diff --git a/CLAUDE.md b/CLAUDE.md
index 72f613f..ee630de 100644
--- a/CLAUDE.md
+++ b/CLAUDE.md
@@ -235,7 +235,48 @@ Sémantique figée :
 
 ---
 
-## 4. Périmètre
+## 4. Solveur de suggestions (OR-Tools CP-SAT)
+
+Module isolé `backend/app/solver/` (mêmes conventions que `validation/` :
+`models.py` types purs, `engine.py` fonction pure `solve()`, `loader.py` seul
+point de contact avec la base). **Ne place jamais personne** : il calcule,
+pour chaque créneau encore sous son effectif idéal, une liste ordonnée de
+bénévoles candidats. La coordination affecte elle-même dans l'écran habituel
+(grille des besoins) ; l'appli fait simplement remonter ces candidats en tête
+de la colonne des choix quand on ouvre le détail d'un poste. Aucune
+affectation n'est jamais persistée par cet endpoint.
+
+- `POST /editions/{id}/solver/suggestions` (COORDINATION ou référent) :
+  recalcule à la demande (rien n'est mis en cache côté serveur) et renvoie
+  `{ suggestions: [{ shift_id, volunteer_ids }], shifts_considered,
+  volunteers_considered }`, `volunteer_ids` du meilleur au moins bon.
+- **Seule contrainte dure** : aucun chevauchement de créneaux pour un même
+  bénévole (règle `SHIFT_OVERLAP`) — à la fois contre les affectations déjà
+  décidées et entre deux créneaux nouvellement suggérés. L'effectif idéal est
+  un plafond dur (le solveur ne sur-staffe jamais).
+- Tout le reste est un terme de l'objectif (maximisation), pas une
+  contrainte — cohérent avec le moteur de validation, qui reste seul juge au
+  moment où la coordination confirme une affectation :
+  - un créneau encore sous son effectif **minimal** prime largement sur tout
+    le reste (le solveur doit presque toujours proposer quelqu'un pour un
+    trou urgent, quitte à ce que ce soit un pis-aller signalé ensuite par un
+    avertissement) ;
+  - bonus si le poste fait partie des vœux du bénévole
+    (`VolunteerPositionWish`) ;
+  - malus proportionnel aux minutes hors des fenêtres de disponibilité
+    déclarées (réutilise `validation.engine.uncovered_minutes`), au dépassement
+    du cumul de 8 h ce jour-là, et si le repos avec une affectation déjà
+    décidée serait `< 8 h 00` ;
+  - léger malus pour les bénévoles déjà bien chargés (répartition de la
+    charge).
+  - Simplification assumée : cumul de 8 h et repos ne sont vérifiés que
+    contre les affectations **déjà décidées**, pas entre deux suggestions du
+    même calcul — la validation finale à la confirmation reste seule juge de
+    ce cas limite.
+
+---
+
+## 5. Périmètre
 
 ### Premier incrément (en cours)
 
@@ -252,15 +293,16 @@ Sémantique figée :
    `[{ position, shifts: [{ shift, min_staff, ideal_staff, assigned }] }]`.
 6. Jeu de données de démonstration : 120 bénévoles, 15 postes, 4 jours,
    quelques trous d'effectif, 2–3 avertissements actifs.
+7. Solveur de suggestions OR-Tools CP-SAT (section 4) — en cours.
 
 ### Hors périmètre (le modèle doit juste pouvoir les accueillir sans refonte)
 
-Solveur OR-Tools · SMS · constructeur de formulaire · pointage sur site ·
+SMS · constructeur de formulaire · pointage sur site ·
 fonctions d'IA. *(L'envoi d'emails par SMTP est en place — voir § 2.)*
 
 ---
 
-## 5. Arborescence
+## 6. Arborescence
 
 ```
 .
@@ -286,12 +328,13 @@ fonctions d'IA. *(L'envoi d'emails par SMTP est en place — voir § 2.)*
 │   │   │                           #   health, auth, accounts, editions,
 │   │   │                           #   day_parts, imports, artists, volunteers,
 │   │   │                           #   availability, positions, shifts,
-│   │   │                           #   assignments, matrix, notifications
+│   │   │                           #   assignments, solver, matrix, notifications
 │   │   ├── auth/                   # mot de passe + lien magique + JWT + rôles
 │   │   ├── email/                  # SMTP (sender) + rendu des emails (templates)
 │   │   ├── importing/              # import CSV/Excel (parser, text, service)
 │   │   ├── models/                 # tables SQLModel
 │   │   ├── validation/             # moteur pur (models, engine) + loader (base)
+│   │   ├── solver/                 # suggestions OR-Tools (models, engine, loader)
 │   │   ├── bootstrap.py            # instance vierge : édition + 1er compte
 │   │   ├── seed.py                 # jeu de démonstration (python -m app.seed)
 │   │   ├── i18n/
@@ -306,7 +349,7 @@ fonctions d'IA. *(L'envoi d'emails par SMTP est en place — voir § 2.)*
 
 ---
 
-## 6. Commandes
+## 7. Commandes
 
 Aucune dépendance locale requise hors Docker.
 
@@ -326,7 +369,7 @@ Aucune dépendance locale requise hors Docker.
 
 ---
 
-## 7. Conventions
+## 8. Conventions
 
 - **Code, base, noms de fichiers en anglais.** Le français vit dans les
   fichiers de traduction et les commits.
@@ -347,7 +390,7 @@ Aucune dépendance locale requise hors Docker.
 
 ---
 
-## 8. Déploiement
+## 9. Déploiement
 
 - Dépôt GitHub. VPS avec Docker.
 - `.github/workflows/deploy.yml` : sur chaque push `main` → build de l'image
@@ -361,7 +404,7 @@ Aucune dépendance locale requise hors Docker.
