Input Data
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| Appliance | Priority Factor | Average Power (kW) | Cost per Hour ($) | Cost for Full Period ($) | Actions |
|---|
Optimal Schedule
Appliance hours allocated in order of Priority Service Factor per dollar.
| Rank | Appliance | Priority Factor | Power (kW) | Cost per Hour ($) | Hours | Share of Period | Cost Allocated ($) | Status |
|---|
Budget Sensitivity
The optimal schedule is piecewise linear in the wallet balance. Markers show the balance at which each appliance starts to receive hours.
Optimal schedule against the unrationed baseline, in which every appliance runs simultaneously until the balance is exhausted.
Cumulative hours by appliance. Appliances are funded strictly in ranking order, so only one appliance is partly served at any balance.
Budget Thresholds
Cumulative cost of serving the appliances ranked above each appliance for the full period.
| Rank | Appliance | PSF per Dollar | Cost for Full Period ($) | Cumulative Threshold ($) |
|---|
Method
The service factor of appliance k is the fraction of the planning period for which it is enabled,
SFk = sk / H. The Priority Service Factor is the priority-weighted sum of the
service factors, and the decision problem is
maximise PSF = Σ μk sk / H
subject to Σ λ Pk sk ≤ Z
0 ≤ sk ≤ H
Each hour of appliance k costs wk = λPk and adds
bk = μk / H to the objective. Because fractional hours are permitted,
the problem is a fractional knapsack and the greedy order by
rk = bk / wk is optimal. The application ranks the appliances,
funds each one for the full period while the balance allows it, and gives the remaining balance to the first
appliance that cannot be funded completely.
The unrationed baseline assumes that all appliances run simultaneously until the balance is exhausted, so each
appliance runs for min(H, Z / (λ ΣP)) hours.