Team Formation and Routing Problem

• TFRP is a class of optimization problems that jointly decide team composition and route scheduling, integrating resource constraints, uncertain travel times, and synchronization.
• Formulations range from fixed-team coordinated routing to integrated coalition-routing models using set covering, branch-price, and metaheuristic approaches.
• Empirical studies show that integrated strategies outperform sequential methods, especially in uncertainty-rich environments like airport baggage handling and dynamic workforce routing.

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The Team Formation and Routing Problem (TFRP) denotes a class of combinatorial optimization problems in which decisions about who should work together and how those teams should move through space and time are made jointly rather than sequentially. Across the literature, the term covers several distinct but structurally related settings: fixed fleets of robots routed under survivability constraints (Jorgensen et al., 2016), homogeneous fixed-wing drone teams assigned Dubins-feasible routes (Sundar et al., 2019), social-network team selection guided by communication distances (Addanki et al., 2020), profitable multi-vehicle task selection and routing (Vidal et al., 2014), human-robot leader-follower team design with routing and replenishment (Chirala et al., 2022), coalition-based multi-agent routing and scheduling (Capezzuto et al., 2021), workforce routing with dependent tasks across multiple days (Pereira et al., 2020), dynamic synchronized multi-skill crew routing (Demiray et al., 2023), and route-based baggage-handling team formation under stochastic travel times (Hagn et al., 2024). The common feature is that team structure and route structure are coupled through resource requirements, communication, uncertainty, synchronization, or shared objective functions, so that solving assignment and routing separately generally destroys optimality.

1. Conceptual scope and problem taxonomy

The expression “team formation and routing” is not used uniformly across the literature. In some works, “team formation” means selecting a fixed number of mobile agents and coordinating their routes, with no endogenous worker composition decision. This is the case in the Team Surviving Orienteers problem, where the team is a given set of $K$ robots and the central problem is survivability-aware path assignment under a shared expected-coverage objective (Jorgensen et al., 2016). A similar interpretation appears in the Dubins Team Orienteering Problem for multiple fixed-wing drones, where the “team” is a fleet of identical drones and the optimization concerns route selection subject to heading and curvature constraints rather than coalition design (Sundar et al., 2019).

A second usage treats team formation as graph-based selection of compatible individuals, often with no explicit routing variables. In communication-aware social-network models, teams are subsets of experts whose skill union covers a task while shortest-path-based communication cost is minimized (Addanki et al., 2020). In sociometric multi-project team allocation, individuals are partitioned into groups to maximize weighted social cohesion under departmental requirements (Esgario et al., 2019). These models are directly relevant to the team-formation side of TFRP but are not routing formulations in the operations-research sense.

A third and more integrated class is closer to the modern meaning of TFRP: teams or coalitions are formed implicitly or explicitly while agents are routed to tasks. In multi-agent routing and scheduling through coalition formation, a task may require a subset $C \subseteq A$ of agents, and coalition choice, routing, and scheduling are encoded jointly through time-indexed variables $x_{v,l,t,C}$ (Capezzuto et al., 2021). In dynamic multi-skill workforce routing with synchronization constraints, tasks can require multiple pre-existing crews to start simultaneously, so the “service team” at a task is a coalition of routed crews (Demiray et al., 2023). In airport baggage handling, working profiles specify team skill compositions and route-based set-covering columns represent both team formation and routing decisions (Hagn et al., 2024).

A useful taxonomic distinction is therefore between fixed-team coordinated routing, team selection on graphs, and integrated coalition-routing formulations. This suggests that TFRP is best viewed as a family of models rather than a single canonical problem class.

2. Core mathematical structure

Despite domain variation, most TFRP formulations combine three interacting decision layers: team composition or coalition choice, task assignment, and route or schedule construction. The simplest integrated route-based structure appears in vehicle-routing-with-profits models, where three coupled decisions are identified explicitly: customer selection, assignment to vehicles, and sequencing of deliveries (Vidal et al., 2014). This decomposition maps almost exactly to many TFRP settings in which tasks are optional, teams have route budgets, and the planner must decide which tasks are served, by which team, and in what order.

