FleetRec: Fleet-Level Recommendation

• FleetRec is a systems concept that compresses multiple entity-level decisions into abstract fleet-level models for sizing, routing, repositioning, and evaluation.
• It employs diverse methods such as graph-theoretic matching, master problems with daily options, and aggregate representations to derive operational recommendations.
• The approach spans applications from on-demand mobility to energy systems, showcasing scalable, resilient, and computationally efficient fleet optimization.

FleetRec, an Editor’s term, can be understood as a family of fleet-level recommendation, representation, and control methods that compress many entity-level decisions into tractable models for sizing, routing, repositioning, charging, or evaluation. In the supplied literature, this label spans retrospective trip chaining in on-demand mobility, long-horizon fleet size-and-mix design, online control of autonomous vehicle fleets, exact aggregate representations for heterogeneous storage fleets, stochastic queueing models for electric-vehicle sharing, robust and resilient routing for electric and robotic fleets, and evaluation infrastructures for federated workloads that are explicitly framed as relevant to “FleetRec” recommender settings (Ye et al., 2022, Bertoli et al., 2017, Filipovska et al., 2022, Skordilis et al., 2021, Angeli et al., 2021, Evans et al., 2018, Deng et al., 2020, Pustilnik et al., 2024, Goutham et al., 2024, Hamdan et al., 30 Aug 2025). This suggests that FleetRec is not a single standardized architecture but a recurring design pattern: derive a compact fleet-level state or feasible set, optimize against that abstraction, and recover operational recommendations for the underlying vehicles, devices, or clients.

1. Scope and recurring abstractions

Across the supplied papers, FleetRec-style formulations differ by application domain but share a common mathematical move: replace large sets of item-level constraints with a lower-dimensional object that still preserves operational meaning. In retrospective fleet sizing, the abstraction is a bipartite graph whose maximum matching determines the minimum number of vehicles (Ye et al., 2022). In long-horizon fleet design, the abstraction is a master problem over daily “options,” each option encoding a feasible day-level fleet mix and routing plan (Bertoli et al., 2017). In storage aggregation, the abstraction is an exact feasible set for the aggregate charging profile $d(t)$ with $O(T)$ variables and $O(T)$ constraints independent of fleet size (Angeli et al., 2021). In discharge-only flexibility analysis, it is the one-dimensional capacity curve $\Omega_{\bar{p},x}(p)$ (Evans et al., 2018). In EV sharing, it is a closed BCMP queueing network over departure, travel, and charging nodes (Deng et al., 2020).

A second recurring abstraction is fleet-level control rather than vehicle-level control. Shared autonomous mobility work formulates repositioning as a system-agent MDP over zones, where the action is a matrix of fractions $A_{ij}^t\in[0,1]$ or a distribution of “phantom requests,” rather than one action per vehicle (Filipovska et al., 2022, Skordilis et al., 2021). In intra-factory robot logistics, the control object is a task-allocation search tree whose nodes encode partial fleet assignments and whose leaves are repaired under perturbations (Goutham et al., 2024). In federated learning evaluation, the fleet-level object is an experiment configuration that jointly controls client containers, network topology, traffic, and telemetry, allowing holistic study of recommender-style FL workloads (Hamdan et al., 30 Aug 2025).

A plausible implication is that FleetRec is best viewed as a systems concept rather than a single algorithmic family. Its essential content is the explicit coupling of a fleet-level representation with an operational decoder: chain reconstruction from a matching, route recovery from a daily option, disaggregation of an aggregate charging profile, task execution from a nominal search tree, or deployment of FL clients inside an emulated topology.

2. Graph-theoretic sizing and long-horizon fleet design

In the retrospective minimum fleet-size problem, trips are given as

$N_i=(p_i,T_i^p,d_i,T_i^d),$

with travel-time function $time(s,t)$. A bipartite graph $G=(D\cup P,E)$ is built with one node for each drop-off in $D$ and one node for each pickup in $P$, and with an edge from $O(T)$0 to $O(T)$1 whenever

$O(T)$2

If $O(T)$3 is the size of a maximum matching in this graph, the minimum fleet size is

$O(T)$4

The paper’s main result strengthens this matching interpretation into a min–max theorem: if $O(T)$5 denotes the problem of finding the maximum number of pairwise incompatible trips, then

$O(T)$6

Equivalently, the minimum number of vehicles needed to cover all trips equals the maximum size of a set of trips that cannot be chained in either order by a single vehicle (Ye et al., 2022). The proof uses the matching–fleet correspondence, König’s theorem, and a combinatorial extraction lemma for whole trip pairs from a large independent set.

