The transportation system with battery-swapping trucks in open-pit mines comprises multiple operational nodes, including loading platforms, unloading zones, and battery-swapping stations. Electric haul trucks cycle continuously between these nodes to transport materials while periodically requiring battery exchanges at designated swapping stations, as depicted in Figure 1.

In line with the workflow depicted in Figure 1, a simple scheduling method for mining truck battery swapping functions as follows. Once unloading is completed, the system assesses whether the truck's remaining battery capacity can support one more haul cycle. If it can, the truck is sent to continue its hauling operations. If not, it is routed to the battery-swapping station with a shorter queue for battery replacement. At the station, trucks in the queue are served strictly on a first-come-first-served (FCFS) basis, without considering any operational priority levels. However, this straightforward scheduling approach may give rise to two issues. Firstly, when the battery depletion moments of a large number of mining trucks approach simultaneously, these trucks will flock to the battery-swapping stations for battery replacement. Due to the limited capacity of the battery-swapping stations and the finite number of fully charged batteries, long queues will be formed, which will affect the operational duration of the mining trucks and cause traffic congestion around the battery-swapping stations. Secondly, FCFS basis is suboptimal and as a result, the total queuing time for battery replacement of the entire fleet may be excessively long.

Discrete Event Simulation (DES) is a computational modeling approach that mimics the dynamic behavior of complex systems by simulating discrete events (e.g., task arrival, service completion) occurring at specific time points (Banks et al., 2013). Unlike continuous simulation, which models systems with smooth state changes (e.g., fluid flow), DES focuses on abrupt state transitions triggered by events. For example, in mining truck scheduling, DES tracks when trucks arrive at battery-swapping stations, how long they queue, and when they resume hauling, considering random battery depletion times and station capacities (Huayanca et al., 2023). Such a simulation can help identify bottlenecks and improve resource allocation.

In this paper, we conduct a discrete event simulation (DES) to model the workflow in open-pit mines. The parameter configurations for the simulation are summarized in Table 1. These settings are based on an actual open-pit coal mine and the work by Huayanca et al. (2023). The simulation framework encompasses three interconnected processes: loading, unloading, and battery-swapping. Initially, all trucks—equipped with a preset state of charge (SoC)—depart from the unloading zone and travel to designated loading platforms. Upon arrival, trucks queue at the loading platform until they are loaded with material. Once loaded, they return to the unloading zone for material discharge. After completing the unloading process, the system evaluates whether the truck's remaining SoC is sufficient for another hauling cycle. If the SoC falls below the required threshold, the truck is redirected to a battery-swapping station to replace its depleted battery with a fully charged one. Given the inherent uncertainties in travel time, spotting time, battery-swapping duration, and other operational variables, the simulation—modeling an 18-hour production period—was executed 100 times to account for stochastic variations. The results yielded an average of 628 total trips completed across all iterations, while the average waiting time for battery-swapping stood at 86.6 minutes. Figure 2 illustrates the relationship between total trips and battery-swapping station wait times through a scatter plot. As shown, a distinct negative correlation emerges between these two metrics, suggesting that prolonged battery-swapping delays directly reduce the number of achievable haulage cycles. This inverse relationship positions battery-swapping operations as a potential critical bottleneck in the production workflow.

To investigate the root cause of prolonged battery-swapping delays, Figure 3 visualizes the state of charge (SoC) time series for all trucks during one representative simulation run. The data reveals a critical synchronization issue: during the first battery-swapping cycle, all trucks converge on the swapping stations approximately 350 min after production initiation. This synchronization creates a demand surge that overwhelmes the stations limited capacity, forcing some trucks in this cohort to endure wait times exceeding two hours for battery replacement. Notably, subsequent swapping cycles exhibite significantly reduced delays, as evidenced by the dispersed timing of later SoC troughs in Figure 3.

This stark contrast between the first and subsequent cycles strongly suggests that synchronized battery-swapping demand–rather than inherent station inefficiency—is the primary driver of bottlenecks. The clustering of trucks at the stations during peak intervals directly correlates with the observed productivity loss (i.e., reduced total trips). These findings imply that decentralizing battery-swapping activity through demand-leveling strategies, such as staggered battery replacement schedules or predictive SoC-based dispatching, could mitigate congestion and unlock throughput gains. Consequently, designing an off-peak battery-swapping protocol emerges as a critical priority for optimizing production efficiency in open-pit mining operations.

