A Risk-Integrated CPM–PERT and Monte Carlo Simulation Approach for Aircraft Overhaul Scheduling: Empirical Evidence from Military Maintenance Systems

Aircraft overhaul scheduling plays a crucial role in ensuring operational readiness and mission effectiveness in military aviation environments [1]. In the context of the Indonesian Air Force (TNI AU), delays in overhaul activities may result in a critical reduction of aircraft availability, compromising both air defense strategy and national security operations [2]. Overhaul scheduling, therefore, must not only comply with technical maintenance protocols but also align with time-sensitive operational mandates. Despite the implementation of standard project scheduling techniques such as the Critical Path Method (CPM) and the Program Evaluation and Review Technique (PERT), existing scheduling practices remain vulnerable to delays caused by unmanaged uncertainties and risk factors throughout the project lifecycle [3].

Traditional project scheduling methods, such as CPM, which assumes deterministic activity durations, and PERT, which introduces probabilistic estimates, have been widely used across various engineering and maintenance contexts. However, both methods are often criticized for their limited capacity in handling complex, dynamic, and multi-risk environments such as military aircraft overhaul projects [4]. These techniques typically fail to account for stochastic variations and interdependent risk propagation that affect the actual duration of activities [5]. In overhaul projects where technical configurations may change abruptly, logistical constraints may arise, or specialized personnel may be unavailable, risk factors can have a compounded effect on project timelines.

To address these limitations, contemporary research has emphasized the integration of risk management into project scheduling models. Risk-integrated scheduling aims to capture the influence of key uncertainties and simulate their impact on project timelines using techniques such as Monte Carlo simulation [6]. This integration is particularly relevant for defense-related maintenance projects where delays have strategic implications. Yet, most existing studies have either focused on commercial aviation contexts or limited their scope to specific technical risks, leaving a gap in research that addresses the unique characteristics of military overhaul operations, particularly within TNI AU [7].

This study proposes the development of a risk-integrated scheduling model that combines CPM, PERT, and Monte Carlo simulation to improve schedule reliability in military aircraft overhaul projects. While previous studies have explored risk-integrated scheduling using probabilistic techniques, most have focused on general engineering or commercial aviation contexts and have not systematically addressed the specific characteristics of military maintenance environments, such as high supply uncertainty, dynamic technical requirements, and mission-critical time constraints [8]. Moreover, limited attention has been given to analyzing the probability of critical-path variability and the relative contribution of individual risk factors under uncertainty.

Accordingly, this research aims to fill these gaps by integrating empirical risk data, probabilistic duration modeling, and simulation-based critical-path analysis within a unified framework tailored to the Indonesian Air Force (TNI AU). The main contributions of this research are threefold: (1) developing a practical risk-integrated scheduling model for aircraft overhaul projects; (2) quantifying schedule uncertainty and critical-path variability using Monte Carlo simulation; and (3) validating the model using historical project data and sensitivity analysis to support risk-informed decision-making [9]. It should be noted that this study focuses on single-project scheduling under uncertainty and does not explicitly model resource-constrained or multi-project scheduling environments. Therefore, the scope is limited to risk-integrated duration estimation and critical-path analysis within individual overhaul projects.

3.1 Research design

This study employs a quantitative model development approach aimed at constructing, simulating, and validating an integrated risk-based scheduling model for military aircraft overhaul projects. The model combines deterministic and probabilistic scheduling techniques (CPM and PERT) with risk identification and Monte Carlo simulation to enhance the accuracy and robustness of project timelines. The research design follows four sequential phases: risk identification, model construction, simulation, and validation.

3.2 Research context and data collection

This study was conducted within the Indonesian Air Force (TNI AU) aircraft maintenance facilities, which operate in high-reliability, mission-critical environments where delays in overhaul projects can jeopardize national defense readiness. Data were collected from three integrated sources to ensure empirical validity and contextual accuracy. Archival project documents from the past five years provided historical insight, while in-depth interviews with maintenance engineers, project managers, and logistics officers offered expert perspectives on risk factors and activity durations. Additionally, field observations of ongoing overhaul operations were conducted to validate process flows and duration estimates. This triangulated approach ensured a comprehensive and reliable foundation for modeling project performance in military aircraft maintenance settings.

3.3 Model development process

The model was developed through the following stages:

3.3.1 Risk identification and classification

A mixed-method approach, combining both qualitative and quantitative techniques, was employed to identify the key risks influencing the duration of overhaul projects. These risks were systematically categorized according to their frequency of occurrence and potential impact on project timelines, following the framework suggested by. Particular attention was given to recurrent issues such as delays in spare part delivery, changes in technical specifications, shortages of skilled manpower, and disruptions caused by environmental or operational factors. Each identified risk was assessed using probability and impact scores, which were derived from expert judgment and supported by historical maintenance records. This structured assessment allowed for a prioritized understanding of the most critical factors affecting project performance (see Table 1), while the detailed activity list and risk–activity mapping are provided in Appendix A (Tables A1 and A2).