 
 ---
 
-## 9. Journal des étapes
+## 10. Journal des étapes
 
 | Étape | Description                                            | État     |
 |-------|-------------------------------------------------------|----------|
@@ -379,7 +422,8 @@ Aucune dépendance locale requise hors Docker.
 | 12    | Créneaux types (`DayPart` CRUD) + génération auto des créneaux 0/0 à la création d'un poste ; case « à définir » / « sureffectif » sur la grille | à valider |
 | 13    | Bénévole : retrait taille de t-shirt / régime ; entité `Artist` (CRUD, par jour) + vœux des bénévoles (artistes, postes) | à valider |
 | 14    | Retrait des compétences (`Skill` et règle `MISSING_REQUIRED_SKILL`) ; disponibilités = fenêtres horaires libres par jour (`GET`/`PUT` availability), prises en compte par `OUTSIDE_AVAILABILITY` | à valider |
+| 15    | Solveur de suggestions OR-Tools CP-SAT (section 4) : `POST /editions/{id}/solver/suggestions`, candidats remontés en tête de liste dans la grille des besoins — aucune affectation automatique | à valider |
 
-**Reste hors périmètre** (modèle prêt à les accueillir) : solveur OR-Tools,
-SMS, constructeur de formulaire, pointage sur site, IA. Frontend :
-squelette + 6 écrans + connexion en place (voir `frontend/`).
+**Reste hors périmètre** (modèle prêt à les accueillir) : SMS, constructeur
+de formulaire, pointage sur site, IA. Frontend : squelette + 6 écrans +
+connexion en place (voir `frontend/`).
diff --git a/backend/app/api/schemas.py b/backend/app/api/schemas.py
index 1380d49..d3cbf21 100644
--- a/backend/app/api/schemas.py
+++ b/backend/app/api/schemas.py
@@ -264,6 +264,21 @@ class AssignmentValidateResult(ApiModel):
     violations: list[Violation] = Field(default_factory=list)
 
 
+# --------------------------------------------------------------------------- #
+# Solveur (suggestions, CP-SAT) — ne place jamais personne                     #
+# --------------------------------------------------------------------------- #
+class SolverSuggestion(ApiModel):
+    shift_id: uuid.UUID
+    # Bénévoles suggérés pour ce créneau, meilleur en tête.
+    volunteer_ids: list[uuid.UUID]
+
+
+class SolverRunResult(ApiModel):
+    suggestions: list[SolverSuggestion]
+    shifts_considered: int
+    volunteers_considered: int
+
+
 # --------------------------------------------------------------------------- #
 # Matrice poste × créneau                                                      #
 # --------------------------------------------------------------------------- #
diff --git a/backend/app/api/solver.py b/backend/app/api/solver.py
new file mode 100644
index 0000000..d6d1f5f
--- /dev/null
+++ b/backend/app/api/solver.py
@@ -0,0 +1,38 @@
+"""Suggestions du solveur (OR-Tools CP-SAT). Ne persiste rien : la
+coordination affecte elle-même, dans l'écran habituel, en tenant compte des
+bénévoles remontés en tête de liste."""
+
+import uuid
+
+from fastapi import APIRouter, Depends
+from sqlmodel import Session
+
+from app.api.deps import get_edition
+from app.api.schemas import SolverRunResult, SolverSuggestion
+from app.auth.deps import require_staff
+from app.db import get_session
+from app.models import Account, Edition
+from app.solver import build_solver_input, solve
+
+router = APIRouter(prefix="/editions/{edition_id}/solver", tags=["solver"])
+
+
+@router.post("/suggestions", response_model=SolverRunResult)
+def run_solver(
+    edition: Edition = Depends(get_edition),
+    _guard: Account = Depends(require_staff),
+    session: Session = Depends(get_session),
+) -> SolverRunResult:
+    data = build_solver_input(session=session, edition=edition)
+    solution = solve(data)
+    return SolverRunResult(
+        suggestions=[
+            SolverSuggestion(
+                shift_id=uuid.UUID(s.shift_id),
+                volunteer_ids=[uuid.UUID(v) for v in s.volunteer_ids],
+            )
+            for s in solution.suggestions
+        ],
+        shifts_considered=len(data.shifts),
+        volunteers_considered=len(data.volunteers),
+    )
diff --git a/backend/app/main.py b/backend/app/main.py
index 6b9aeca..1ddb22e 100644
--- a/backend/app/main.py
+++ b/backend/app/main.py
@@ -14,6 +14,7 @@ from app.api.matrix import router as matrix_router
 from app.api.notifications import router as notification_router
 from app.api.positions import router as position_router
 from app.api.shifts import router as shift_router
+from app.api.solver import router as solver_router
 from app.api.volunteers import router as volunteer_router
 from app.config import get_settings
 from app.logging_config import configure_logging
@@ -44,5 +45,6 @@ app.include_router(availability_router)
 app.include_router(position_router)
 app.include_router(shift_router)
 app.include_router(assignment_router)
+app.include_router(solver_router)
 app.include_router(matrix_router)
 app.include_router(notification_router)
diff --git a/backend/app/solver/__init__.py b/backend/app/solver/__init__.py
new file mode 100644
index 0000000..45d38de
--- /dev/null
+++ b/backend/app/solver/__init__.py
@@ -0,0 +1,22 @@
+"""Solveur de suggestions (OR-Tools CP-SAT) — voir `engine.py` pour le détail
+des règles. Ne place jamais personne : seule la coordination affecte."""
+
+from app.solver.engine import solve
+from app.solver.loader import build_solver_input
+from app.solver.models import (
+    ShiftSuggestion,
+    SolverInput,
+    SolverShift,
+    SolverSolution,
+    SolverVolunteer,
+)
+
+__all__ = [
+    "ShiftSuggestion",
+    "SolverInput",
+    "SolverShift",
+    "SolverSolution",
+    "SolverVolunteer",
+    "build_solver_input",
+    "solve",
+]
diff --git a/backend/app/solver/engine.py b/backend/app/solver/engine.py
new file mode 100644
index 0000000..8e3a295
--- /dev/null
+++ b/backend/app/solver/engine.py
@@ -0,0 +1,190 @@
+"""Solveur de suggestions (OR-Tools CP-SAT) — cœur du produit, second moteur.