To further validate these findings, we designed a proactive staggered battery-swapping strategy to mitigate synchronization-induced bottlenecks. The strategy involves dynamically selecting Z trucks with state of charge (SoC) below Y% at X-minute intervals for prioritized battery replacement, contingent on the availability of fully charged batteries at the swapping stations. To prevent overloading station capacity, the parameter Z caps the maximum number of trucks dispatched per interval–even when surplus charged batteries are available, only Z trucks are proactively rerouted. To identify the optimal parameter combination (X, Y, Z), we performed a grid search over the hyperparameter space: X:[10, 15, 20, 25] × Y:[40, 50, 60, 70] × Z:[2, 3, 4, 5]. For each combination, the simulation was replicated 100 times, with results averaged to compute total trips completed and average battery-swapping wait time. The optimal combination (X = 25, Y = 70, Z = 3) yielded 665 total trips—a 5.7% improvement over the baseline (628 trips)—while reducing average battery-swapping wait time to 32.5 min (from 86.5 min). Figure 4 illustrates the SoC time series under this configuration, demonstrating the near-elimination of prolonged delays during the initial battery-swapping cycle. Meanwhile, Figure 5 plots total trips against average wait time across all parameter combinations, reaffirming the negative correlation observed earlier. This consistent trend underscores battery-swapping efficiency as a leverage point for systemic productivity gains, with suboptimal scheduling directly constraining haulage throughput.

Another way to assess whether battery-swapping efficiency constitutes the dominant bottleneck is by analyzing the relationship between total haulage trips and the number of battery-swapping stations. As demonstrated in Figure 6, increasing the number of stations initially drives a near-linear improvement in total trips, followed by a plateau (even though the waiting time decreases sharply) as the system transitions to being constrained by other workflow components–such as truck fleet size, shovel loading capacity, or crusher throughput. Notably, expanding the number of stations to 4 achieves a throughput (667 trips) parity with the optimized staggered battery-swapping strategy proposed earlier (665 trips).

While both approaches alleviate battery-swapping congestion, their cost implications diverge significantly. Deploying additional stations necessitates substantial capital investment in infrastructure and battery inventory. In contrast, the staggered scheduling strategy–requiring no hardware expansion–achieves comparable efficiency gains through operational optimization. This contrast underscores that smarter dispatching protocols, rather than infrastructure scaling, represent a cost-effective lever for mitigating bottlenecks in open-pit mining operations.

Building on the operational insights derived from the simulation experiments, the subsequent section proposes an optimization-driven framework for battery-swapping scheduling. This framework systematically reduces synchronization induced delays by integrating real-time state of charge (SoC) monitoring, station capacity constraints, and dynamic truck dispatching, thereby establishing a generalizable methodology to alleviate bottlenecks in open-pit mining operations.

Given the predicted battery-swapping demand moments during the first battery-swapping cycle (Section 2), the scheduling of electric mining trucks across multiple stations is formulated as a Mixed-Integer Linear Programming (MILP) model. The formulation begins with a temporal discretization step, where continuous time is partitioned into fixed intervals. This approach converts the intractable continuous-time optimization problem into a discrete, computationally tractable counterpart. Crucially, temporal discretization enhances robustness against demand prediction uncertainties by enabling probabilistic adjustments to resource allocations within each interval—a mechanism that mitigates timing discrepancies between forecasted and actual demand. For illustration, Figure 7 demonstrates a 5-minute time-slice configuration. This discretization eliminates the need for exact demand timing predictions (e.g., 16:15). Instead, when a demand surge is projected for the third time slice, any occurrence within the corresponding 16:15 − 16:20 window remains operationally viable. Such flexibility ensures resilience to minor temporal prediction errors while maintaining scheduling feasibility.

Within this discretized framework, the decision variable in the MILP model is defined as a binary parameter:

Here, x_{i, j, t} = 1 indicates that the dispatching system allocates truck i to the j−th station for battery swapping at the t−th time slice, while x_{i, j, t} = 0 denotes no such assignment. For a fleet of 36 electric mining trucks with projected battery-swapping demands over a 4-hour horizon, the MILP model's total number of decision variables is calculated as 36(trucks) × 48(time slices) × 2(stations) = 3, 456, where the temporal resolution is discretized into 5-min time slices (yielding 4×605=48 intervals) and two battery-swapping stations are available. This parameterization ensures the model systematically encodes all potential scheduling permutations through the binary variable x_{i, j, t}—defined in Equation 1—while maintaining computational tractability under the discretized temporal and spatial constraints outlined in Section 2.

