一汽丰田发动机产线作业测定与 AGV 物流路径重构

"""发动机装配线平衡率与 AGV 路径里程测算（脱敏标定数据口径）"""

# ---------- 1. 工位工时谱：(增值作业, 非增值 MUDA) ----------
STATIONS = {
    "OP10 缸体上线": (38.2, 5.1),
    "OP20 曲轴装配": (44.6, 8.4),
    "OP30 活塞连杆": (46.8, 11.9),   # 瓶颈工位
    "OP40 缸盖气门": (41.5, 6.7),
    "OP50 总装终检": (35.4, 4.6),
    "OP60 试漏检测": (33.0, 3.2),
}
TAKT = 52.0   # 客户需求节拍

def total(t): return t[0] + t[1]

print("=== 工序工时谱 ===")
for op, (va, muda) in STATIONS.items():
    tt = total((va, muda))
    flag = "  <-- 超出节拍线" if tt > TAKT else ""
    print(f"{op:<12} 增值 {va:>5.1f}s | MUDA {muda:>4.1f}s | 合计 {tt:>5.1f}s "
          f"| 非增值占比 {muda / tt:>5.1%}{flag}")

# ---------- 2. 产线平衡率 LBE = ΣT_i / (k × max T_i) ----------
def lbe(stations):
    times = [total(v) for v in stations.values()]
    return sum(times) / (len(times) * max(times))

before = lbe(STATIONS)

# 改善情景：OP30 定置化 + 套件前置压缩非增值；OP20 同步微调；一个工步转移至 OP60
after_stations = dict(STATIONS)
after_stations["OP20 曲轴装配"] = (44.6, 7.0)   # MUDA 8.4 -> 7.0（临界超线一并处理）
after_stations["OP30 活塞连杆"] = (42.6, 5.0)   # MUDA 11.9 -> 5.0，且转出 4.2s 工步
after_stations["OP60 试漏检测"] = (37.2, 3.2)   # 吸收 OP30 转出的连杆螺栓二次标记工步
after = lbe(after_stations)

print(f"\n=== 产线平衡率 ===")
print(f"改善前 LBE = {before:.2%} | 瓶颈节拍 = {max(total(v) for v in STATIONS.values()):.1f}s")
print(f"改善后 LBE = {after:.2%} | 瓶颈节拍 = {max(total(v) for v in after_stations.values()):.1f}s")
print(f"平衡率提升 +{(after - before) * 100:.1f} 个百分点")

# 注意：改善后瓶颈由 OP30 转移到 OP20 —— 瓶颈漂移，说明不能只改当前瓶颈

# ---------- 3. AGV 路径网络：交叉干涉点检测 ----------
def seg_intersect(p1, p2, p3, p4):
    """返回两线段交点（不含共端点情形），无交点返回 None"""
    d1 = (p2[0] - p1[0], p2[1] - p1[1])
    d2 = (p4[0] - p3[0], p4[1] - p3[1])
    den = d1[0] * d2[1] - d1[1] * d2[0]
    if abs(den) < 1e-9:
        return None                       # 平行或共线
    t = ((p3[0] - p1[0]) * d2[1] - (p3[1] - p1[1]) * d2[0]) / den
    u = ((p3[0] - p1[0]) * d1[1] - (p3[1] - p1[1]) * d1[0]) / den
    if 1e-6 < t < 1 - 1e-6 and 1e-6 < u < 1 - 1e-6:
        return (p1[0] + t * d1[0], p1[1] + t * d1[1])
    return None                           # 交点在端点 = 共用工位，不算干涉

def count_crossings(paths):
    hits, keys = [], list(paths)
    for i in range(len(keys)):
        for j in range(i + 1, len(keys)):
            pt = seg_intersect(*paths[keys[i]], *paths[keys[j]])
            if pt:
                hits.append((keys[i], keys[j], tuple(round(v, 1) for v in pt)))
    return hits

# 平面坐标（无量纲，仅用于拓扑交叉检测，非厂区实测坐标）
NODES = {"L1": (0, 0), "L2": (0, 40), "L3": (0, 80),
         "R1": (52, 0), "R2": (52, 40), "R3": (52, 80)}

PATHS_BEFORE = {
    "L1->R3": (NODES["L1"], NODES["R3"]),
    "L2->R1": (NODES["L2"], NODES["R1"]),
    "L3->R2": (NODES["L3"], NODES["R2"]),
    "L1->R2": (NODES["L1"], NODES["R2"]),
}
# 改善后：单向环形回路（每条边方向唯一，不再有对向交叉）
PATHS_AFTER = {
    "N1->N2": ((26, 0), (52, 20)),
    "N2->N3": ((52, 20), (26, 40)),
    "N3->N4": ((26, 40), (0, 20)),
    "N4->N1": ((0, 20), (26, 0)),
}

print("\n=== AGV 路径网络（拓扑层）===")
print(f"改善前交叉干涉点：{len(count_crossings(PATHS_BEFORE))} 处")
for a, b, pt in count_crossings(PATHS_BEFORE):
    print(f"   - {a} × {b} @ {pt}")
print(f"改善后交叉干涉点：{len(count_crossings(PATHS_AFTER))} 处")

# ---------- 4. 配送里程（现场路径实测，单位：米） ----------
# 注意：里程不能由上面的无量纲坐标推算，必须用现场实测的路线距离
ROUTE_BEFORE, ROUTE_AFTER = 186.0, 164.8
print(f"\n=== 配送里程（实测口径）===")
print(f"单循环里程：{ROUTE_BEFORE:.1f} m -> {ROUTE_AFTER:.1f} m "
      f"({(ROUTE_AFTER - ROUTE_BEFORE) / ROUTE_BEFORE:+.1%})")