AI排跨夜班：最短休息约束与无可行方案报告

{
  "policy": "每个班次必须一人覆盖；同一员工两班之间至少休息11小时。",
  "employees": [
    "A",
    "B"
  ],
  "shifts": [
    {
      "id": "N1",
      "start": "2026-10-01T20:00",
      "end": "2026-10-02T04:00",
      "allowed": [
        "A"
      ]
    },
    {
      "id": "M1",
      "start": "2026-10-02T08:00",
      "end": "2026-10-02T12:00",
      "allowed": [
        "A",
        "B"
      ]
    },
    {
      "id": "E1",
      "start": "2026-10-02T18:00",
      "end": "2026-10-02T22:00",
      "allowed": [
        "B"
      ]
    }
  ]
}

python3 -m venv .venv
source .venv/bin/activate
python -m pip install -r requirements.txt
python run.py

{
  "model": "gemini-2.5-flash-lite",
  "messages": [
    {
      "role": "system",
      "content": "严格只输出单个JSON对象，不要Markdown代码围栏，不要解释。只处理给定原创虚构材料，只输出JSON。从排班政策提取min_rest_hours整数、must_cover_all布尔值。不要生成排班方案，程序会做跨日约束求解。 输出结构：{\"min_rest_hours\": \"number\", \"must_cover_all\": \"boolean\"}"
    },
    {
      "role": "user",
      "content": "任务约束（只输出JSON对象，不用代码围栏）：\n只处理给定原创虚构材料，只输出JSON。从排班政策提取min_rest_hours整数、must_cover_all布尔值。不要生成排班方案，程序会做跨日约束求解。 输出结构：{\"min_rest_hours\": \"number\", \"must_cover_all\": \"boolean\"}\n待处理合成材料：\n{\"policy\": \"每个班次必须一人覆盖；同一员工两班之间至少休息11小时。\", \"employees\": [\"A\", \"B\"], \"shifts\": [{\"id\": \"N1\", \"start\": \"2026-10-01T20:00\", \"end\": \"2026-10-02T04:00\", \"allowed\": [\"A\"]}, {\"id\": \"M1\", \"start\": \"2026-10-02T08:00\", \"end\": \"2026-10-02T12:00\", \"allowed\": [\"A\", \"B\"]}, {\"id\": \"E1\", \"start\": \"2026-10-02T18:00\", \"end\": \"2026-10-02T22:00\", \"allowed\": [\"B\"]}]}"
    }
  ],
  "temperature": 0,
  "max_tokens": 1024,
  "provider": {
    "sort": "success_rate"
  },
  "response_format": {
    "type": "json_object"
  }
}

import itertools
shifts = data['shifts']
rest = output['min_rest_hours']

def solve(items):
    answers = []
    for people in itertools.product(*(r['allowed'] for r in items)):
        assignment = dict(zip((r['id'] for r in items), people))
        ok = True
        for a, b in itertools.combinations(items, 2):
            if assignment[a['id']] != assignment[b['id']]:
                continue
            first, last = sorted([a, b], key=lambda r: r['start'])
            gap = (datetime.fromisoformat(last['start']) - datetime.fromisoformat(first['end'])).total_seconds() / 3600
            if gap < rest:
                ok = False
                break
        if ok:
            answers.append(assignment)
    return answers
answers = solve(shifts)
core = []
if not answers:
    for n in range(1, len(shifts) + 1):
        found = next((list(items) for items in itertools.combinations(shifts, n) if not solve(list(items))), None)
        if found is not None:
            core = [r['id'] for r in found]
            break
relaxed = copy.deepcopy(shifts)
relaxed[-1]['allowed'] = ['A', 'B']
relaxed_answers = solve(relaxed)
check('原约束全局不可行而不是漏分配', answers == [])
check('最小不可行核心包含三个班次', core == ['N1', 'M1', 'E1'])
check('移除核心任一班次都可行', all((solve([s for s in shifts if s['id'] != removed]) for removed in core)))
check('明确修改候选后才出现解', len(relaxed_answers) > 0)
jout('shift-infeasibility.json', {'status': 'infeasible', 'min_rest_hours': rest, 'minimal_core': core, 'original_assignments': answers, 'relaxed_counterexample': relaxed_answers})
result = {'status': 'infeasible', 'minimal_core': core, 'relaxed_examples': relaxed_answers}

{
  "status": "infeasible",
  "minimal_core": [
    "N1",
    "M1",
    "E1"
  ],
  "relaxed_examples": [
    {
      "N1": "A",
      "M1": "B",
      "E1": "A"
    }
  ]
}