Solving the model

Prerequisites

Get the solution

The resulting output

Set Covering

For better understanding we visualized the output below. When activating the set covering constraint we choose subset 3,4 and 5. 

Optimizing the Model...
Optimize a model with 5 rows, 5 columns and 10 nonzeros
Coefficient statistics:
  Matrix range    [1e+00, 1e+00]
  Objective range [6e+00, 2e+01]
  Bounds range    [1e+00, 1e+00]
  RHS range       [1e+00, 1e+00]
Found heuristic solution: objective 31
Presolve removed 5 rows and 5 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.21 seconds
Thread count was 1 (of 4 available processors)

Optimal solution found (tolerance 0.00e+00)
Best objective 2.800000000000e+01, best bound 2.800000000000e+01, gap 0.0%
[Sum of all set costs, 28]
Status of set subset_1_B            : 0
Status of set subset_2_E            : 0
Status of set subset_3_F            : 1
Status of set subset_4_C            : 1
Status of set subset_5_D            : 1

Set Packing

Since Set Packing minimizes the cost by choosing no subset it is not included here.

Set Partitioning

For better understanding we visualized the output below. When activating the set packing constraint we choose subset 2 and 5. 

Performing presolve of the model to compute set of removed variables...
Presolve removed 10 rows and 5 columns
Presolve time: 0.00s
Optimizing the Model...
Optimize a model with 10 rows, 5 columns and 20 nonzeros
Coefficient statistics:
  Matrix range    [1e+00, 1e+00]
  Objective range [6e+00, 2e+01]
  Bounds range    [1e+00, 1e+00]
  RHS range       [1e+00, 1e+00]
Found heuristic solution: objective 31
Presolve removed 10 rows and 5 columns
Presolve time: 0.00s
Presolve: All rows and columns removed

Explored 0 nodes (0 simplex iterations) in 0.12 seconds
Thread count was 1 (of 4 available processors)

Optimal solution found (tolerance 0.00e+00)
Best objective 3.100000000000e+01, best bound 3.100000000000e+01, gap 0.0%
[Sum of all set costs, 31]
Status of set subset_1_B            : 0
Status of set subset_2_E            : 1
Status of set subset_3_F            : 0
Status of set subset_4_C            : 1
Status of set subset_5_D            : 0

Next Step

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