Constraints and Scoring Rules

This document describes all constraints and scoring rules for the OptaPlanner solver.

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1. SCORE STRUCTURE

1.1 HardMediumSoftScore

OptaPlanner uses lexicographic comparison on 3 levels:

Score = (Hard, Medium, Soft)

Comparison:
  (0, 0, -1000) > (-1, 0, +999999)   // Hard dominates everything
  (0, 0, -1000) > (0, -1, +999999)   // Medium dominates Soft

Level	Role	Goal
HARD	Feasibility	Must = 0
MEDIUM	Coverage	Should = 0
SOFT	Quality	Maximize

1.2 Violation Degree Principle

Always specify the degree of violation to guide the solver:

// BAD: no gradient
if (violation) → -100h

// GOOD: gradient for solver
for each violation → -100h

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2. HARD CONSTRAINTS (Feasibility)

Hard score < 0 = INVALID solution

2.1 Complete List

ID	Constraint	Rule	Penalty
H1	Time conflict	1 staff = 1 shift max per period	-100h per conflict
H2	Skill eligibility	Staff must have the required skill	-100h per violation
H2b	Site eligibility	Staff must have the site in preferences	-100h per violation
H3	Surgical-Distant exclusion	Surgical + Distant site same day = forbidden	-100h per violation
H4	Florence Bron 2F Tuesday	Absolute prohibition	-100h
H5	Lucie Pratillo 2F/3F	Absolute prohibition	-100h
H6	Exact days (flexible)	Flexible staff = exactly days_per_week	-100h per day difference
H7	Absence	Staff cannot be assigned during absence	-100h per violation
H8	Closing continuity	1R/2F = same person morning AND afternoon	-100h per violation

2.2 Constraint Details

H1 - Time Conflict

A staff member can only be assigned to 1 shift per period.

Violation: Marie assigned to Ophtalmo AND Dermato Monday morning
Penalty: -100h

H2 - Skill Eligibility

Staff must have the skill in their preferences to be assigned.

Violation: Pierre assigned to Accueil Dermato but doesn't have this skill
Penalty: -100h

For Surgical Block: Staff must have a preference for the required skill (e.g., Instrumentiste, Circulante).

Violation: Marie assigned as Instrumentiste but doesn't have this skill in preferences
Penalty: -100h

Note: Skills are unified - same eligibility check for consultation and surgical skills.

H2b - Site Eligibility

Staff must have the site in preferences (P1, P2, P3 or P4) to be assigned.

Violation: Pierre assigned to Porrentruy but doesn't have this site in preferences
Penalty: -100h

Note: Staff without site preference for a location CANNOT be assigned there.

H3 - Surgical-Distant Site Exclusion

Forbidden combinations on the same day:

Morning	Afternoon	Forbidden
Surgical block	Porrentruy	✓
Surgical block	Vieille Ville	✓
Porrentruy	Surgical block	✓
Vieille Ville	Surgical block	✓

H4 & H5 - Individual Rules

Staff	ID	Prohibition
Florence Bron	1e5339aa-5e82-4295-b918-e15a580b3396	2F on Tuesday
Lucie Pratillo	5d3af9e3-674b-48d6-b54f-bd84c9eee670	2F and 3F always

H6 - Exact Days (Flexible Staff)

For has_flexible_schedule = true:

days_assigned MUST == days_per_week

Example:
  Marie: days_per_week = 4
  Assigned 3 days → -100h (1 day difference)
  Assigned 5 days → -100h (1 day difference)

H7 - Absence

Staff with absence can never be assigned during that slot.