The model's objective function explicitly minimizes the total queuing time, addressing the synchronization-induced bottlenecks identified in Section 2, while enforcing operational constraints such as station capacity limits, battery availability, and truck SoC thresholds. The objective function is defined as:

where I is the total number of trucks, S_i denotes the start time of battery-swapping for truck i and A_i represents the arrival time of truck i, which corresponds to the predicted battery-swapping demand time (an input to the MILP model). The start time S_i is derived from the binary decision variable x_{i, j, t}—defined in Equation 1, which assigns truck i to station j at time slice t, and is calculated as:

where J is the total number of battery-swapping stations, T is the total number of discrete time slices, and t indexes the time slices (e.g., t = 0, 1, …, T−1). This formulation ensures that each truck is assigned to exactly one station within a single time slice, translating the continuous-time scheduling problem into a tractable discrete optimization framework.

To ensure the MILP model aligns with operational realities, four critical constraints are incorporated. First, Equation 4 enforces that each truck undergoes exactly one battery-swapping event within the planning horizon, reflecting the focus on the first battery-swapping cycle:

where, x_{i, j, t} is defined in Equation 1. Second, Equation 5 ensures causality by requiring battery-swapping to occur after arrival:

where S_i and A_i are defined in Equations 3 and 2, respectively. Third, station throughput limitations are modeled via Equation 6, which restricts each station j to servicing at most one truck within any sliding time window of length T_e (battery-swapping and preparation time):

Fourth, battery availability constraints (Equation 7) approximate the finite battery inventory and charging cycle without explicitly tracking individual battery states—a simplification to maintain model tractability. For station j with capacity N_j (maximum stored batteries), the cumulative swaps within the charging time window T_c (time to recharge a depleted battery) must not exceed N_j:

This formulation implicitly enforces that each battery used at time t becomes available again at t+T_c, aligning with the charging cycle while avoiding combinatorial complexity from per-battery tracking.

Batteries are charged in batches at a fixed rate (0.95%/minute), so the charging time window T_c (time to fully recharge a depleted battery) can be precomputed as a deterministic parameter (e.g., 105 minutes for a 100% SoC recovery, consistent with the 700–800 kWh battery capacity). Spare batteries are maintained as a shared pool (5 per station) rather than assigned to specific trucks. Thus, the cumulative number of swaps within T_c directly reflects the maximum number of batteries that can be cycled (used → charged → reused), making the constraint (Equation 7) a reasonable proxy for actual inventory limits. Furthermore, the constraint (Equation 7) could be reformulated as a dynamic one. For a battery-swapping station with multiple charging batteries, their remaining charging times can be estimated and sorted in ascending order. As operational time progresses (e.g., across the MILP's discrete time slices; Section 3.1), each time the time exceeds a remaining charging time in the sorted list, the station's available battery count increases by 1–aligning with the study's operational context.

The proposed MILP model (Equations 1–7) is solved using the open-source solver SCIP (Vigerske and Gleixner, 2016), which outputs the battery replacement schedule–specifically, the optimal battery-swapping station assignment and service order for each mining truck. To generate the model's input (i.e., the predicted battery-swapping demand times during the first cycle), we propose a state-based prediction method tailored to the operational logic of mining trucks. Unlike passenger electric vehicles, where battery-swapping demand can arise continuously, mining trucks can only request battery replacement after completing unloading tasks. This discrete demand pattern arises because trucks must first finish unloading and travel from the unloading zone to a battery-swapping station. The state-based method estimates available battery-swapping moments based on a truck's current operational state:

This approach ensures that battery-swapping demands align with the discrete operational milestones inherent to mining workflows, thereby enabling accurate input generation for the MILP model. The state-based method generates outputs such as those illustrated in Table 2, where mandatory battery-swapping times correspond to instances when the battery is depleted (i.e., the remaining state of charge, SoC, is insufficient to sustain another operational cycle), and n₁, n₂, …, n_I denote the number of available battery-swapping times for trucks 1, 2, …, I, respectively. The final input to the MILP model is an aggregated set of predicted demand times, structured as [t_{1, 2}, t_{2, 1}, ⋯ , t_{i, l}, ⋯ , t_{I, k}] from Table 2. Here, t_{i, l} represents the l−th battery-swapping time scheduled for truck i, and t_{I, k} denotes the k−th time allocated to truck I, where I is the total number of trucks in the fleet.