Table 1. Risk rating scale

3.3.2 Risk impact formulation

Risk impacts on activity duration were modeled using a multiplicative adjustment approach, allowing proportional changes based on risk realization. The duration of activity iii in simulation run k is defined as:

$D_i^{(k)}=T_{e, i} \times\left(1+\sum_j R_{i, j} \cdot X_j^{(k)}\right)$

where,

• $T_{e, i}$: expected duration from PERT
• $R_{i, j}$: risk-activity mapping
• $X_j^{(k)}$: stochastic impact of risk j in iteration k

Multiple risks affecting the same activity are assumed to be additive in proportional effect. This formulation captures compounded delays while maintaining computational stability.

3.3.3 Critical Path Method/Program Evaluation and Review Technique network construction

A baseline project network was developed using CPM, which included all major work packages and activities involved in the overhaul process. Duration estimates for each activity were then adapted using PERT by incorporating three-time estimates:

• Optimistic (O),
• Most Likely (M),
• Pessimistic (P).

The expected duration (Te) for each activity was calculated using the PERT formula: Te = (O + 4M + P) / 6 and variance: V = [(P – O)/6]². The probability and impact levels used in the analysis are defined in Table 2.

Table 2. Risk rating scale

3.3.4 Risk integration via Monte Carlo simulation

Each identified risk was mapped to the activities it may affect. Probability distributions (typically triangular or beta) were assigned to activity durations reflecting risk impacts. Monte Carlo simulation with 10,000 iterations was applied to simulate the probabilistic completion time of the project. The simulation allowed recalculation of the critical path under risk scenarios, providing a dynamic representation of schedule uncertainty. The model also allowed for “what-if” analysis based on mitigation scenarios.

The classification of risks based on probability and impact is illustrated in Figure 1.

Figure 1. Risk frequency–impact matrix

3.3.5 Distribution selection and parameterization

Two types of probability distributions were used to represent uncertainty in activity durations and risk impacts, based on data availability and the level of information detail.

The triangular distribution was applied when only expert estimates were available, defined by three parameters: optimistic (O), most likely (M), and pessimistic (P) durations. This distribution was selected due to its simplicity and suitability for situations with limited empirical data, which is common in military maintenance environments.

The beta distribution was applied when sufficient historical data were available, allowing for more flexible modeling of skewed or asymmetric duration patterns. The beta distribution parameters were estimated using historical duration records and fitted to observed data to better capture variability. Parameter estimation was conducted using two approaches:

• Expert-based estimation: values of (O), (M), and (P) were elicited from maintenance engineers and project managers through structured interviews and validated against historical project records.
• Data-driven estimation: historical activity durations were used to fit probability distributions, with parameters estimated using maximum likelihood estimation (MLE).

Distribution selection criteria were based on data availability and goodness-of-fit performance. Goodness-of-fit was evaluated using the Kolmogorov–Smirnov (K–S) test at a significance level of α = 0.05. When historical data were insufficient or did not satisfy goodness-of-fit criteria, the triangular distribution was retained as a conservative approximation.

This hybrid approach ensures consistency between expert judgment and empirical data while maintaining model robustness and reproducibility under varying data conditions.

3.3.6 Monte Carlo simulation procedure

For k = 1 to 10,000:

For each activity i:

Sample base duration from PERT distribution

For each risk j affecting i:

Sample risk impact X_j

Compute adjusted duration D_i(k)

Construct project network with D_i(k)

Perform forward pass → compute earliest times

Perform backward pass → compute latest times

Identify critical path (zero float)

Store:

Total project duration

Critical path configuration.

3.3.7 Critical path identification per iteration 

The critical path in each simulation run was defined as the sequence of activities with zero total float. A critical path change was recorded when the set of critical activities differed from the baseline CPM path.

In cases of multiple critical paths (ties), all paths with zero float were recorded. The frequency of occurrence of each unique critical path configuration was calculated as:

$P\left(C P_m\right)=\frac{\text { Number of iterations with path } m}{\text { Total iterations }}$

3.3.8 Sensitivity analysis method

Sensitivity analysis was conducted using the Spearman's rank correlation coefficient between input risk variables and total project duration. The contribution of each risk to output variance was computed based on normalized correlation values.

Input ranges were defined using the same probability distributions applied in the simulation, ensuring consistency between simulation and sensitivity analysis.

3.3.9 Risk mitigation strategies

Mitigation strategies were designed based on the most sensitive risks identified from the simulation results. These included:

• Enhanced logistics coordination for spare part delivery,
• Adaptive technical specifications documentation,
• Dynamic reallocation of skilled personnel,
• Schedule re-optimization based on updated risk profiles.