In route-based exact formulations, a common pattern is a set covering or set packing master problem over feasible team routes. In the baggage-handling TFRP, each column represents a feasible team route $(r,q)$, where $r$ is a route and $q$ is a working profile specifying the number of workers of each qualification threshold (Hagn et al., 2024). The aggregated master problem is

$$\min \sum_{(r,q)\in\mathcal{R}} \mathbb E(c^r)\lambda^r_q$$

subject to task-covering constraints

$$\sum_{(r,q)\in\mathcal{R}: \ i\in\mathcal{I}^r} \lambda^r_q \geq 1 \qquad \forall i\in\mathcal{I}$$

and workforce-capacity constraints

$$\sum_{(r,q)\in\mathcal{R}} b_{k,\tau}^{r,q}\lambda^r_q\leq N_k \qquad \forall k\in\mathcal{K},\ \forall \tau\in \mathcal{T}.$$

Here a column simultaneously determines the route, the team profile, time-dependent workforce occupancy, and expected service cost (Hagn et al., 2024). This is a prototypical TFRP structure because team formation is embedded directly into the route variable.

Time-indexed coalition formulations take a different form. In MARSC, the central variable is

$x_{v,l,t,C}\in\{0,1\},$

indicating that coalition $C \subseteq A$0 serves task $C \subseteq A$1 at location $C \subseteq A$2 during time $C \subseteq A$3 (Capezzuto et al., 2021). Coalition effectiveness is encoded through

$C \subseteq A$4

and workload completion is enforced by

$C \subseteq A$5

which couples coalition size and composition to task duration (Capezzuto et al., 2021). This structure is especially expressive when tasks can be completed cumulatively by changing coalitions over time.

At the graph-theoretic end of the spectrum, some formulations omit explicit routing but still encode communication via shortest-path structure. In community-based expert team formation, feasibility is

$C \subseteq A$6

while team quality is measured by metrics such as leader distance

$C \subseteq A$7

sum distance, or diameter (Addanki et al., 2020). These models are not route-construction problems, but they preserve the TFRP motif that team quality depends on network path structure.

3. Team formation mechanisms

The “team formation” component varies sharply by application. In many routing-centric papers, team size or team membership is fixed, and formation is implicit in route assignment. The TSO problem, for example, assumes a fixed homogeneous team of $C \subseteq A$8 robots and optimizes only the set of risky paths $C \subseteq A$9 (Jorgensen et al., 2016). The team objective is not additive over robots but defined through expected coverage of nodes visited by at least one surviving robot: $x_{v,l,t,C}$0 with overall objective

$x_{v,l,t,C}$1

Here “team formation” is route coordination for a fixed team rather than combinatorial team composition (Jorgensen et al., 2016).

A more explicit team-design layer appears when tasks require heterogeneous skills. In the stochastic baggage-handling TFRP, a working profile $x_{v,l,t,C}$2 is defined by qualification requirements $x_{v,l,t,C}$3, where $x_{v,l,t,C}$4 is the number of workers with at least skill $x_{v,l,t,C}$5 (Hagn et al., 2024). A finer-grained skill composition $x_{v,l,t,C}$6 disaggregates a profile into exact counts of workers by skill level and must satisfy

$x_{v,l,t,C}$7

and

$x_{v,l,t,C}$8

Thus, formation is the selection of a mode-dependent team composition compatible with each route (Hagn et al., 2024).

In dynamic workforce routing with synchronization, crews are fixed but task-level teams are endogenous. Skill coverage is enforced by

$x_{v,l,t,C}$9

so a task may require several crews whose combined skills cover the requirement vector (Demiray et al., 2023). The heuristic explicitly computes irreducible compatible crew combinations $(r,q)$0 for each task, making task-specific coalition formation a first-class decision even though physical crews are pre-existing (Demiray et al., 2023).

