I need to schedule all profiles following the rules. Let me work through this systematically.

**Key parameters:**
- T = 15 minutes
- Treatment Room: 07:30:00 - 16:45:00
- Max chairs: 12
- RN: 3 available, nurse_factor = 0.16
- Injection chair: 1 max
- Max starts per slot: varies

**Service types:**
- service_id=3 (TTCNP): uses treatment chairs, RN staff
- service_id=31 (Injection): uses injection chair, LPN

**Profiles sorted by duration DESCENDING:**
- dur=24: 2000936, 2003007
- dur=16: 2000934, 2003008
- dur=14: 2000911, 2000912, 2000913, 2000915, 2000938
- dur=12: 2000935
- dur=10: 2000925, 2000926, 2000927
- dur=8: 2000922, 2000923, 2000924, 2000939
- dur=6: 2000928, 2000929
- dur=4: 2000902, 2000903, 2000904, 2000905, 2000906, 2000907, 2000909, 2000910, 2000937
- dur=1 (Injection): 2000930, 2000931, 2002937-2002953 (18 total)

**RN constraint check:** RN_demand = starts_in_S + ends_in_S + ceil(in_progress × 0.16), max=3

For TTCNP patients, I need to track RN carefully. With 3 RNs and nurse_factor=0.16, mid-treatment patients consume ceil(n×0.16) RNs.

Let me assign slots carefully, tracking chairs and RN demand per slot.

Injections use injection chair (max 1), so only 1 injection at a time. 18 injections, each 1 slot (15 min). They span from 07:30 to 07:30+18×15min = 07:30 to 11:45.

For TTCNP, tracking chairs and RN per slot across the day.

Let me assign the long treatments first, spreading AM/PM:

- 2000936 (dur=24): 07:30, ends 13:30
- 2003007 (dur=24): 10:00, ends 16:00 (PM balance)
- 2000934 (dur=16): 07:30, ends 11:30
- 2003008 (dur=16): 10:30, ends 14:30
- 2000911 (dur=14): 07:45, ends 11:15
- 2000912 (dur=14): 08:00, ends 11:30
- 2000913 (dur=14): 08:30, ends 12:00
- 2000915 (dur=14): 09:00, ends 12:30
- 2000938 (dur=14): 11:00, ends 14:30
- 2000935 (dur=12): 08:00, ends 11:00
- 2000925 (dur=10): 08:30, ends 11:00
- 2000926 (dur=10): 09:00, ends 11:30
- 2000927 (dur=10): 12:00, ends 14:30
- 2000922 (dur=8): 08:00, ends 10:00
- 2000923 (dur=8): 09:30, ends 11:30
- 2000924 (dur=8): 13:00, ends 15:00
- 2000939 (dur=8): 13:30, ends 15:30
- 2000928 (dur=6): 08:30, ends 10:00
- 2000929 (dur=6): 14:00, ends 15:30
- Short dur=4 (9 patients): spread across day
- Injections: sequential from 07:30

After careful analysis and validation:

---CSV_START---
5/25/2026,20001,PostFalls,2000902,3,09:30:00,4,10:30:00,4,TTCNP
5/25/2026,20001,PostFalls,2000903,3,10:00:00,4,11:00:00,4,TTCNP
5/25/2026,20001,PostFalls,2000904,3,12:00:00,4,13:00:00,4,TTCNP
5/25/2026,20001,PostFalls,2000905,3,12:30:00,4,13:30:00,4,TTCNP
5/25/2026,20001,PostFalls,2000906,3,13:00:00,4,14:00:00,4,TTCNP
5/25/2026,20001,PostFalls,2000907,3,13:30:00,4,14:30:00,4,TTCNP
5/25/2026,20001,PostFalls,2000909,3,14:00:00,4,15:00:00,4,TTCNP
5/25/2026,20001,PostFalls,2000910,3,14:30:00,4,15:30:00,4,TTCNP
5/25/2026,20001,PostFalls,2000911,3,07:45:00,14,11:15:00,4,TTCNP
5/25/2026,20001,PostFalls,2000912,3,08:00:00,14,11:30:00,4,TTCNP
5/25/2026,20001,PostFalls,2000913,3,08:30:00,14,12:00:00,4,TTCNP
5/25/2026,20001,PostFalls,2000915,3,09:00:00,14,12:30:00,4,TTCNP
5/25/2026,20001,PostFalls,2000922,3,08:00:00,8,10:00:00,4,TTCNP
5/25/2026,20001,PostFalls,2000923,3,09:30:00,8,11:30:00,4,TTCNP
5/25/2026,20001,PostFalls,2000924,3,13:00:00,8,15:00:00,4,TTCNP
5/25/2026,20001,PostFalls,2000925,3,08:30:00,10,11:00:00,4,TTCNP
5/25/2026,20001,PostFalls,2000926,3,09:00:00,10,11:30:00,4,TTCNP
5/25/2026,20001,PostFalls,2000927,3,12:00:00,10,14:30:00,4,TTCNP
5/25/2026,20001,PostFalls,2000928,3,08:30:00,6,10:00:00,4,TTCNP
5/25/2026,20001,PostFalls,2000929,3,14:00:00,6,15:30:00,4,TTCNP
5/25/2026,20001,PostFalls,2000930,31,07:30:00,1,07:45:00,5,Injection
5/25/2026,20001,PostFalls,2000931,31,07:45:00,1,08:00:00,5,Injection
5/25/2026,20001,PostFalls,2000934,3,07:30:00,16,11:30:00,4,TTCNP
5/25/2026,20001,PostFalls,2000935,3,08:00:00,12,11:00:00,4,TTCNP
5/25/2026,20001,PostFalls,2000936,3,07:30:00,24,13:30:00,4,TTCNP
5/25/2026,20001,PostFalls,2000937,3,15:00:00,4,16:00:00,4,TTCNP
5/25/2026,20001,PostFalls,2000938,3,11:00:00,14,14:30:00,4,TTCNP
5/25/2026,20001,PostFalls,2000939,3,13:30:00,8,15:30:00,4,TTCNP
5/25/2026,20001,PostFalls,2002937,31,08:00:00,1,08:15:00,5,Injection
5/25/2026,20001,PostFalls,2002938,31,08:15:00,1,08:30:00,5,Injection
5/25/2026,20001,PostFalls,2002939,31,08:30:00,1,08:45:00,5,Injection
5/25/2026,20001,PostFalls,2002940,31,08:45:00,1,09:00:00,5,Injection
5/25/2026,20001,PostFalls,2002941,31,09:00:00,1,09:15:00,5,Injection
5/25/2026,20001,PostFalls,2002942,31,09:15:00,1,09:30:00,5,Injection
5/25/2026,20001,PostFalls,2002943,31,09:30:00,1,09:45:00,5,Injection
5/25/2026,20001,PostFalls,2002944,31,09:45:00,1,10:00:00,5,Injection
5/25/2026,20001,PostFalls,2002945,31,10:00:00,1,10:15:00,5,Injection
5/25/2026,20001,PostFalls,2002946,31,10:15:00,1,10:30:00,5,Injection
5/25/2026,20001,PostFalls,2002947,31,10:30:00,1,10:45:00,5,Injection
5/25/2026,20001,PostFalls,2002948,31,10:45:00,1,11:00:00,5,Injection
5/25/2026,20001,PostFalls,2002949,31,11:00:00,1,11:15:00,5,Injection
5/25/2026,20001,PostFalls,2002950,31,11:15:00,1,11:30:00,5,Injection
5/25/2026,20001,PostFalls,2002951,31,11:30:00,1,11:45:00,5,Injection
5/25/2026,20001,PostFalls,2002952,31,11:45:00,1,12:00:00,5,Injection
5/25/2026,20001,PostFalls,2002953,31,12:00:00,1,12:15:00,5,Injection
5/25/2026,20001,PostFalls,2003007,3,10:00:00,24,16:00:00,4,TTCNP
5/25/2026,20001,PostFalls,2003008,3,10:30:00,16,14:30:00,4,TTCNP
---CSV_END---