For long-horizon fleet size-and-mix design, the abstraction changes from individual trips to day-level “options.” For each day $O(T)$7, an option $O(T)$8 specifies a feasible routing plan and fleet usage $O(T)$9 for every vehicle type $O(T)$0, with operating cost $O(T)$1. The master problem chooses global fleet counts $O(T)$2 and one option per day through binary variables $O(T)$3, minimizing fixed acquisition cost plus total operating cost over the horizon. The method applies column generation, with daily subproblems solved by any single-day fleet size-and-mix solver, including solvers with rich constraints such as time windows, compatibility restrictions, multiple compartments, split deliveries, and multiple trips per vehicle (Bertoli et al., 2017). The central significance is that a fleet is recommended from all days simultaneously rather than from a single “representative day,” which the paper reports yields much higher fleet utilization and substantially smaller fleets than union-of-daily or subset-of-days baselines.

Taken together, these two lines of work define one of the clearest FleetRec themes: fleet recommendation can be posed as a covering or design problem over combinatorial objects—trip chains or daily options—where optimality is mediated by graph-theoretic or decomposition-based structure rather than by direct simulation of every vehicle trajectory.

3. Online control, repositioning, and transfer

In the VIPAFLEET framework, the environment is a metric space $O(T)$4 induced by a connected network $O(T)$5, with a depot $O(T)$6, a time horizon $O(T)$7, and subnetworks $O(T)$8 that may be lines or circuits. Requests are modeled as tuples such as $O(T)$9, and the fleet can operate in tram mode, elevator mode, or taxi mode. On circuits, the paper analyzes SIR (“Stop If Requested”), SIF$\Omega_{\bar{p},x}(p)$0 (“Start If Fully loaded” for the morning scenario), and SIF$\Omega_{\bar{p},x}(p)$1 (the analogous evening rule); on lines, it analyzes MAIN (“Move Away If Necessary”). Competitive analysis gives strong scenario dependence: SIR is $\Omega_{\bar{p},x}(p)$2-competitive for total tour length on a general circuit, but $\Omega_{\bar{p},x}(p)$3-competitive in morning and evening scenarios; SIF$\Omega_{\bar{p},x}(p)$4 and SIF$\Omega_{\bar{p},x}(p)$5 are $\Omega_{\bar{p},x}(p)$6-competitive for total tour length in morning and evening settings, respectively; MAIN is $\Omega_{\bar{p},x}(p)$7-competitive for makespan in the morning scenario and $\Omega_{\bar{p},x}(p)$8-competitive for total tour length on a line in that scenario (Bsaybes et al., 2017). The framework explicitly recommends switching subnetworks and modes by period of day, including parking-centered subnetworks in morning/evening, restaurant-centered subnetworks at lunch, and a Hamilton cycle in emergency mode.

A later reinforcement-learning line replaces these hand-designed online rules with centralized system-agent policies. One framework treats dispatch as part of the environment and uses state and action spaces defined as distributions over grid cells. The action is a distribution of “phantom requests,” which induces the existing dispatcher to move idle vehicles toward desired regions. Because both state and action are probability distributions rather than raw counts, the method claims scale-invariant transfer learning between problem instances with similar vehicle and request distributions (Skordilis et al., 2021). This formulation is modular by construction: dispatch is exogenous, rebalancing is learned, and the learned policy interacts with whichever dispatch algorithm is embedded in the simulator.

A more detailed SAMS formulation defines a fully observed MDP

$\Omega_{\bar{p},x}(p)$9

over a zone graph, with node features including idle vehicles, repositioning vehicles, passenger-carrying vehicles that will arrive, and recent demand counts. The fleet-level action is

$A_{ij}^t\in[0,1]$0

where $A_{ij}^t\in[0,1]$1 is the fraction of idle vehicles in zone $A_{ij}^t\in[0,1]$2 to reposition toward zone $A_{ij}^t\in[0,1]$3. The reward is

$A_{ij}^t\in[0,1]$4

which the paper shows can be tuned to approximate negative mean wait time. The main method, integrated system-agent repositioning (ISR), uses A2C with a GAT-plus-GCN architecture and a Dirichlet policy over fleet-level repositioning actions; it is compared against externally guided repositioning (EGR), which augments the state with explicit demand forecasts, and a forecast-based joint optimization baseline (JO). The reported numerical result is that the learning-based repositioning approaches achieve substantial reductions in passenger wait times, over 50%, relative to JO, while ISR remains comparable on average to forecast-driven EGR despite bypassing explicit demand forecasting (Filipovska et al., 2022).