Human-robot leader-follower routing introduces yet another mechanism. In the multi-vehicle routing problem considering human-robot interactions, an MGV leads a variable number of follower UGVs, and the optimization simultaneously decides how many follower UGVs each leader carries, where replenishment occurs, and how many MGV-UGV teams are deployed (Chirala et al., 2022). Team-size discretization is modeled by

$(r,q)$1

with HRI cost

$(r,q)$2

so team composition is a route-dependent decision driven by supervisory burden (Chirala et al., 2022).

By contrast, stable-team-formation models outside routing focus on interpersonal preferences and coalition blocking. In that setting, the planner partitions agents into equal-sized teams and balances total utility against maximum uplift of any blocking coalition (Yekta et al., 2018). Although routing is absent, this literature supplies transferable coalition-formation machinery for TFRP when self-interested workers or riders may deviate.

4. Routing, scheduling, and uncertainty

Routing components in TFRP often depart substantially from classical VRP structure because route feasibility depends on team composition, precedence, communication, or risk.

In survivability-constrained multi-robot routing, a path $(r,q)$3 is a sequence of unique nodes, and survival is multiplicative over edges: $(r,q)$4 The chance constraint

$(r,q)$5

can be transformed into an additive budget

$(r,q)$6

which enables reduction to an orienteering subproblem (Jorgensen et al., 2016). This is a characteristic TFRP pattern: team-level objectives may be submodular and coupled, yet single-route feasibility can still be mapped to familiar shortest-path or resource-budget structures.

Motion constraints can radically alter the routing layer. In fixed-wing drone team orienteering, headings are discretized into a finite set $(r,q)$7, each target $(r,q)$8 becomes a set $(r,q)$9 of heading-state vertices, and edge costs $r$0 are shortest Dubins path lengths between heading states (Sundar et al., 2019). The master problem is then a path-based set-packing model

$r$1

subject to

$r$2

This illustrates how TFRP routing may operate on a state-expanded graph rather than on physical locations alone (Sundar et al., 2019).

Precedence and multiperiod structure are central in workforce settings. In the MWSRPDT, the route graph is extended to customer-task vertices $r$3, and tasks of the same customer are connected by zero-travel arcs (Pereira et al., 2020). Task coverage is enforced by

$r$4

while precedence across days and teams is captured by a start-time inequality comparing absolute start time of successor $r$5 to completion time of predecessor $r$6 (Pereira et al., 2020). This yields a genuine team-assignment–routing–scheduling model with repeated visits and cross-team temporal coupling.

Uncertainty enters TFRP in several distinct ways. TSO uses edge survival probabilities and chance constraints on route success (Jorgensen et al., 2016). Platoon formation uses deterministic travel times but emphasizes route overlap and departure-time coordination, with platoons emerging when two vehicles traverse the same edge at the same time; the optimization minimizes

$r$7

over routes and departure delays (Sokolov et al., 2017). The airport baggage-handling formulation models stochastic travel times explicitly through finite-support distributions, exact finish-time propagation, per-task chance constraints

$r$8

and bounded worst-case lateness

$r$9

(Hagn et al., 2024). This yields a route-feasible-column structure under uncertainty rather than a recourse model.

A plausible implication is that uncertainty modeling in TFRP tends to remain tractable when uncertainty is route-internal and can be pushed into column evaluation or single-route feasibility checks. Once uncertainty couples routes directly, substantially richer stochastic or dynamic formulations are likely required.

5. Algorithmic paradigms

TFRP has no dominant universal algorithmic template, but several paradigms recur.

A major line exploits submodularity and approximate greedy selection. In TSO, the team objective

$q$0

is normalized, nonnegative, monotone, and submodular (Jorgensen et al., 2016). The marginal gain of adding route $q$1 to an existing team is

$q$2

and a linearized orienteering surrogate yields an $q$3 approximate greedy step. The resulting guarantee is

$q$4

This is one of the clearest theoretical results in the area because it links route-level approximation to global team-level approximation under a submodular objective (Jorgensen et al., 2016).