First, we evaluate the potential of the MILP model to mitigate queuing delays for mining trucks at battery-swapping stations. To this end, input parameters for the MILP model are generated using a normal distribution with a mean of 210 (i.e., 3.5 hours after the current time). By systematically varying the standard deviation (σ), we simulate distinct temporal distributions of battery-swapping demand times across a fleet of 36 mining trucks. Smaller σ values produce more clustered demand profiles, emulating scenarios with synchronized battery depletion–a critical bottleneck in mining operations. Figure 8 compares the average waiting times achieved by MILP-optimized scheduling against the baseline First-Come-First-Served (FCFS) strategy. The results reveal a maximum reduction of 15 minutes in queuing time at σ = 35, whereas the minimum reduction of 12 minutes occurs under the most concentrated demand scenario (σ = 0.5). This demonstrates that merely enhancing intrinsic station throughput (e.g., faster battery swapping) cannot resolve synchronization-induced congestion, underscoring the necessity of off-peak scheduling to address systemic inefficiencies.

Figure 8 reveals that greater dispersion in battery-swapping demand distributions correlates with shorter average waiting times, regardless of scheduling strategy (MILP or FCFS). This observation suggests an intuitive off-peak strategy: by systematically exploring all feasible battery-swapping time combinations derived from Table 2, one could theoretically identify the optimal schedule with minimal queuing time. However, this approach is computationally intractable due to combinatorial explosion. To illustrate, consider a fleet of 40 mining trucks, each with 4 candidate battery-swapping times before battery depletion. The total number of combinations is 4⁴⁰≈10²⁴. Assuming an MILP solver requires 1 second per combination, exhaustive evaluation would demand 10²⁴ seconds (≈10¹⁶ years)–a timescale exceeding practical feasibility.

Bayesian optimization is a data-driven method for efficiently optimizing black-box functions (e.g., complex systems with unknown analytical forms). Its core mechanism involves constructing a probabilistic surrogate model—typically a Gaussian process—to approximate the objective function. By iteratively updating this model with prior observations, Bayesian optimization computes a posterior distribution that balances exploration (sampling uncertain regions) and exploitation (refining known promising regions), thereby guiding the search toward globally optimal solutions. To address the combinatorial explosion inherent in scheduling problems, Bayesian optimization circumvents exhaustive enumeration of all combinations. Instead, it leverages the surrogate model's probability estimates to prioritize candidate solutions with higher likelihoods of optimality. This is achieved through an acquisition function (e.g., Expected Improvement), which intelligently selects the next evaluation point based on the posterior distribution. By focusing computational resources on high-potential regions, Bayesian optimization dramatically reduces the effective search space, mitigating the computational burden caused by combinatorial explosion (e.g., reducing 10²⁴ combinations to a tractable subset).

For the off-peak battery-swapping scheduling problem under study, the objective function approximated via Bayesian optimization is formally defined as:

where C denotes the feasible solution space of battery-swapping time combinations, and ℝ maps to the real-valued output of either the MILP model (Equations 1–7) or the FCFS queuing time calculation. One sample in C can be expressed as c=[t1,2,t2,1,…,ti,l,…,tI,k]T, with t_{i, l} representing the l−th battery-swapping time scheduled for truck i as defined in Table 2. By treating f as a computationally expensive black-box function, Bayesian optimization constructs a probabilistic surrogate model (e.g., Gaussian process) trained on prior evaluations to guide the search toward high-potential regions of C, thereby avoiding exhaustive enumeration of all combinations (e.g., 4⁴⁰) and balancing exploration-exploitation trade-offs through acquisition functions like Expected Improvement (EI) and Upper Confidence Bound (UCB).

At the core of the Gaussian process (GP) lies the assumption that the function values of any finite set of points follow a joint Gaussian distribution, formally expressed as:

where μ_f(c) is the mean function (set to 0 due to the absence of prior knowledge, ensuring reliance on the kernel for localized feature capture) and k(c, c′) is the covariance kernel quantifying similarity between combinations c and c′. We employ the Matérn 5/2 kernel, defined as:

where r=∥c-c′∥2 is the L2-norm distance between c and c′. This kernel's twice-differentiable properties balance smoothness and flexibility, critical for modeling queuing time trends and localized demand variations in battery-swapping scheduling. Another advantage of this kernel function is that there is no need for hyperparameter optimization.

