我可能會有 2 種作法
不確定 pandas 是不是還有更好的方法，歡迎提供

1. 把值切開計算再加回去

g = "10/7/11"
t = "A/B/B"
time_val = 2

gs = g.split("/")
ts = t.split("/")
result = []

for (gi, ti) in zip(gs, ts):
    if ti == "A":
        ans = int(gi) * time_val * 0.3
    elif ti == "B":
        ans = int(gi) * time_val * 0.5
    result.append(str(ans))

result_str = "/".join(result)
print(result_str)
# 6.0/7.0/11.0

2. 把值拆開，變成新欄位，但要知道最多會拆成幾種
   試了幾種合併方式，都不太能單獨處理

import pandas as pd

df = pd.DataFrame({
    "goat": ["15/10", "10/7/11"],
    "type": ["A/B", "A/B/B"]
})

# 切開補空值
df[['g1', 'g2', 'g3']] = df.goat.str.split('/', expand=True)
df[['t1', 't2', 't3']] = df.type.str.split('/', expand=True)
df.fillna("", inplace=True)

# 各種合併
df['all1'] = df[['g1', 'g2', 'g3']].agg('/'.join, axis=1)
df['all2'] = df.t1.str.cat(df[['t2', 't3']], sep='/')
df['all3'] = df[['t1', 't2', 't3']].apply(lambda x: '/'.join(x), axis=1)

def addcheck(row):
    st = ''
    for i in range(len(row)):
        if row[i] != '':
            if st != '':
                st += "/"
            st += row[i]
    return st

df['all4'] = df[['t1', 't2', 't3']].apply(addcheck, axis=1)

print(df)

      goat   type  g1  g2  g3 t1 t2 t3     all1   all2   all3   all4
0    15/10    A/B  15  10      A  B      15/10/   A/B/   A/B/    A/B
1  10/7/11  A/B/B  10   7  11  A  B  B  10/7/11  A/B/B  A/B/B  A/B/B

Combine two columns of text in pandas dataframe

提供一個不是很 python 的寫法

import pandas as pd

df = pd.DataFrame(
    {
      'GROUP':   ['R','W','W','R','R','W'],
      'GOAT':    ['15/10','10/7/11','9','12','8/13','10'],
      'TYPE':    ['A/B','A/B/B','A','B','B/A','B'],
      'TIME': [2,3,2,2,3,2]
    }
)

def apply_fx(r):
  arrG = r['GOAT'].split("/")
  arrT = r['TYPE'].split("/")
  arrR = []
  
  for (g, t) in zip(arrG, arrT):
    if r['GROUP']=='R' and t=='A':
      moa = int(g) * r['TIME'] * 0.3
    elif r['GROUP']=='R' and t=='B':
      moa = int(g) * r['TIME'] * 0.5
    elif r['GROUP']=='W' and t=='A':
      moa = int(g) * r['TIME'] * 0.4
    elif r['GROUP']=='W' and t=='B':
      moa = int(g) * r['TIME'] * 0.3
    else:
      moa = -1
    arrR.append(str(moa))

  strret = "/".join(arrR)
  return strret
  
df['RESULT'] = df.apply(apply_fx, axis=1)

print(df)

雖然有前輩早就提供解答了，
但還是想試著自己寫看看。
平常沒有很常寫程式，一些語法也不熟。
斷斷續續利用有閒的時間嘗試，總算也解出來了!!

import pandas as pd
import numpy as np

df = pd.DataFrame(
    {
      'GROUP':   ['R','W','W','R','R','W'],
      'GOAT':    ['15/10','10/7/11','9','12','8/13','10'],
      'TYPE':    ['A/B','A/B/B','A','B','B/A','B'],
      'TIME': [2,3,2,2,3,2]
    }
)

df

df_temp = df.copy()
df_temp['GOAT_sub'] = df_temp['GOAT'].str.split('/').tolist()
df_temp['TYPE_sub'] = df_temp['TYPE'].str.split('/').tolist()

df_temp

# 設定solution來存最後結果
solution = []
for i in range(len(df_temp)):
    #設定temp_RESULT來存暫時的結果
    temp_RESULT = []
    for j in range(len(df_temp['TYPE_sub'][i])):
        if ((df_temp['GROUP'][i] == 'R') & (df_temp['TYPE_sub'][i][j] == 'A')):
            df_temp['temp'+str(j)] = int(df_temp['GOAT_sub'][i][j])*df_temp['TIME'][i]*0.3
        elif ((df_temp['GROUP'][i] == 'R') & (df_temp['TYPE_sub'][i][j] == 'B')):
            df_temp['temp'+str(j)] = int(df_temp['GOAT_sub'][i][j])*df_temp['TIME'][i]*0.5
        elif ((df_temp['GROUP'][i] == 'W') & (df_temp['TYPE_sub'][i][j] == 'A')):
            df_temp['temp'+str(j)] = int(df_temp['GOAT_sub'][i][j])*df_temp['TIME'][i]*0.4
        elif ((df_temp['GROUP'][i] == 'W') & (df_temp['TYPE_sub'][i][j] == 'B')):
            df_temp['temp'+str(j)] = int(df_temp['GOAT_sub'][i][j])*df_temp['TIME'][i]*0.3
        L = str(df_temp['temp'+str(j)][0])
        temp_RESULT.append(L)
    temp_RESULT = '/'.join(temp_RESULT)
    solution.append(temp_RESULT)

    print(temp_RESULT)

solution

df['RESULT'] = solution
df

##另一種寫法：

import pandas as pd
import numpy as np

df = pd.DataFrame(
    {
      'GROUP':   ['R','W','W','R','R','W'],
      'GOAT':    ['15/10','10/7/11','9','12','8/13','10'],
      'TYPE':    ['A/B','A/B/B','A','B','B/A','B'],
      'TIME': [2,3,2,2,3,2]
    }
)

go = df['GOAT'].str.split('/')
ty = df['TYPE'].str.split('/')
co = range(len(df))
result = []
for a, b, c in zip(go, ty, co):
    re = []
    for i in range(len(b)):
        gr = df['GROUP'][c]
        ti = df['TIME'][c]
        if ((gr == 'R') & (b[i] == 'A')):
            r = int(a[i])*int(ti)*0.3
        elif ((gr == 'R') & (b[i] == 'B')):
            r = int(a[i])*int(ti)*0.5
        elif ((gr == 'W') & (b[i] == 'A')):
            r = int(a[i])*int(ti)*0.4
        elif ((gr == 'W') & (b[i] == 'B')):
            r = int(a[i])*int(ti)*0.3

        li = str(r)
        re.append(li)
        #print(a[i], b[i], gr, ti, r)
    #print('/'.join(re))
    result.append('/'.join(re))
    
df['RESULT'] = result
df