3.4 Model validation

The model was validated through two complementary methods:

3.4.1 Historical data comparison

Projected schedules from the model were compared against actual completion times of prior overhaul projects. The improvement in schedule accuracy was assessed using a paired t-test, with a significance threshold set at p < 0.05.

3.4.2 Sensitivity analysis

A sensitivity analysis was conducted to determine the influence of individual risk variables on project duration. This enabled the identification of high-impact risks and the evaluation of the effectiveness of proposed mitigation strategies.

The 150-day on-time completion threshold was derived from historical project performance data and operational benchmarks within TNI AU maintenance units, representing the typical planned duration used in prior overhaul schedules. This threshold was therefore adopted as a realistic baseline for evaluating schedule performance and completion probability.

The 30% variance reduction scenario reflects feasible improvements in logistics coordination, particularly in spare-part delivery processes, as identified through expert consultation with maintenance engineers and analysis of historical delay patterns. This scenario does not represent an arbitrary assumption, but rather a realistic improvement level observed in prior operational optimization efforts within similar maintenance contexts.

3.5 Tools and implementation workflow

The implementation workflow integrates multiple tools as follows:

• Microsoft Project: used to construct the baseline CPM/PERT network and define activity dependencies.
• @Risk (Palisade): used to perform Monte Carlo simulation and generate probabilistic duration outputs.
• SPSS: used for statistical validation (paired t-test and correlation analysis).

The simulation process was executed within @Risk, where activity durations were dynamically updated, and critical-path calculations were performed at each iteration using embedded scheduling functions.

The results of this study provide compelling evidence that integrating risk management into CPM and PERT scheduling models significantly enhances the accuracy and robustness of aircraft overhaul schedules in military contexts [21]. The simulation-based approach successfully captured the variability inherent in project environments characterized by uncertainty, resource interdependencies, and operational constraints.

The observed 15.4% improvement in schedule accuracy, statistically validated through paired t-testing, confirms prior findings, that emphasized the importance of incorporating probabilistic risk into CPM structures to reflect real-world project variability [22]. Furthermore, the dynamic nature of the critical path under stochastic conditions substantiates the argument of that traditional CPM needs to evolve into adaptive scheduling frameworks to manage uncertainty effectively [23].

Building upon this, our study moves beyond conceptual modeling by grounding the proposed framework in empirical data from actual overhaul operations conducted by the TNI AU [24]. This real-world application distinguishes our contribution from prior research that largely relied on hypothetical datasets or commercial aviation settings [25]. The ability to simulate risk impacts and mitigation scenarios using local data illustrates the model's operational viability in defense logistics and high-reliability organizations.

The sensitivity analysis further confirmed that logistical risks (especially spare part delays) and technical specification changes are the most significant contributors to schedule variance. These results are consistent with who identified similar factors in aircraft maintenance delays across defense projects [26]. The demonstrated effectiveness of mitigation strategies such as logistics coordination and dynamic resource reallocation indicates that the model can serve not only as a planning instrument but also as a decision-support system for operational commanders and project managers [27].

From a theoretical standpoint, the integration of deterministic (CPM) and probabilistic (PERT and Monte Carlo) techniques provides a methodological bridge for risk-based scheduling. This hybrid structure addresses the critique posed that traditional PERT models often fall short in adapting to shifting risk conditions [28]. The model’s flexibility allows decision-makers to visualize multiple future states of project completion under different risk loads.

Moreover, in a broader sense, the proposed model contributes to military readiness and strategic maintenance planning by enhancing predictability, accountability, and proactive risk mitigation key components in ongoing efforts to modernize defense logistics and asset availability management within institutional frameworks like TNI AU.

Nonetheless, this research has limitations. The model's performance is highly dependent on the accuracy of historical data and expert estimations, particularly in defining probability distributions [29]. As highlighted, insufficient data quality may skew simulation outcomes. Additionally, although the sample size (n = 12) is reflective of the major overhaul activities within the past five years, a broader dataset could enhance the model’s generalizability. Future studies should consider cross-unit validation within or across other branches of the armed forces.

Another limitation is that the model focuses on time-related risks only. Cost considerations, while indirectly affected, were not formally integrated into the framework [30]. Emphasized the importance of balancing time, cost, and resource constraints, especially in budget-sensitive military projects. Therefore, expanding the model to include multi-objective optimization that incorporates cost and manpower trade-offs is recommended [31].

Lastly, the model does not explicitly account for exogenous risks, such as changes in defense policy, geopolitical disruptions, or global supply chain crises. These higher-order uncertainties, though harder to quantify, may have cascading effects on project timelines [32]. Future research could incorporate scenario-based planning or agent-based simulation to reflect these dynamic macro-conditions.

The authors would like to express their sincere appreciation to Institut Teknologi Nasional, Malang, East Java, Indonesia, for providing academic support and research resources essential to the completion of this study. Gratitude is also extended to the TNI AU maintenance personnel for their cooperation and contribution during data collection and field observation.