A distinct but structurally related control formulation appears in coregionalized Gaussian Process Policy Iteration for fleets of nearly identical machines. There, a fleet MDP $A_{ij}^t\in[0,1]$5 shares state and action spaces across members but assigns each member its own transition function $A_{ij}^t\in[0,1]$6. Cross-member similarity is captured by a coregionalized kernel

$A_{ij}^t\in[0,1]$7

yielding member-specific posterior dynamics while sharing information across similar fleet members. The method significantly outperforms both individual learning and naive pooled learning on mountain car, cart-pole, and a wind-farm setting, indicating that FleetRec-style control can also mean similarity-aware recommendation of actions across a fleet of related but nonidentical assets (Verstraeten et al., 2019).

4. Exact aggregate representations in energy and EV systems

For heterogeneous charging fleets of storage devices, the central FleetRec object is the aggregate charging demand

$A_{ij}^t\in[0,1]$8

together with an exact polyhedral feasible set. If device $A_{ij}^t\in[0,1]$9 has charging limit $N_i=(p_i,T_i^p,d_i,T_i^d),$0, total energy requirement $N_i=(p_i,T_i^p,d_i,T_i^d),$1, and availability window $N_i=(p_i,T_i^p,d_i,T_i^d),$2, then the aggregate feasible set is characterized by

$N_i=(p_i,T_i^p,d_i,T_i^d),$3

plus nonnegativity and a total-energy equality. The key result is that, under the paper’s assumptions, this exact aggregate model can be reduced to $N_i=(p_i,T_i^p,d_i,T_i^d),$4 constraints independent of the fleet size $N_i=(p_i,T_i^p,d_i,T_i^d),$5. In the full-availability case $N_i=(p_i,T_i^p,d_i,T_i^d),$6, the relevant constraints are nested cumulative inequalities over times sorted by inflexible demand; in the partial-availability case, exactness is preserved by enforcing inequalities only on a precomputable family of sets $N_i=(p_i,T_i^p,d_i,T_i^d),$7 defined through a “maximum average demand” functional (Angeli et al., 2021). This gives a lossless fleet-level representation that can be embedded directly in unit-commitment-like or economic-dispatch formulations.

A complementary aggregate representation appears in the discharge-only flexibility model for heterogeneous storage units. Each device $N_i=(p_i,T_i^p,d_i,T_i^d),$8 has extractable energy $N_i=(p_i,T_i^p,d_i,T_i^d),$9, maximum discharge power $time(s,t)$0, and state $time(s,t)$1. For any nonnegative service request $time(s,t)$2, the paper defines the $time(s,t)$3-$time(s,t)$4 transform

$time(s,t)$5

and the fleet capacity curve

$time(s,t)$6

where $time(s,t)$7 is the worst-case reference obtained by discharging every device at full power until depletion. The core theorem is the exact feasibility equivalence

$time(s,t)$8

Hence a one-dimensional curve summarizes the entire feasible set of demand traces for the fleet, and fleet comparison reduces to dominance of capacity curves (Evans et al., 2018). In FleetRec terms, this is a highly compact representation layer that supports immediate feasibility checks and structural comparison between fleet configurations.

Electric-vehicle sharing introduces a stochastic steady-state version of the same design problem. The system is modeled as a closed BCMP queueing network with single-server departure points, infinite-server travel links, and finite-server charging points. If $time(s,t)$9 is the throughput for fleet size $G=(D\cup P,E)$0 and $G=(D\cup P,E)$1 the visit ratio of node $G=(D\cup P,E)$2, then availability at departure node $G=(D\cup P,E)$3 is

$G=(D\cup P,E)$4

and the fleet-sizing profit is

$G=(D\cup P,E)$5

The paper proves that $G=(D\cup P,E)$6 is concave in $G=(D\cup P,E)$7, that each $G=(D\cup P,E)$8 is nondecreasing in $G=(D\cup P,E)$9, and that the optimal fleet-sizing problem has at most two optimal solutions under a coercive cost $D$0. It also proves that system throughput and station availability are increasing concave functions of each charger count $D$1, which motivates a greedy marginal-allocation algorithm for charger siting (Deng et al., 2020). Particularly notable is the result that two slow chargers may outperform one fast charger when the variance of charging time becomes relatively large in comparison to the mean charging time, a point that turns charger-type selection into a variance-sensitive design decision rather than a simple mean-rate comparison.