With the Gaussian process framework (Equations 9–10), the queuing time for a mining truck fleet under a new battery-swapping schedule can be probabilistically predicted using observed historical data. Let C=[c1,c2,…,cm]⊂C denote a set of m observed combinations of battery-swapping times, and f = [f(c¹), f(c²), …, f(c^m)]T represent their corresponding queuing times (computed via MILP or FCFS). For a candidate combination c^*, Bayesian inference yields the posterior distribution of its predicted queuing time::

where the posterior mean μ(c^*) and variance σ(c^*) are derived as:

Here:

Once the Gaussian process surrogate model is established, the Upper Confidence Bound (UCB) acquisition function guides the selection of the next candidate solution to evaluate. The UCB is defined as:

where μ(c^*) and σ(c^*) are the posterior mean and standard deviation from Equation 12, and κ = 2.5 is a hyperparameter balancing exploration (prioritizing uncertain regions) and exploitation (refining known optima). At each Bayesian optimization iteration:

After N iterations, the augmented datasets become:

The optimal battery-swapping schedule c^best corresponds to the combination with the minimum queuing time in f_{iter = N}. This iterative process efficiently navigates the combinatorial space C, avoiding exhaustive evaluation of all 4⁴⁰ combinations while balancing data-driven exploration and exploitation.

With both the inner MILP model (Equations 1–7) and the outer Bayesian optimization (Equations 9–14) rigorously defined, the proposed hierarchical optimization framework is systematically established (detailed in Algorithm 1), as illustrated in Figure 9. To adapt Bayesian optimization—originally designed for continuous decision variables—to the discrete combinatorial space C, a binary search-based discretization module (detailed in Algorithm 2) is integrated. This module maps continuous samples generated by the Gaussian process surrogate model to the nearest valid discrete battery-swapping times (Table 2), ensuring feasibility while preserving the probabilistic exploration-exploitation balance. The hierarchical integration of MILP (exact queuing time calculation) and Bayesian optimization (global search guidance) enables near-optimal scheduling with drastically reduced computational effort.

The first scenario simulates battery-swapping operations in an open-pit mine with one loading platform (equipped with two excavators) and one unloading zone (serving a single crusher). Key operational parameters include:

These settings are based on an actual open-pit coal mine. Using these inputs, the state-based prediction module (Section 3) generates a discrete battery-swapping schedule (Table 2) by simulating truck trajectories, energy consumption, and queuing dynamics. This table provides all feasible battery-swapping time windows for the fleet, serving as input to the hierarchical optimization framework (Figure 9) for minimizing queuing delays.

A systematic sensitivity analysis evaluates the impact of initial sampling points (init_points) and Bayesian optimization iterations (n_iter) on solution quality. As shown in Table 3, increasing init_points enhances solution optimality initially but plateaus beyond a threshold (e.g., init_points=30), suggesting sufficient exploration of the combinatorial space C. In contrast, increasingn_iter beyond 5 yields diminishing returns, indicating rapid convergence of the Gaussian process surrogate model. Based on these findings, subsequent experiments adoptinit_points=30 and n_iter=5, balancing computational efficiency with solution quality. This configuration ensures robust exploration-exploitation trade-offs while aligning with the hierarchical framework's goal of mitigating combinatorial explosion (Section 3).

Figure 10 illustrates the scheduling outcomes generated by the Hierarchical Framework (Section 3). The results demonstrate that the framework proactively schedules more than 50% of trucks for battery swaps prior to SoC depletion, effectively dispersing demand peaks and reducing total queuing time. The optimized schedule achieves an average queuing time of 41.3 min at the battery-swapping station, representing a 65% reduction compared to the MILP baseline (116.4 min) and a 68% improvement over the FCFS strategy (128.4 min) when both use mandatory battery-depletion moments (Table 2) as input. This performance underscores the framework's ability to balance proactive scheduling (exploiting demand dispersion) with computational efficiency (avoiding the 4⁴⁰ combinatorial search space), validating its superiority over conventional rule-based or exhaustive optimization approaches.

The second scenario models battery-swapping operations in an open-pit mine with two loading platforms (each equipped with two excavators) and one unloading zone (serving a single crusher). Key operational parameters include:

Using these inputs, the state-based prediction module (Section 3) simulates truck trajectories, energy consumption, and queuing dynamics to generate a discrete battery-swapping schedule (Table 2). This schedule enumerates all feasible battery-swapping time windows, which serve as input to the hierarchical optimization framework (Figure 9) for minimizing queuing delays through proactive demand dispersion.