A second paradigm is branch-and-price / column generation over route columns. This is central in Dubins team orienteering (Sundar et al., 2019) and airport baggage-handling TFRP (Hagn et al., 2024). In D-DTOP, the master is a set-packing formulation over route columns, while pricing is a resource-constrained elementary shortest path problem solved by bounded bidirectional labeling with decremental state space relaxation (Sundar et al., 2019). In baggage handling, pricing is an ESPPRC over stochastic-feasible routes, solved by a labeling algorithm with stochastic finish-time resources and dominance rules (Hagn et al., 2024). The recent partial-column-generation work adds a GNN-based selector that predicts which of multiple pricing problems are likely to yield negative reduced-cost columns, retaining exactness by solving all remaining pricing problems when no improving column is found (Dall'Olio et al., 18 Sep 2025). This suggests that TFRP is particularly amenable to ML-assisted exact methods when pricing decomposes by team profile.

A third paradigm is large-neighborhood or metaheuristic search. For vehicle-routing-with-profits formulations closely related to TFRP, an exhaustive-route representation combined with an RCSP-based Select procedure implicitly optimizes which customers are active on each route (Vidal et al., 2014). This gives very large neighborhoods because one explicit route modification implicitly reoptimizes customer selection. In dynamic synchronized workforce routing, ALNS alternates destroy and repair operators over crew-task assignments and synchronized insertions, using irreducible compatible team combinations $q$5 inside repair heuristics (Demiray et al., 2023). In HRI-aware leader-follower routing, skewed variable neighborhood search perturbs routes and recomputes team compositions and replenishment assignments after each move (Chirala et al., 2022). These heuristics are motivated by the fact that local changes in team composition often have global timing and routing consequences, making ordinary VRP neighborhoods weak.

A fourth paradigm is game-theoretic or coalition-theoretic optimization, usually on the team-formation side. The rotating proposer mechanism implements a subgame perfect Nash equilibrium of a sequential proposer game for bounded-size teams (Low et al., 2022), while stable-and-efficient team formation uses a bi-level-to-single-level reformulation and branch-cut-and-price over coalition columns (Yekta et al., 2018). Although not routing models, these methods provide coalition-selection structures and stability criteria that could be layered onto TFRP.

6. Applications and empirical patterns

The application range of TFRP is unusually broad. Risk-aware robot routing targets disaster or war-zone aid delivery (Jorgensen et al., 2016). Fixed-wing drone team orienteering addresses routing under minimum-turn-radius constraints (Sundar et al., 2019). Multi-agent coalition routing is motivated by disaster response and firefighter mobilization, using London Fire Brigade records and up to 347,588 tasks in the benchmark generator (Capezzuto et al., 2021). Workforce scheduling and routing with dependent tasks models field-service organizations that send heterogeneous teams across customers over multiple days (Pereira et al., 2020). Dynamic synchronized workforce routing is aimed at on-demand home services (Demiray et al., 2023). Human-robot team routing with HRI penalties is motivated by manned-unmanned teaming in civilian and military missions (Chirala et al., 2022). Cooperative air-ground routing under communication constraints targets ISR missions with one ground vehicle and one UAV (Manyam et al., 2018). Platoon formation through route and departure-time coordination models centralized freight or connected-vehicle operations (Sokolov et al., 2017). Airport baggage handling has become a prominent benchmark domain for exact and ML-assisted branch-price algorithms (Hagn et al., 2024, Dall'Olio et al., 18 Sep 2025).

Several empirical regularities recur across these papers. First, integrated solutions materially outperform sequential or myopic baselines. In MARSC, the heuristic finds solutions up to 3.25 times better than Earliest Deadline First on instances with up to 150 agents and 3000 tasks (Capezzuto et al., 2021). In dynamic workforce routing, ALNS reduces total weighted throughput time by 15.97% on average versus the constructive heuristic on large dynamic instances (Demiray et al., 2023). In TSO, greedy routes are nearly optimal on a 19-node, 6-robot graph and scale to hundreds of nodes (Jorgensen et al., 2016). In baggage handling, the full Branch-Price-Cut-and-Switch approach solves 88.67% of feasible instances to optimality within 180 seconds, versus 68.67% for the basic variant (Hagn et al., 2024).