+
+Ne place jamais personne : il propose, pour chaque créneau encore sous son
+effectif idéal, une liste ordonnée de bénévoles candidats. C'est la
+coordination qui affecte (dans l'app, via l'écran habituel — le solveur se
+contente de faire remonter ces candidats en tête de liste).
+
+Contrainte dure : aucun chevauchement de créneaux pour un même bénévole (règle
+`SHIFT_OVERLAP`, cf. `app.validation`). Tout le reste (disponibilité, cumul de
+8 h, repos, vœu de poste, équité de charge) est un terme de l'objectif, pas
+une contrainte — comme le moteur de validation, qui reste seul juge au moment
+où la coordination confirme une affectation.
+"""
+
+import datetime as dt
+
+from ortools.sat.python import cp_model
+
+from app.solver.models import (
+    ShiftSuggestion,
+    SolverInput,
+    SolverShift,
+    SolverSolution,
+    SolverVolunteer,
+)
+from app.validation.engine import uncovered_minutes
+from app.validation.models import DayPartWindow, ShiftInfo
+
+_EIGHT_HOURS_MIN = 8 * 60
+
+# Poids de l'objectif (unités arbitraires, cf. docstring de `_score`).
+# L'écart à un effectif minimal non atteint prime sur tout le reste : le
+# solveur doit toujours proposer quelqu'un pour un créneau sous-staffé, quitte
+# à ce que la disponibilité soit imparfaite (avertissement, pas un blocage —
+# la validation reste seule juge à la confirmation). Au-delà du minimum, un
+# candidat mal assorti peut légitimement ne pas être suggéré du tout.
+_URGENT_BASE = 1000  # créneau encore sous son effectif minimal
+_NORMAL_BASE = 20  # créneau entre effectif minimal et idéal
+_WISH_BONUS = 30
+_AVAIL_PENALTY_PER_HALF_HOUR = 5
+_DAILY_OVERAGE_PENALTY_PER_MIN = 2
+_REST_PENALTY = 60
+_FAIRNESS_PENALTY_PER_HOUR = 2
+
+
+def _overlaps(a: ShiftInfo, b: ShiftInfo) -> bool:
+    return a.starts_at < b.ends_at and b.starts_at < a.ends_at
+
+
+def _day_boundary(day_parts: tuple[DayPartWindow, ...]) -> dt.time:
+    if not day_parts:
+        return dt.time(0, 0)
+    return min(day_parts, key=lambda part: part.order).start_time
+
+
+def _day_key(moment: dt.datetime, boundary: dt.time) -> dt.date:
+    if moment.time() >= boundary:
+        return moment.date()
+    return moment.date() - dt.timedelta(days=1)
+
+
+def _daily_overage_minutes(
+    volunteer: SolverVolunteer, shift: SolverShift, boundary: dt.time
+) -> int:
+    """Minutes qui dépasseraient les 8 h de la journée du créneau, en ne
+    comptant que les affectations déjà décidées (pas les autres suggestions
+    du même calcul — ce cas limite reste sous la vigilance du moteur de
+    validation au moment de la confirmation)."""
+    key = _day_key(shift.starts_at, boundary)
+    total = shift.ends_at - shift.starts_at
+    for other in volunteer.existing_shifts:
+        if _day_key(other.starts_at, boundary) == key:
+            total += other.ends_at - other.starts_at
+    minutes = int(total.total_seconds() // 60)
+    return max(0, minutes - _EIGHT_HOURS_MIN)
+
+
+def _has_insufficient_rest(volunteer: SolverVolunteer, shift: SolverShift) -> bool:
+    candidate = shift.shift_info
+    for other in volunteer.existing_shifts:
+        if _overlaps(candidate, other):
+            continue
+        if other.ends_at <= candidate.starts_at:
+            gap = candidate.starts_at - other.ends_at
+        elif candidate.ends_at <= other.starts_at:
+            gap = other.starts_at - candidate.ends_at
+        else:
+            continue
+        if gap < dt.timedelta(minutes=_EIGHT_HOURS_MIN):
+            return True
+    return False
+
+
+def _score(
+    volunteer: SolverVolunteer,
+    shift: SolverShift,
+    day_boundary: dt.time,
+) -> int:
+    """Score d'affinité (bénévole, créneau) : plus haut = meilleur candidat.
+
+    Purement additif (aucune interaction entre deux affectations proposées),
+    ce qui garde le modèle CP-SAT linéaire simple. Cumul de 8 h et repos ne
+    sont vérifiés que contre les affectations déjà décidées, pas entre deux
+    suggestions du même calcul : la validation finale (à la confirmation)
+    reste seule juge en cas de cas limite entre deux suggestions.
+    """
+    score = _URGENT_BASE if shift.already_assigned < shift.min_staff else _NORMAL_BASE
+    if shift.position_id in volunteer.wished_position_ids:
+        score += _WISH_BONUS
+    missed = uncovered_minutes(shift.shift_info, volunteer.availability)
+    score -= (missed // 30) * _AVAIL_PENALTY_PER_HALF_HOUR
+    score -= _DAILY_OVERAGE_PENALTY_PER_MIN * _daily_overage_minutes(
+        volunteer, shift, day_boundary
+    )
+    if _has_insufficient_rest(volunteer, shift):
+        score -= _REST_PENALTY
+    score -= (_FAIRNESS_PENALTY_PER_HOUR * volunteer.existing_minutes) // 60
+    return score
+
+
+def solve(
+    data: SolverInput,
+    *,
+    time_limit_seconds: float = 8.0,
+    seed: int = 42,
+) -> SolverSolution:
+    """Calcule les suggestions. Fonction pure : ne touche jamais la base."""