Figure 11 illustrates the scheduling outcomes generated by the Hierarchical Framework (Section 3). Compared to Case Study 1 (single loading platform), the framework proactively schedules 75% of trucks (versus 50% in Case 1) for battery swaps prior to SoC depletion, achieving enhanced demand dispersion across the dual-platform configuration. The optimized schedule attains an average queuing time of 26.4 min at the battery-swapping station, demonstrating a 78% reduction compared to the MILP baseline (122.5 min) and an 80% improvement over the FCFS strategy (132.1 min), both of which rely on mandatory battery-depletion moments (Table 2).

The third scenario extends the battery-swapping operations to a Discrete Event Simulation (DES)-integrated environment, maintaining the dual loading platforms (each with two excavators) and a single unloading zone (serving one crusher). Key enhancements include:

Key operational parameters include:

Instead of the state-based prediction module (Section 3), DES generates the discrete battery-swapping schedule (Table 2), enumerating feasible time windows while accounting for real-world variability (e.g., traffic, equipment downtime). This DES-derived schedule serves as input to the hierarchical optimization framework (Figure 9), which minimizes queuing delays through proactive demand dispersion.

Figure 12 illustrates the scheduling outcomes generated by the Hierarchical Framework (Section 3) for Case Study 3. The framework converges to a high-quality solution, reducing the total waiting time to 30 minutes by proactively scheduling 100% of trucks for battery swaps prior to SoC depletion during the first operational cycle, demonstrating a 99% reduction compared to the MILP baseline (79.6 minutes) and an 99% improvement over the FCFS strategy (96.0 minutes). It is worth noting that DES yields an average waiting time of 81.3 minutes and 599 total trips completed. It can be inferred that the solution results based on the above hierarchical framework will significantly increase transport trip throughput by the DES.

The scheduling solution derived by the Hierarchical Framework (Figure 12, Section 3) is coupled into the Discrete Event Simulation (DES) environment to validate its real-world applicability. Prior to integration, the solution undergoes an operational translation: The framework's time-based battery-swapping assignments (e.g., “swap at 10:15 AM”) are converted into trip-triggered thresholds (e.g., “swap after completing 3 trips”), aligning the proactive scheduling logic with DES's discrete, event-driven architecture. This transformation ensures seamless integration of the hierarchical schedule into DES, enabling rigorous testing of its robustness under dynamic operational variability. The scheduling solution derived by the Hierarchical Framework achieves 630 total transport trips—a 5.2% throughput increase over the DES baseline (599 trips)—while reducing the average battery-swapping wait time to 4.5 min, a 94.5% reduction from the DES benchmark of 81.3 minutes. Figure 13 illustrates the SoC time series with and without the framework's solution, demonstrating near-elimination of prolonged queuing delays during the initial battery-swapping cycle through proactive demand dispersion (Figure 12). The nonlinear scalability of total transport trips—despite the 94.5% reduction in battery-swapping queuing time—highlights that the bottlenecks inherent to open-pit mining operations have changed from battery-swapping to other subsystems (e.g., Truck fleet throughput, Excavator loading rates and Crusher processing capacity). To validate the hypothesis that mechanical subsystems—not battery-swapping efficiency—govern ultimate productivity, we tested the hierarchical framework's scalability by incrementally expanding the number of loading platforms and unloading zones. Figure 14 (left) shows that increasing loading platforms from 2 to 3 elevates total transport trips by 10.6% (from 688 to 761 trips), significantly exceeding the 5.2% gain observed in the dual-platform configuration. This nonlinear scalability confirms that excavator loading capacity (fixed at 5 min per truck) becomes the dominant bottleneck as platforms scale, overriding energy management optimizations. Conversely, Figure 14 (right) reveals marginal diminishing returns when expanding unloading zones: increasing zones from 1 to 2 raises trip gains by only 1.1% (10.6% → 11.7%, 11.7% is obtained by the increment from 695 to 776 trips), with no further improvement when adding a third zone. This plateau—attributable to the crusher's fixed processing capacity (3 min per unload)—demonstrates that unloading zone availability ceases to constrain productivity beyond a critical threshold. While these results clarify the hierarchical framework's role in resolving energy-time bottlenecks (e.g., battery queuing), holistic optimization of mechanical subsystems (e.g., excavator cycle times, crusher throughput) remains an open challenge beyond this study's scope.