Marie: absence Wednesday (full day)
Violation: Marie assigned Wednesday morning
Penalty: -100h

H8 - Closing Continuity

At a location with closing, if physicians present morning AND afternoon:

1R and 2F roles must be the SAME person all day

Example (VALID):
  Ophtalmo Monday morning: Marie (1R), Pierre (2F)
  Ophtalmo Monday PM: Marie (1R), Pierre (2F) ✓

Example (INVALID):
  Ophtalmo Monday morning: Marie (1R), Pierre (2F)
  Ophtalmo Monday PM: Anna (1R), Luc (2F) ✗ → -200h (2 violations)

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3. MEDIUM CONSTRAINTS (Coverage)

Medium score < 0 = unmet needs

3.1 Complete List

ID	Constraint	Rule	Penalty
M1	Missing skill	Each required skill must be covered	-1000m per skill
M2	Uncovered closing	Sites with closing missing 1R or 2F	-1000m per role

3.2 Justification for -1000m

Medium penalty must be greater than worst Soft accumulation:

Worst Soft accumulation ≈ 810:
  - P234 day 5+: -200
  - Closing tier 4: -500
  - Cumulative: -50
  - Site change: -20
  - Lost preference: -40

With -1000m:
  Solver ALWAYS prefers filling a shift (even with -810 soft)
  rather than leaving it empty (-1000m) and putting staff in Admin (+15 soft)

3.3 Examples

M1 - Missing Skill

Dermato Monday morning with 2 physicians:
  Need: 2 Aide Dermato + 2 Accueil Dermato = 4 staff
  Assigned: 2 Aide + 1 Accueil = 3 staff

  Violation: 1 Accueil Dermato missing
  Penalty: -1000m

M2 - Uncovered Closing

Ophtalmo Monday (physicians morning + PM):
  Need: 1R + 2F
  Assigned: 1R only

  Violation: 2F missing
  Penalty: -1000m

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4. SOFT CONSTRAINTS (Quality)

Soft score = solution quality

4.1 Preferences (3 Dimensions)

Take the MAX of 3 scores for each assignment.

Dimension	P1	P2	P3	P4
Skill	+100	+80	+60	-
Physician	+70	+50	-	-
Site	+40	+35	+30	+25

Assignment_Score = max(Skill_Score, Physician_Score, Site_Score)

Example:

Marie assigned to Ophtalmo La Vallée with Dr. Martin:
  - Skill Accueil Ophtalmo: P1 → +100
  - Site La Vallée: P1 → +40
  - Physician Dr. Martin: P2 → +50

Score = max(100, 40, 50) = +100 soft

4.2 Site Continuity

Situation	Score
Same site morning + afternoon	+20
Site change	-20
Admin involved (either side)	0

Marie: Ophtalmo morning + Ophtalmo PM → +20 soft
Pierre: Dermato morning + Porrentruy PM → -20 soft
Anna: Ophtalmo morning + Admin PM → 0 soft

4.3 Load Fairness

Quadratic formula to encourage balancing:

fairness_score -= Σ (load_r)²

Why quadratic?

Transfer 1 shift from Marie (5 shifts) to Pierre (2 shifts):
  Before: 5² + 2² = 29
  After: 4² + 3² = 25
  Improvement: +4 soft ✓

4.4 Distant Site Balancing (P234)

For staff whose site is P2/P3/P4:

Day # at distant site	Penalty
1st	0
2nd	-20
3rd	-50
4th	-100
5th+	-200

Marie (Porrentruy = P3):
  Day 1: 0
  Day 2: -20
  Day 3: -50
  Total if 3 days: -70 soft

4.5 Closing Role Balancing

Load score = days_1R × 10 + days_2F × 12

Score	Penalty
≤ 22	0
23-29	-30
30-31	-80
32-35	-150
> 35	-500

Only the highest tier applies.

Marie this week: 2 days 1R + 1 day 2F
Score = 2×10 + 1×12 = 32 → -150 soft

4.6 Admin Bonus

Staff with prefers_admin = true

Condition	Bonus
Admin shift up to admin_half_days_target	+15 per shift
Admin shift beyond	+5 per shift

Staff with prefers_admin = false

Decreasing score: +10, +9, +8, +7...