+    boundary = _day_boundary(data.day_parts)
+
+    model = cp_model.CpModel()
+    variables: dict[tuple[int, int], cp_model.IntVar] = {}
+    scores: dict[tuple[int, int], int] = {}
+
+    for si, shift in enumerate(data.shifts):
+        gap = shift.ideal_staff - shift.already_assigned
+        if gap <= 0:
+            continue
+        for vi, volunteer in enumerate(data.volunteers):
+            if any(_overlaps(shift.shift_info, other) for other in volunteer.existing_shifts):
+                continue
+            key = (vi, si)
+            variables[key] = model.NewBoolVar(f"x_{vi}_{si}")
+            scores[key] = _score(volunteer, shift, boundary)
+
+    if not variables:
+        return SolverSolution()
+
+    # Effectif idéal comme plafond dur — le solveur ne sur-staffe jamais.
+    for si, shift in enumerate(data.shifts):
+        gap = shift.ideal_staff - shift.already_assigned
+        n_volunteers = len(data.volunteers)
+        shift_vars = [variables[vi, si] for vi in range(n_volunteers) if (vi, si) in variables]
+        if shift_vars and gap > 0:
+            model.Add(sum(shift_vars) <= gap)
+
+    # Aucun chevauchement entre deux créneaux nouvellement suggérés au même
+    # bénévole (règle `SHIFT_OVERLAP`, bloquante).
+    for vi in range(len(data.volunteers)):
+        my_shifts = [si for si in range(len(data.shifts)) if (vi, si) in variables]
+        for a in range(len(my_shifts)):
+            for b in range(a + 1, len(my_shifts)):
+                si_a, si_b = my_shifts[a], my_shifts[b]
+                if _overlaps(data.shifts[si_a].shift_info, data.shifts[si_b].shift_info):
+                    model.Add(variables[vi, si_a] + variables[vi, si_b] <= 1)
+
+    model.Maximize(sum(score * variables[key] for key, score in scores.items()))
+
+    solver = cp_model.CpSolver()
+    solver.parameters.max_time_in_seconds = time_limit_seconds
+    solver.parameters.num_search_workers = 1
+    solver.parameters.random_seed = seed
+    status = solver.Solve(model)
+
+    chosen: dict[int, list[int]] = {}
+    if status in (cp_model.OPTIMAL, cp_model.FEASIBLE):
+        for (vi, si), var in variables.items():
+            if solver.Value(var):
+                chosen.setdefault(si, []).append(vi)
+
+    suggestions: list[ShiftSuggestion] = []
+    for si, shift in enumerate(data.shifts):
+        picked = sorted(chosen.get(si, []), key=lambda vi: -scores[(vi, si)])
+        if picked:
+            suggestions.append(
+                ShiftSuggestion(
+                    shift_id=shift.id,
+                    volunteer_ids=tuple(data.volunteers[vi].id for vi in picked),
+                )
+            )
+    return SolverSolution(suggestions=tuple(suggestions))
diff --git a/backend/app/solver/loader.py b/backend/app/solver/loader.py
new file mode 100644
index 0000000..13569cd
--- /dev/null
+++ b/backend/app/solver/loader.py
@@ -0,0 +1,97 @@
+"""Construit un `SolverInput` depuis la base pour une édition. Couche de
+liaison : c'est le seul endroit du module `solver` qui connaît la base."""
+
+from collections import defaultdict
+
+from sqlmodel import Session, select
+
+from app.models import (
+    Assignment,
+    Availability,
+    DayPart,
+    Edition,
+    Shift,
+    Volunteer,
+    VolunteerPositionWish,
+)
+from app.solver.models import SolverInput, SolverShift, SolverVolunteer
+from app.validation.models import AvailabilityWindow, DayPartWindow, ShiftInfo
+
+
+def build_solver_input(*, session: Session, edition: Edition) -> SolverInput:
+    day_parts = list(
+        session.exec(select(DayPart).where(DayPart.edition_id == edition.id))
+    )
+
+    shifts = list(session.exec(select(Shift).where(Shift.edition_id == edition.id)))
+    assignments = list(
+        session.exec(select(Assignment).where(Assignment.edition_id == edition.id))
+    )
+    shifts_by_id = {s.id: s for s in shifts}
+
+    assigned_count: dict = defaultdict(int)
+    shifts_by_volunteer: dict = defaultdict(list)
+    for a in assignments:
+        assigned_count[a.shift_id] += 1
+        shift = shifts_by_id.get(a.shift_id)
+        if shift is not None:
+            shifts_by_volunteer[a.volunteer_id].append(shift)
+
+    solver_shifts = tuple(
+        SolverShift(
+            id=str(s.id),
+            position_id=str(s.position_id),
+            starts_at=s.starts_at,
+            ends_at=s.ends_at,
+            min_staff=s.min_staff,
+            ideal_staff=s.ideal_staff,
+            already_assigned=assigned_count.get(s.id, 0),
+        )
+        for s in shifts
+        if assigned_count.get(s.id, 0) < s.ideal_staff
+    )
+
+    availabilities: dict = defaultdict(list)
+    for a in session.exec(
+        select(Availability).where(Availability.edition_id == edition.id)
+    ):
+        availabilities[a.volunteer_id].append(
+            AvailabilityWindow(date=a.date, start_time=a.start_time, end_time=a.end_time)
+        )
+
+    wishes: dict = defaultdict(set)
+    for w in session.exec(
+        select(VolunteerPositionWish).join(
+            Volunteer, Volunteer.id == VolunteerPositionWish.volunteer_id
+        ).where(Volunteer.edition_id == edition.id)
+    ):
+        wishes[w.volunteer_id].add(str(w.position_id))
+
+    volunteers = list(
+        session.exec(select(Volunteer).where(Volunteer.edition_id == edition.id))
+    )
+    solver_volunteers = tuple(
+        SolverVolunteer(
+            id=str(v.id),
+            availability=tuple(availabilities.get(v.id, ())),
+            wished_position_ids=frozenset(wishes.get(v.id, ())),
+            existing_shifts=tuple(
+                ShiftInfo(id=str(s.id), starts_at=s.starts_at, ends_at=s.ends_at)
+                for s in shifts_by_volunteer.get(v.id, ())
+            ),
+            existing_minutes=sum(
+                int((s.ends_at - s.starts_at).total_seconds() // 60)
+                for s in shifts_by_volunteer.get(v.id, ())
+            ),
+        )
+        for v in volunteers
+    )
+
+    return SolverInput(
+        shifts=solver_shifts,
+        volunteers=solver_volunteers,
+        day_parts=tuple(
+            DayPartWindow(dp.code, dp.start_time, dp.end_time, dp.order)
+            for dp in day_parts
+        ),
+    )
diff --git a/backend/app/solver/models.py b/backend/app/solver/models.py
new file mode 100644
index 0000000..f0c4737
--- /dev/null
+++ b/backend/app/solver/models.py
@@ -0,0 +1,60 @@
+"""Types d'entrée/sortie du solveur — suggestions, pas d'affectation automatique.