Second, resource-tight or uncertainty-rich instances magnify the value of integration. In HRI-aware routing, changing weights on travel, HRI, and team cost shifts the optimal balance between carried UGVs, replenishment, and number of deployed teams (Chirala et al., 2022). In baggage handling, stochastic modeling dominates best-case, median, and worst-case deterministic surrogates in service reliability and expected penalty, with the stochastic model achieving feasible solutions on all 600 stochastic-feasible instances considered, while best-case deterministic planning remains stochastic-feasible on only 25 of 728 deterministic-feasible cases (Hagn et al., 2024).

Third, inter-route reassignment often matters more than intra-route reordering. The HRI routing paper reports that inter-route neighborhoods such as POI-swap-inter and segment exchange dominate intra-route neighborhoods because moving tasks across teams changes optimal coalition sizes and replenishment patterns (Chirala et al., 2022). This suggests that in TFRP the combinatorial boundary between team allocation and route design is often where most improvement potential lies.

7. Limitations, controversies, and research directions

A recurring limitation is that many papers called “team formation and routing” do not perform endogenous team assembly from individuals. TSO, D-DTOP, cooperative air-ground routing, and many vehicle-based formulations assume a fixed team or fleet (Jorgensen et al., 2016, Sundar et al., 2019, Manyam et al., 2018). Even workforce papers frequently assume pre-existing crews and optimize only crew-task assignment plus routing (Pereira et al., 2020, Demiray et al., 2023). Thus, one common misconception is that TFRP uniformly includes personnel composition. Much of the literature instead studies route coordination for fixed teams or task-level coalitioning over existing crews.

Another limitation is that synchronization is often handled imperfectly or only heuristically. In the dynamic multi-skill workforce model, the narrative requires that multiple crews assigned to one task start simultaneously, but the printed MIP does not contain a clean explicit equality-of-start-times constraint, relying instead on shared completion-time variables and heuristic insertion logic (Demiray et al., 2023). This suggests that synchronization remains one of the more delicate modeling aspects of TFRP.

Scalability remains difficult for exact methods. Column generation helps, but pricing subproblems are often ESPPRCs with additional stochastic, temporal, or skill-based resources. The GNN-guided partial pricing strategy improves performance under tight time limits but degrades in longer runs because late-stage pricing problems become harder to classify and training data are skewed toward earlier iterations (Dall'Olio et al., 18 Sep 2025). This suggests that ML-assisted branch-price for TFRP is most promising in repeated operational environments with strict runtime limits, not necessarily in long exact certification runs.

A further unresolved issue is operational realism versus tractability. Stochastic baggage handling uses finite-support independent travel times and no recourse (Hagn et al., 2024). MARSC allows coalition members to begin work without synchronization, which suits cumulative-work tasks but not settings requiring simultaneous presence (Capezzuto et al., 2021). Social-network team formation relies on shortest-path communication costs without modeling actual communication flows or congestion (Addanki et al., 2020). These are not flaws so much as structural compromises, but they delimit transferability across domains.

Several directions emerge naturally from the current literature. One is richer integration of team composition, routing, and uncertainty in a single exact framework, rather than fixing one layer. Another is importing stability, preference, and coalition-blocking ideas from team-formation theory into route-based models (Yekta et al., 2018, Low et al., 2022). A third is extending route-column methods with learning-guided pricing, branching, or cut selection beyond airport operations (Dall'Olio et al., 18 Sep 2025). A fourth is better treatment of synchronization, communication, and adaptive replanning, especially in dynamic human-robot or workforce settings (Chirala et al., 2022, Demiray et al., 2023).

Taken together, these works indicate that TFRP is best understood as a unifying label for optimization problems in which the value or feasibility of a route depends on who travels together, and the value or feasibility of a team depends on where and when it travels. That reciprocity between coalition structure and route structure is the defining feature of the field.