Pierre (prefers_admin = false), 3 admin shifts:
  Shift 1: +10
  Shift 2: +9
  Shift 3: +8
  Total: +27 soft

4.7 P234 + Closing Cumulative

If a staff member has simultaneously:

• Active P234 penalty (≥2 days at distant site)
• Active closing penalty (score > 22)

Additional penalty: -50 soft

4.8 Admin Preference for Closing Role (Half-day)

If a site with closing has physicians only morning OR afternoon:

Situation	Bonus
Staff 1R/2F in morning → Admin in afternoon	+30
Staff 1R/2F in afternoon → Admin in morning	+30

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5. SPECIAL RULES

5.1 Paul Jacquier and 3F Role

Staff	ID
Paul Jacquier	121dc7d9-99dc-46bd-9b6c-d240ac6dc6c8

Rule: If Paul Jacquier is present Thursday AND Friday at a location with closing, a 3F role is required.

5.2 Physician-Staff Bonus

Physician	Staff	Bonus
Dr. fda323f4 (fda323f4-3efd-4c78-8b63-7d660fcd7eea)	Sara Bortolon, Mirlinda Hasani	+50 soft

Staff	ID
Sara Bortolon	68e74e31-12a7-4fd3-836d-41e8abf57792
Mirlinda Hasani	324639fa-2e3d-4903-a143-323a17b0d988

5.3 Obstetrician Alone at Ophtalmo Site

If an Ophtalmo site has no standard physicians but has ≥1 obstetrician:

Demand = 1 Accueil Ophtalmo (instead of 0)

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6. SCORE SUMMARY

6.1 Hard Constraints (-100h each)

• H1: Time conflict
• H2: Skill eligibility
• H2b: Site eligibility
• H3: Surgical-Distant exclusion
• H4: Florence Bron 2F Tuesday
• H5: Lucie Pratillo 2F/3F
• H6: Exact days (flexible)
• H7: Absence
• H8: Closing continuity

6.2 Medium Constraints

Constraint	Penalty
Missing skill	-1000m
Missing closing role	-1000m

6.3 Soft Constraints - Bonuses

Element	Score
Skill P1	+100
Skill P2	+80
Skill P3	+60
Physician P1	+70
Physician P2	+50
Site P1	+40
Site P2	+35
Site P3	+30
Site P4	+25
Site continuity	+20
Admin (preferred)	+15
Admin (not preferred)	+10 decreasing
Admin if closing role half-day	+30
Dr. fda323f4 bonus	+50

6.4 Soft Constraints - Penalties

Element	Score
Site change	-20
P234 day 2	-20
P234 day 3	-50
P234 day 4	-100
P234 day 5+	-200
Closing tier 1 (23-29)	-30
Closing tier 2 (30-31)	-80
Closing tier 3 (32-35)	-150
Closing tier 4 (>35)	-500
P234 + closing cumulative	-50
Fairness	-Σ(load²)

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7. GLOBAL FORMULA

Score = HardMediumSoftScore(

   hard = Σ violations_H1_to_H8 × (-100),

   medium = Σ missing_skills × (-1000)
          + Σ missing_closing_roles × (-1000),

   soft = Σ max(skill_score, physician_score, site_score)  // Preferences
        + Σ site_continuity_bonus                           // +20 if same site
        + Σ admin_bonus                                     // +15 or decreasing
        + Σ closing_admin_bonus                             // +30 if half-day
        + Σ special_physician_bonus                         // +50 Dr. fda323f4
        - Σ site_change_penalties                           // -20
        - Σ P234_penalties                                  // -20 to -200
        - Σ closing_penalties                               // -30 to -500
        - Σ cumulative_penalties                            // -50
        - Σ (load_r)²                                       // Quadratic fairness
)

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OptaPlanner constraint specification document See also: 1_DOMAIN_MODEL.md, 2_NEEDS_CALCULATION.md, 4_OUTPUT.md