+
+Le solveur ne connaît que ces structures simples (jamais les modèles
+SQLModel), comme le moteur de validation dont il réutilise les briques
+(`app.validation.models`, `app.validation.engine.uncovered_minutes`).
+"""
+
+import datetime as dt
+from dataclasses import dataclass, field
+
+from app.validation.models import AvailabilityWindow, DayPartWindow, ShiftInfo
+
+
+@dataclass(frozen=True)
+class SolverShift:
+    """Un créneau à compléter (`assigned < ideal_staff`)."""
+
+    id: str
+    position_id: str
+    starts_at: dt.datetime
+    ends_at: dt.datetime
+    min_staff: int
+    ideal_staff: int
+    already_assigned: int
+
+    @property
+    def shift_info(self) -> ShiftInfo:
+        return ShiftInfo(id=self.id, starts_at=self.starts_at, ends_at=self.ends_at)
+
+
+@dataclass(frozen=True)
+class SolverVolunteer:
+    id: str
+    availability: tuple[AvailabilityWindow, ...] = ()
+    wished_position_ids: frozenset[str] = frozenset()
+    # Créneaux déjà occupés (affectations existantes, décisions figées) :
+    # comptent pour chevauchement, cumul journalier, repos.
+    existing_shifts: tuple[ShiftInfo, ...] = ()
+    # Total déjà affecté sur l'édition (minutes), pour répartir la charge.
+    existing_minutes: int = 0
+
+
+@dataclass(frozen=True)
+class SolverInput:
+    shifts: tuple[SolverShift, ...] = field(default_factory=tuple)
+    volunteers: tuple[SolverVolunteer, ...] = field(default_factory=tuple)
+    day_parts: tuple[DayPartWindow, ...] = field(default_factory=tuple)
+
+
+@dataclass(frozen=True)
+class ShiftSuggestion:
+    """Bénévoles suggérés pour un créneau, meilleur en tête."""
+
+    shift_id: str
+    volunteer_ids: tuple[str, ...]
+
+
+@dataclass(frozen=True)
+class SolverSolution:
+    suggestions: tuple[ShiftSuggestion, ...] = field(default_factory=tuple)
diff --git a/backend/pyproject.toml b/backend/pyproject.toml
index 05107ad..7ebb6ee 100644
--- a/backend/pyproject.toml
+++ b/backend/pyproject.toml
@@ -14,6 +14,7 @@ dependencies = [
     "openpyxl>=3.1",
     "pyjwt>=2.9",
     "bcrypt>=4.1",
+    "ortools>=9.11",
 ]
 
 [dependency-groups]
diff --git a/backend/tests/test_api_solver.py b/backend/tests/test_api_solver.py
new file mode 100644
index 0000000..b61d918
--- /dev/null
+++ b/backend/tests/test_api_solver.py
@@ -0,0 +1,68 @@
+import uuid
+
+from app.models import Role
+from tests.factories import dt_at, make_position, make_shift, make_volunteer
+
+
+def _url(edition, suffix=""):
+    return f"/editions/{edition.id}/solver{suffix}"
+
+
+def test_suggests_a_free_volunteer_for_an_understaffed_shift(client, edition, session):
+    position = make_position(session, edition)
+    shift = make_shift(
+        session, edition, position,
+        start=dt_at(10, 14), end=dt_at(10, 18), min_staff=1, ideal_staff=1,
+    )
+    volunteer = make_volunteer(session, edition, email="v@ex.fr")
+
+    resp = client.post(_url(edition, "/suggestions"))
+    assert resp.status_code == 200
+    body = resp.json()
+    assert body["shifts_considered"] == 1
+    assert body["volunteers_considered"] == 1
+    suggestion = next(s for s in body["suggestions"] if s["shift_id"] == str(shift.id))
+    assert suggestion["volunteer_ids"] == [str(volunteer.id)]
+
+
+def test_fully_staffed_shift_has_no_suggestion(client, edition, session):
+    from app.models import Assignment
+
+    position = make_position(session, edition)
+    shift = make_shift(
+        session, edition, position,
+        start=dt_at(10, 14), end=dt_at(10, 18), min_staff=1, ideal_staff=1,
+    )
+    volunteer = make_volunteer(session, edition, email="v@ex.fr")
+    session.add(
+        Assignment(edition_id=edition.id, volunteer_id=volunteer.id, shift_id=shift.id)
+    )
+    session.commit()
+
+    resp = client.post(_url(edition, "/suggestions"))
+    assert resp.status_code == 200
+    shift_ids = {s["shift_id"] for s in resp.json()["suggestions"]}
+    assert str(shift.id) not in shift_ids
+
+
+def test_unknown_edition_is_404(client):
+    assert client.post(f"/editions/{uuid.uuid4()}/solver/suggestions").status_code == 404
+
+
+def test_volunteer_role_forbidden(edition, session, make_account, as_account):
+    account = make_account(Role.VOLUNTEER, email="v@e.fr")
+    api = as_account(account)
+    assert api.post(_url(edition, "/suggestions")).status_code == 403
+
+
+def test_does_not_persist_any_assignment(client, edition, session):
+    from sqlmodel import select
+
+    from app.models import Assignment
+
+    position = make_position(session, edition)
+    make_shift(session, edition, position, start=dt_at(10, 14), end=dt_at(10, 18))
+    make_volunteer(session, edition, email="v@ex.fr")
+
+    client.post(_url(edition, "/suggestions"))
+    assert session.exec(select(Assignment)).all() == []
diff --git a/backend/tests/test_solver_engine.py b/backend/tests/test_solver_engine.py
new file mode 100644
index 0000000..d43c1a9
--- /dev/null
+++ b/backend/tests/test_solver_engine.py
@@ -0,0 +1,148 @@
+"""Tests du solveur (suggestions, jamais d'affectation automatique)."""
