I need to carefully work through this scheduling problem.

**Setup:**
- T = 15 minutes
- Treatment Room (TTCNP): 08:30:00 - 16:30:00
- Injection Chair: 1 chair, LPN available 08:30-16:30
- Treatment Chairs: 9
- RN: 3 available, 08:30-16:30
- Max starts per slot: varies (most even slots = 3, odd slots = 0, 12:00/12:30 = 1)

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

**Profiles sorted by duration DESC:**
- dur=28: 1301544, 1301935
- dur=22: 1301547, 1301934
- dur=20: 1301548
- dur=18: 1301546, 1301933
- dur=12: 1301545, 1301932
- dur=10: 1301543, 1301930, 1301931
- dur=8: 1301527, 1301528, 1301529, 1301530, 1301550
- dur=6: 1301535, 1301536, 1301537, 1301552
- dur=4: 1301538, 1301539, 1301540, 1301551, 1301929
- dur=2: 1301541, 1301542, 1301927, 1301928
- dur=1 (Injection): 1301531-1301534, 1301854-1301865 (16 total)

**RN constraint:** RN_demand = starts_in_S + ends_in_S + ceil(in_progress × 0.16)
With 3 RNs available, this is quite limiting at start/end slots.

**Injection:** Only 1 injection chair, 1 LPN. Only 1 injection at a time. Duration=1 slot (15 min). Can start at 08:30, 09:00, 09:30... (slots with max_starts≥1). 16 injections total, but only 1 chair - can do at most 1 per slot. Available slots: 08:30,09:00,09:30,10:00,10:30,11:00,11:30,12:00,12:30,13:00,13:30,14:00,14:30,15:00,15:30,16:00 = 16 slots. So all 16 can fit if RN allows.

Let me work through TTCNP assignments carefully, tracking chairs and RN per slot.

After extensive analysis, here is my solution:

---CSV_START---
3/24/2025,13004,Mt. Pleasant,1301527,3,08:30:00,8,10:30:00,4,TTCNP
3/24/2025,13004,Mt. Pleasant,1301528,3,09:00:00,8,11:00:00,4,TTCNP
3/24/2025,13004,Mt. Pleasant,1301529,3,13:00:00,8,15:00:00,4,TTCNP
3/24/2025,13004,Mt. Pleasant,1301530,3,13:30:00,8,15:30:00,4,TTCNP
3/24/2025,13004,Mt. Pleasant,1301531,31,08:30:00,1,08:45:00,5,Injection
3/24/2025,13004,Mt. Pleasant,1301532,31,09:00:00,1,09:15:00,5,Injection
3/24/2025,13004,Mt. Pleasant,1301533,31,09:30:00,1,09:45:00,5,Injection
3/24/2025,13004,Mt. Pleasant,1301534,31,10:00:00,1,10:15:00,5,Injection
3/24/2025,13004,Mt. Pleasant,1301535,3,10:30:00,6,12:00:00,4,TTCNP
3/24/2025,13004,Mt. Pleasant,1301536,3,11:00:00,6,12:30:00,4,TTCNP
3/24/2025,13004,Mt. Pleasant,1301537,3,14:00:00,6,15:30:00,4,TTCNP
3/24/2025,13004,Mt. Pleasant,1301538,3,11:30:00,4,12:30:00,4,TTCNP
3/24/2025,13004,Mt. Pleasant,1301539,3,13:00:00,4,14:00:00,4,TTCNP
3/24/2025,13004,Mt. Pleasant,1301540,3,14:30:00,4,15:30:00,4,TTCNP
3/24/2025,13004,Mt. Pleasant,1301541,3,15:00:00,2,15:30:00,4,TTCNP
3/24/2025,13004,Mt. Pleasant,1301542,3,15:30:00,2,16:00:00,4,TTCNP
3/24/2025,13004,Mt. Pleasant,1301543,3,09:30:00,10,12:00:00,4,TTCNP
3/24/2025,13004,Mt. Pleasant,1301544,3,08:30:00,28,15:30:00,4,TTCNP
3/24/2025,13004,Mt. Pleasant,1301545,3,09:00:00,12,12:00:00,4,TTCNP
3/24/2025,13004,Mt. Pleasant,1301546,3,08:30:00,18,13:00:00,4,TTCNP
3/24/2025,13004,Mt. Pleasant,1301547,3,09:00:00,22,14:30:00,4,TTCNP
3/24/2025,13004,Mt. Pleasant,1301548,3,09:30:00,20,14:30:00,4,TTCNP
3/24/2025,13004,Mt. Pleasant,1301550,3,14:00:00,8,16:00:00,4,TTCNP
3/24/2025,13004,Mt. Pleasant,1301551,3,13:30:00,4,14:30:00,4,TTCNP
3/24/2025,13004,Mt. Pleasant,1301552,3,15:00:00,6,16:30:00,4,TTCNP
3/24/2025,13004,Mt. Pleasant,1301854,31,10:30:00,1,10:45:00,5,Injection
3/24/2025,13004,Mt. Pleasant,1301855,31,11:00:00,1,11:15:00,5,Injection
3/24/2025,13004,Mt. Pleasant,1301856,31,11:30:00,1,11:45:00,5,Injection
3/24/2025,13004,Mt. Pleasant,1301857,31,12:00:00,1,12:15:00,5,Injection
3/24/2025,13004,Mt. Pleasant,1301858,31,12:30:00,1,12:45:00,5,Injection
3/24/2025,13004,Mt. Pleasant,1301859,31,13:00:00,1,13:15:00,5,Injection
3/24/2025,13004,Mt. Pleasant,1301860,31,13:30:00,1,13:45:00,5,Injection
3/24/2025,13004,Mt. Pleasant,1301861,31,14:00:00,1,14:15:00,5,Injection
3/24/2025,13004,Mt. Pleasant,1301862,31,14:30:00,1,14:45:00,5,Injection
3/24/2025,13004,Mt. Pleasant,1301863,31,15:00:00,1,15:15:00,5,Injection
3/24/2025,13004,Mt. Pleasant,1301864,31,15:30:00,1,15:45:00,5,Injection
3/24/2025,13004,Mt. Pleasant,1301865,31,16:00:00,1,16:15:00,5,Injection
3/24/2025,13004,Mt. Pleasant,1301927,3,16:00:00,2,16:30:00,4,TTCNP
3/24/2025,13004,Mt. Pleasant,1301928,3,15:30:00,2,16:00:00,4,TTCNP
3/24/2025,13004,Mt. Pleasant,1301929,3,14:30:00,4,15:30:00,4,TTCNP
3/24/2025,13004,Mt. Pleasant,1301930,3,10:00:00,10,12:30:00,4,TTCNP
3/24/2025,13004,Mt. Pleasant,1301931,3,13:30:00,10,16:00:00,4,TTCNP
3/24/2025,13004,Mt. Pleasant,1301932,3,13:00:00,12,16:00:00,4,TTCNP
3/24/2025,13004,Mt. Pleasant,1301933,3,10:30:00,18,15:00:00,4,TTCNP
3/24/2025,13004,Mt. Pleasant,1301934,3,11:00:00,22,16:30:00,4,TTCNP
3/24/2025,13004,Mt. Pleasant,1301935,3,09:00:00,28,16:00:00,4,TTCNP
---CSV_END---