5. Robust and resilient operational backends

For electric fleets under uncertainty, the Robust Energy Capacitated Vehicle Routing Problem (RECVRP) couples routing, payload, and battery feasibility. The network is a fully connected graph $D$2 over depots $D$3, customers $D$4, and charging stations $D$5; travel time $D$6 and energy consumption $D$7 on each edge are modeled as Gaussian random variables with known mean and variance. The formulation uses binary routing variables $D$8, MTZ-style subtour elimination, load propagation, charging times $D$9, and chance constraints on state of charge. The robust objective minimizes a time quantile

$P$0

while energy feasibility is enforced through quantile-based lower bounds on the SoC along the route and on the return to the depot (Pustilnik et al., 2024). Because the full stochastic mixed-integer model is expensive, the paper decomposes it via customer clustering into per-vehicle Robust Energy Constrained TSPs, uses a combined time–energy cost matrix

$P$1

and reports fast, high-quality solutions on standard benchmarks. For large deterministic instances, reported gaps to best-known solutions are often small while run times are several times faster than prior methods.

A different resilience mechanism appears in energy-aware intra-factory robot logistics. The nominal problem is solved a priori by Monte Carlo Tree Search over task assignments, with a routing Branch-and-Bound subroutine evaluating each leaf. When a disruption perturbs edge energy costs $P$2, battery capacities $P$3, or payload capacities $P$4, the method does not rebuild the search from scratch. Instead, it copies the nominal tree topology, resets node statistics, re-evaluates a $P$5-percentile of the best nominal leaf nodes under the perturbed parameters, backpropagates those updated costs, and then resumes MCTS on the perturbed tree (Goutham et al., 2024). Computational experiments compare this centralized tree-reuse strategy to both decentralized no-reassignment recovery and centralized MCTS from scratch, and the paper reports lower-cost incumbents at short time budgets together with real-time capability for the tested scenarios.

These two backends define a robust-operational branch of FleetRec. Inference from the supplied material suggests a common structure: represent perturbations as parameter changes in an otherwise stable fleet model, preserve a reusable nominal solution object—clusters, search trees, or route skeletons—and exploit that object to restore feasibility and quality rapidly after the disruption.

6. Evaluation infrastructure, reproducibility, and limitations

The paper “FLEET: A Federated Learning Emulation and Evaluation Testbed for Holistic Research” supplies a systems-oriented interpretation of FleetRec in which the “fleet” is a set of heterogeneous FL clients, potentially running recommender workloads, embedded in an emulated network. FLEET combines Flower as a framework-agnostic FL layer with Containernet as a container-based network emulator, integrates TopoHub topologies, and configures experiments through three TOML files covering FL, Containernet, and general settings (Hamdan et al., 30 Aug 2025). The testbed logs FL metrics such as loss, accuracy, round timings, and communication time; system metrics such as per-client CPU and memory utilization; and network metrics such as TX/RX bytes and rates. It also supports background traffic via Iperf3 or TCPReplay using Poisson, Bursty, Uniform, Normal (Gaussian), and SineWave patterns, and the paper demonstrates these capabilities on CIFAR-10 with MobileNetV3-Large and on IMDB with DistilBERT under realistic WAN congestion. In the supplied reading, this infrastructure is presented as directly useful for “FleetRec” recommender research because it can run actual PyTorch or TensorFlow recommender code under heterogeneous compute and network constraints.

Across the broader literature, the strongest limitations are domain-specific but structurally similar. The retrospective min–max fleet-sizing theorem assumes deterministic trip times, single-vehicle service per trip, and no maximum waiting-time window beyond feasibility; the authors explicitly state that they do not know of an analogous result once an upper bound $P$6 on early waiting is imposed (Ye et al., 2022). Exact aggregate storage models assume charging-only independent devices, no internal network constraints, and deterministic availability windows (Angeli et al., 2021). The graphical flexibility model is discharge-only and single-bus, with no charging, locational constraints, or uncertainty built into the core theory (Evans et al., 2018). EV-sharing sizing assumes Poisson arrivals, passenger loss instead of passenger waiting, and stationary routing probabilities (Deng et al., 2020). Learning-based repositioning for SAMS uses static Manhattan travel times, no ride sharing, no cancellations, and fixed fleet size, and its transferability weakens on unseen full-day weekday demand with a PM peak absent from training (Filipovska et al., 2022). FLEET itself acknowledges limited wireless realism, single-host scaling, and the absence of secure aggregation, differential privacy, adversarial models, and energy modeling in its current implementation (Hamdan et al., 30 Aug 2025).

A common misconception would be to treat FleetRec as either a purely routing problem or a purely recommender-systems problem. The supplied literature instead supports a broader interpretation: FleetRec methods operate wherever a fleet-level object—matching, option set, aggregate polytope, capacity curve, queueing network, system-agent policy, search tree, or emulated client topology—can be used to generate decisions that are both computationally tractable and operationally interpretable.