+
+import datetime as dt
+
+from app.solver.engine import solve
+from app.solver.models import SolverInput, SolverShift, SolverVolunteer
+from app.validation.models import AvailabilityWindow, ShiftInfo
+
+
+def _dt(day: int, hour: int, minute: int = 0) -> dt.datetime:
+    return dt.datetime(2026, 7, day, hour, minute)
+
+
+def _shift(
+    sid: str = "s1",
+    *,
+    position_id: str = "p1",
+    start: dt.datetime | None = None,
+    end: dt.datetime | None = None,
+    min_staff=1,
+    ideal_staff=1,
+    already_assigned=0,
+) -> SolverShift:
+    return SolverShift(
+        id=sid,
+        position_id=position_id,
+        starts_at=start or _dt(10, 14),
+        ends_at=end or _dt(10, 18),
+        min_staff=min_staff,
+        ideal_staff=ideal_staff,
+        already_assigned=already_assigned,
+    )
+
+
+def _volunteer(
+    vid: str,
+    *,
+    availability=(),
+    wished_position_ids=frozenset(),
+    existing_shifts=(),
+    existing_minutes=0,
+) -> SolverVolunteer:
+    return SolverVolunteer(
+        id=vid,
+        availability=tuple(availability),
+        wished_position_ids=frozenset(wished_position_ids),
+        existing_shifts=tuple(existing_shifts),
+        existing_minutes=existing_minutes,
+    )
+
+
+def _full_day(day: int) -> AvailabilityWindow:
+    return AvailabilityWindow(dt.date(2026, 7, day), dt.time(6, 0), dt.time(4, 0))
+
+
+def _by_shift(solution, shift_id: str) -> tuple[str, ...]:
+    for s in solution.suggestions:
+        if s.shift_id == shift_id:
+            return s.volunteer_ids
+    return ()
+
+
+def test_no_variables_returns_empty_solution():
+    data = SolverInput(shifts=(), volunteers=())
+    assert solve(data).suggestions == ()
+
+
+def test_fully_staffed_shift_gets_no_suggestion():
+    shift = _shift(ideal_staff=1, already_assigned=1)
+    volunteer = _volunteer("v1", availability=[_full_day(10)])
+    solution = solve(SolverInput(shifts=(shift,), volunteers=(volunteer,)))
+    assert solution.suggestions == ()
+
+
+def test_picks_the_only_free_volunteer_over_a_busy_one():
+    shift = _shift()
+    busy = _volunteer(
+        "busy",
+        availability=[_full_day(10)],
+        existing_shifts=[ShiftInfo(id="e", starts_at=_dt(10, 15), ends_at=_dt(10, 19))],
+    )
+    free = _volunteer("free", availability=[_full_day(10)])
+    solution = solve(SolverInput(shifts=(shift,), volunteers=(busy, free)))
+    assert _by_shift(solution, "s1") == ("free",)
+
+
+def test_does_not_exceed_ideal_staff_cap():
+    shift = _shift(ideal_staff=2, already_assigned=1)  # il ne manque qu'une place
+    a = _volunteer("a", availability=[_full_day(10)])
+    b = _volunteer("b", availability=[_full_day(10)])
+    solution = solve(SolverInput(shifts=(shift,), volunteers=(a, b)))
+    assert len(_by_shift(solution, "s1")) == 1
+
+
+def test_prefers_volunteer_with_matching_position_wish():
+    shift = _shift(position_id="regie")
+    plain = _volunteer("plain", availability=[_full_day(10)])
+    wisher = _volunteer(
+        "wisher", availability=[_full_day(10)], wished_position_ids={"regie"}
+    )
+    solution = solve(SolverInput(shifts=(shift,), volunteers=(plain, wisher)))
+    assert _by_shift(solution, "s1") == ("wisher",)
+
+
+def test_prefers_fully_available_volunteer_over_partially_available():
+    shift = _shift(start=_dt(10, 14), end=_dt(10, 18))
+    full = _volunteer("full", availability=[_full_day(10)])
+    partial = _volunteer(
+        "partial",
+        availability=[AvailabilityWindow(dt.date(2026, 7, 10), dt.time(14, 0), dt.time(16, 0))],
+    )
+    solution = solve(SolverInput(shifts=(shift,), volunteers=(full, partial)))
+    assert _by_shift(solution, "s1") == ("full",)
+
+
+def test_ranks_both_candidates_when_two_slots_are_open():
+    shift = _shift(ideal_staff=2)
+    full = _volunteer("full", availability=[_full_day(10)])
+    partial = _volunteer(
+        "partial",
+        availability=[AvailabilityWindow(dt.date(2026, 7, 10), dt.time(14, 0), dt.time(16, 0))],
+    )
+    solution = solve(SolverInput(shifts=(shift,), volunteers=(full, partial)))
+    assert _by_shift(solution, "s1") == ("full", "partial")
+
+
+def test_never_double_books_a_volunteer_across_two_new_suggestions():
+    # Deux créneaux qui se chevauchent, un seul bénévole disponible pour les
+    # deux : le solveur ne le propose qu'une fois.
