Specifying lowBound and upBound in PuLP(Python)

Question

My decision variable, which is to be minimized is this:

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}
          }

It is similar to the transportation problem except, the objective function will be: 0.71*cost*DV2 + 0.29*risk*DV2, where cost is :

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}
      }

And risk is:

   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 will be:

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 will be:

      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}
}

Will be very grateful if somebody could show me how to formulize the objective function in this scenario, since lowBound and upBound are supposed to take real numbers only(this is the error I'm getting).

Its the original format. I'm trying to generate the LpVariable.dicts with the lower and upper bounds as stated above — IndigoChild, Mar 12 '18 at 10:03

Erwin Kalvelagen · Accepted Answer · 2018-03-12T19:40:40.703

1

For scalar bounds:

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

For indexed bounds use constraints:

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]

The LP/MIP solver will internally make bounds from singleton constraints in the presolve phase.

edited Mar 12 '18 at 19:40

answered Mar 12 '18 at 18:47

Erwin Kalvelagen

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Specifying lowBound and upBound in PuLP(Python)

1 Answers1