Fleet

nimopt.models.fleet is the same problem as dispatch. It is declared as one variable per unit over the snapshots alone, and the terms of the units are added into one balance row. The optimum is the same merit order, and the cost of the declaration differs.

minimize    Σ_t Σ_u cost_u[t] · u[t]
subject to  Σ_u u[t] == load[t]          for each snapshot t
            0 ≤ u[t] ≤ p_max_u[t]        for each unit u

definition takes a scale here: the number of variables is a property of the declaration, not of the data.

from nimopt.models import fleet

print(fleet.definition().explain())

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Output

fleet  min  not built
  sets        T
  parameters  load (T) · p_max_g0_0 (T) · cost_g0_0 (T) · p_max_g1_0 (T) · cost_g1_0 (T) · p_max_g2_0 (T) · cost_g2_0 (T)
  variables   g0_0 (T) [0.0, p_max_g0_0] · g1_0 (T) [0.0, p_max_g1_0] · g2_0 (T) [0.0, p_max_g2_0]
  constraint  balance (T)  g0_0[T] + g1_0[T] + g2_0[T] == load[T]
  objective   min  Sum(T, cost_g0_0[T] * g0_0[T]) + Sum(T, cost_g1_0[T] * g1_0[T]) + Sum(T, cost_g2_0[T] * g2_0[T])

from nimopt.models import fleet

inputs = fleet.data()
model = fleet.definition().build(inputs)
solution = model.solve()
print(len(model.variables), "variables,", model.n_columns, "columns")
print(solution.objective, fleet.reference(inputs))

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Output

3 variables, 12 columns
8900.0 8900.0

One balance row per hour, and every unit appears in every row.

from nimopt.models import fleet

model = fleet.definition().build(fleet.data())
print(model.absent("balance"))

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Output

balance  4 of 4 rows  stated by terms