+    shift_a = _shift("a", start=_dt(10, 14), end=_dt(10, 18))
+    shift_b = _shift("b", start=_dt(10, 16), end=_dt(10, 20))
+    only = _volunteer("only", availability=[_full_day(10)])
+    solution = solve(SolverInput(shifts=(shift_a, shift_b), volunteers=(only,)))
+    picked_a = _by_shift(solution, "a")
+    picked_b = _by_shift(solution, "b")
+    assert len(picked_a) + len(picked_b) == 1
+
+
+def test_avoids_volunteer_who_would_exceed_eight_hours_that_day():
+    shift = _shift(start=_dt(10, 14), end=_dt(10, 18))  # 4 h
+    tired = _volunteer(
+        "tired",
+        availability=[_full_day(10)],
+        existing_shifts=[ShiftInfo(id="e", starts_at=_dt(10, 6), ends_at=_dt(10, 12))],  # 6 h déjà
+    )
+    fresh = _volunteer("fresh", availability=[_full_day(10)])
+    solution = solve(SolverInput(shifts=(shift,), volunteers=(tired, fresh)))
+    assert _by_shift(solution, "s1") == ("fresh",)
diff --git a/backend/uv.lock b/backend/uv.lock
index 64e3a4d..214ed75 100644
--- a/backend/uv.lock
+++ b/backend/uv.lock
@@ -1,5 +1,19 @@
 version = 1
 requires-python = "==3.12.*"
+resolution-markers = [
+    "sys_platform == 'win32'",
+    "sys_platform == 'emscripten'",
+    "sys_platform != 'emscripten' and sys_platform != 'win32'",
+]
+
+[[package]]
+name = "absl-py"
+version = "2.5.0"
+source = { registry = "https://pypi.org/simple" }
+sdist = { url = "https://files.pythonhosted.org/packages/d0/4f/d79676ab82f2e42fc3611618139f13a9c4c31d0cff4b486982047679a802/absl_py-2.5.0.tar.gz", hash = "sha256:0c996f25c0490700fadabe6351630f6111534fa0ae252cc6d2014ea3b141135f", size = 118119 }
+wheels = [
+    { url = "https://files.pythonhosted.org/packages/58/0a/a10b45aab35b175aded078a462dc8d0c698f5b13946e7cb0869097b78bb6/absl_py-2.5.0-py3-none-any.whl", hash = "sha256:0f17b89f2a4eaaedc4f28c622998aa690564b3012a396a4ffad0821007fe03ba", size = 137410 },
+]
 
 [[package]]
 name = "alembic"
@@ -93,6 +107,7 @@ dependencies = [
     { name = "bcrypt" },
     { name = "fastapi" },
     { name = "openpyxl" },
+    { name = "ortools" },
     { name = "psycopg", extra = ["binary"] },
     { name = "pydantic-settings" },
     { name = "pyjwt" },
@@ -115,6 +130,7 @@ requires-dist = [
     { name = "bcrypt", specifier = ">=4.1" },
     { name = "fastapi", specifier = ">=0.115" },
     { name = "openpyxl", specifier = ">=3.1" },
+    { name = "ortools", specifier = ">=9.11" },
     { name = "psycopg", extras = ["binary"], specifier = ">=3.2" },
     { name = "pydantic-settings", specifier = ">=2.6" },
     { name = "pyjwt", specifier = ">=2.9" },
@@ -286,6 +302,15 @@ wheels = [
     { url = "https://files.pythonhosted.org/packages/57/b0/0e52c878c53f245edd3a11020f20979b3f490f245af532c7cae3027754b5/idna-3.19-py3-none-any.whl", hash = "sha256:815e7be7a7806d54abb586dc943addc79e8b2ee16915059658cbeff4b1b43bf4", size = 68550 },
 ]
 
+[[package]]
+name = "immutabledict"
+version = "4.3.1"
+source = { registry = "https://pypi.org/simple" }
+sdist = { url = "https://files.pythonhosted.org/packages/1d/e6/718471048fea0366c3e3d1df3acfd914ca66d571cdffcf6d37bbcd725708/immutabledict-4.3.1.tar.gz", hash = "sha256:f844a669106cfdc73f47b1a9da003782fb17dc955a54c80972e0d93d1c63c514", size = 7806 }
+wheels = [
+    { url = "https://files.pythonhosted.org/packages/a3/ce/f9018bf69ae91b273b6391a095e7c93fa5e1617f25b6ba81ad4b20c9df10/immutabledict-4.3.1-py3-none-any.whl", hash = "sha256:c9facdc0ff30fdb8e35bd16532026cac472a549e182c94fa201b51b25e4bf7bf", size = 5000 },
+]
+
 [[package]]
 name = "iniconfig"
 version = "2.3.0"
@@ -326,6 +351,25 @@ wheels = [
     { url = "https://files.pythonhosted.org/packages/e5/f1/216fc1bbfd74011693a4fd837e7026152e89c4bcf3e77b6692fba9923123/markupsafe-3.0.3-cp312-cp312-win_arm64.whl", hash = "sha256:35add3b638a5d900e807944a078b51922212fb3dedb01633a8defc4b01a3c85f", size = 13906 },
 ]
 
+[[package]]
+name = "numpy"
+version = "2.5.3"
+source = { registry = "https://pypi.org/simple" }
+sdist = { url = "https://files.pythonhosted.org/packages/13/01/11703282db468b85f6f7b8c7f22d058de5970d5c7e60a3a8aaa313c3de36/numpy-2.5.3.tar.gz", hash = "sha256:df2d5874ff183595a4ba404edd04f6bd9b5505c1d7708573f6a6c17489a67563", size = 20791231 }
