively. The top panel displays the patterns-such as level, trends, seasonality, and cycles-of the monthly volume of passengers transported, while the bottom panel illustrates the annual patterns of the number of FTE drivers. Blue represents historical data, red indicates future forecasts, green represents the estimated Current REQD, and yellow denotes the forecasted Future REQD. There are clear monthly patterns in level, trend (i.e., an increasing incline in the volume patterns, as shown in the top panel of Figure 4), and 12-month seasonality. Therefore, it makes sense that the total projected Current and Future REQD would increase (in this case, from 12 to 15 FTEs). .

Results and Conclusions

The results of this study were obtained in accordance with the methodology and analysis process described in the previous section. Both the baseline and endpoint scenarios were analyzed using the outlined methodology, with the results presented in Figure 4 and Table 1. The baseline scenario reflects the initial FTE numbers (AUTH and ONBD), while the endpoint scenario projects the staffing requirements (REQD) for the current and future states, based on the study's scope and all acquired data. Accordingly, the findings from Figure 4 are summarized in Table 1 below. Finally, based on the above results, the following summarizes the key findings. The Endpoint Analysis results for this WS scope align with the Initial Analysis from the Passenger Volume plots (see the blue curve in the top panel of Figure 4), which indicate that the passenger volume trend is steadily increasing with 12-month seasonality. Consequently, the projected volume and the corresponding need for additional FTEs are reflected as follows: 12 and 15 drivers for the current and future requirements, respectively, increasing from 10 and 11 current onboard and authorized drivers. Therefore, although the organization currently has only 10 onboard drivers (slightly below the funded position of 11), the actual required number of drivers to perform the EMF is 12 FTEs, with a forecasted future requirement of 15 drivers. By proactively calculating and determining these current and future staffing needs, the shuttle-van company can strategically manage and maintain its operations.

We conclude that, in this paper, we have developed a workload-based staffing methodology using statistical timeseries hierarchical modeling to determine the manpower requirements for an organization's EMF. This methodology expands upon the generic (naïve) modeling introduced earlier in Rahardja (2025) [10] . We have also provided a walkthrough example case for illustration. This developed staffing methodology will be highly useful for practitioners and researchers across various applied fields (e.g., business, human resources, social sciences, psychology, manufacturing, medicine, industry, government, healthcare, etc.) to determine both the current and future staffing needs to perform an EMF within an organization. The implementation of this staffing methodology for each EMF in an organization can be updated every three years or as determined by the organization's management.

Disclaimer Statement

This research represents the authors own work and opinion. It does not reflect any policy nor represent the official position of the U.S. Department of Defense nor any other U.S. Federal Agency.

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