python - 在 PuLP(Python) 中指定 lowBound 和 upBound

Question

我要最小化的决策变量是:

DV2 = {   "P1" : {"V1" : 38.11, "V2" : 21.47, "V3" : 27.98, "V4" : 24.95, "V5" :25.22},
          "P2" : {"V1" : 31.10355934, "V2" : 34.20506007, "V3" : 30.46890595, "V4" : 33.74346353, "V5" : 29.47098217},
          "P3" : {"V1" : 29.13518894, "V2" : 38.89035574, "V3" : 30.97508704, "V4" : 33.50849106, "V5" : 34.94861333}
          }

它与运输问题类似，不同之处在于目标函数为:0.71*成本*DV2 + 0.29*风险*DV2，其中成本为:

cost= { "P1" : {"V1" : 0.2, "V2" : 0.22, "V3" : 0.2, "V4" : 0.2, "V5" :0.17},
          "P2" : {"V1" : 0.2, "V2" : 0.21, "V3" : 0.19, "V4" : 0.19, "V5" : 0.19},
          "P3" : {"V1" : 0.19, "V2" : 0.19, "V3" : 0.2, "V4" : 0.19, "V5" : 0.2}
      }

风险是:

   risk= { "P1" : {"V1" : 0.5, "V2" : 0.52, "V3" : 0.25, "V4" : 0.25, "V5" :0.57},
              "P2" : {"V1" : 0.5, "V2" : 0.51, "V3" : 0.9, "V4" : 0.9, "V5" : 0.9},
              "P3" : {"V1" : 0.6, "V2" : 0.6, "V3" : 0.7, "V4" : 0.8, "V5" : 0.9}
              }

lowBound 将是:

min1= { "P1" : {"V1" : 500, "V2" : 500, "V3" : 500, "V4" : 0, "V5" :500},
          "P2" : {"V1" : 500, "V2" : 0, "V3" : 500, "V4" : 500, "V5" : 0},
          "P3" : {"V1" : 500, "V2" : 500, "V3" : 500, "V4" : 500, "V5" : 500}
      }

upBound 将是:

      max1= { "P1" : {"V1" : 5000, "V2" : 5000, "V3" : 5000, "V4" : 0, "V5" :5000},
              "P2" : {"V1" : 5000, "V2" : 0, "V3" : 5000, "V4" : 5000, "V5" : 0},
              "P3" : {"V1" : 5000, "V2" : 5000, "V3" : 5000, "V4" : 5000, "V5" : 5000}
}

如果有人能告诉我如何在这种情况下制定目标函数，我将非常感激，因为 lowBound 和 upBound 应该只采用实数(这是我得到的错误)。

Answer 1

对于标量边界:

L = 1.0
U = 2.0
x = LpVariable.dicts("x",J,L,U,LpContinuous)

对于索引边界使用约束:

L = {"a": 0.2, "b" : 0.3}
U = {"a": 1.2, "b" : 1.3}
for j in J:
    prob += x[j] >= L[j]
    prob += x[j] <= U[j]

LP/MIP 求解器将在预求解阶段内部对单例约束进行限制。