+wheels = [
+    { url = "https://files.pythonhosted.org/packages/d6/50/8fdbb16af64895706a45f06a4068e29db732ec180f3c1375f14123359138/numpy-2.5.3-cp312-cp312-macosx_10_13_x86_64.whl", hash = "sha256:cb189f09db39283b26bfd061ec16189e14f71c6755207f72a0f7540867afe5b9", size = 16994982 },
+    { url = "https://files.pythonhosted.org/packages/60/39/789131c1188c078dcb3a1692e72e1e050c68b88ffe72c9ccaac9bcd7a9cd/numpy-2.5.3-cp312-cp312-macosx_11_0_arm64.whl", hash = "sha256:f59a878c33d6b88122d80d239bb3b845d58708750b0cb06a09aebb9b18ec696c", size = 12009327 },
+    { url = "https://files.pythonhosted.org/packages/9c/59/a312e95696e5f601914dd8b6dd844692ba61670807417e24b68e337b5c70/numpy-2.5.3-cp312-cp312-macosx_14_0_arm64.whl", hash = "sha256:a72f874bc9e10e4b8f80426fb49716d5141f64442a0c8418065093ec8017fbb0", size = 5445405 },
+    { url = "https://files.pythonhosted.org/packages/30/d0/5623a1707ed4fe16e3909fe3cf5ee3da004ae677ad23d83bbf3adf1a6faf/numpy-2.5.3-cp312-cp312-macosx_14_0_x86_64.whl", hash = "sha256:fc36dc566135b5eceec4cf89758fcb719266a019ef07dae1754ae7c9f617ef3e", size = 6783213 },
+    { url = "https://files.pythonhosted.org/packages/f1/32/84146fc020ad3c25f805f70ab60da46fe3c540a21369754a7e4369754b6f/numpy-2.5.3-cp312-cp312-manylinux_2_27_aarch64.manylinux_2_28_aarch64.whl", hash = "sha256:76c2c1e6bfa5c84adc6434dfbf013aa92096a7985221762c8f11fedfd20fff58", size = 15687872 },
+    { url = "https://files.pythonhosted.org/packages/65/af/aa78d1a88805456e212b65461354cd943197fb9acecc4c90fd12295123a3/numpy-2.5.3-cp312-cp312-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl", hash = "sha256:b7e18c623bb5c95acb3b3328861272816ba199fb531921c5d6d0b675f1fde9e3", size = 16717410 },
+    { url = "https://files.pythonhosted.org/packages/3b/24/faa79d865e69a97ba17473b23a1b74094b2259c03e820c70297293b9ea49/numpy-2.5.3-cp312-cp312-musllinux_1_2_aarch64.whl", hash = "sha256:4f8929ee6c96bfbd7b4ed2032e0c03af86fe1826740ab61ddabf9072d06e57ff", size = 17040975 },
+    { url = "https://files.pythonhosted.org/packages/62/4a/8877e629445a7176297dffcaf9c485faa96a95d81728a62521ad55bd4c0f/numpy-2.5.3-cp312-cp312-musllinux_1_2_x86_64.whl", hash = "sha256:b5d93cf48f687479941d12b69c873ad2cc76bbd487f0091c2200636497f34034", size = 18476479 },
+    { url = "https://files.pythonhosted.org/packages/c8/db/35e1c2d38b04cbd5b731f9d71495e055e813197669d22b612f11748d2ff9/numpy-2.5.3-cp312-cp312-win32.whl", hash = "sha256:bf63afbe037eb5d2fe87fbcc7778e61da53ebaf21d938a4515aa73b62532a5d4", size = 6133378 },
+    { url = "https://files.pythonhosted.org/packages/3c/a1/accf6d4f0c80c5d9ba9735d6b1550e444180599f34dec69ca01360f717ad/numpy-2.5.3-cp312-cp312-win_amd64.whl", hash = "sha256:0a59a421a32580a009e8a1751345bf829631b990dc1794b80514ab722b435def", size = 12567828 },
+    { url = "https://files.pythonhosted.org/packages/22/43/1764aff32e4652526ae2f71fa8b3efd8d25c8a3d6926914454e47138ed1e/numpy-2.5.3-cp312-cp312-win_arm64.whl", hash = "sha256:ccb32e0525d29e8b0572eb84c9a57af0e7a4e615726927506f55063c62414034", size = 10485432 },
+]
+
 [[package]]
 name = "openpyxl"
 version = "3.1.5"
@@ -338,6 +382,26 @@ wheels = [
     { url = "https://files.pythonhosted.org/packages/c0/da/977ded879c29cbd04de313843e76868e6e13408a94ed6b987245dc7c8506/openpyxl-3.1.5-py2.py3-none-any.whl", hash = "sha256:5282c12b107bffeef825f4617dc029afaf41d0ea60823bbb665ef3079dc79de2", size = 250910 },
 ]
 
+[[package]]
+name = "ortools"
+version = "9.15.6755"
+source = { registry = "https://pypi.org/simple" }
+dependencies = [
+    { name = "absl-py" },
+    { name = "immutabledict" },
+    { name = "numpy" },
+    { name = "pandas" },
+    { name = "protobuf" },
+    { name = "typing-extensions" },
+]
+wheels = [
+    { url = "https://files.pythonhosted.org/packages/6a/fc/9fa53f1a13710e6183df4d00fe4988c79a55b501e282645d49f1e250437f/ortools-9.15.6755-cp312-cp312-macosx_10_15_x86_64.whl", hash = "sha256:ae1c6e1fd844b4d756b22eb6c0ed574ea4342ee206d807c4f903039e748228fa", size = 23926322 },
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