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Add emission limits and penalties

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Alinson S. Xavier
2025-09-17 15:03:51 -05:00
parent 003922ac70
commit f35c84abe9
8 changed files with 183 additions and 38 deletions
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30
docs/src/format.md
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@@ -44,7 +44,7 @@ RELOG accepts as input a JSON file with four sections: `parameters`, `products`,
"CO2": 0.052,
"CH4": 0.003
},
"disposal limit (tonne)": 100.0,
"disposal limit (tonne)": 100.0
}
}
}
@@ -218,3 +218,31 @@ keys:
}
}
```
## Emissions
| Key | Description |
| :------------------ | :------------------------------------------------------------------------------------------------------------------------------------- |
| `limit (tonne)` | Maximum amount of this greenhouse gas allowed to be emitted per year across the entire supply chain. Entry may be `null` if unlimited. |
| `penalty ($/tonne)` | Penalty cost per tonne of this greenhouse gas emitted. |
#### Example
```json
{
"emissions": {
"CO2": {
"limit (tonne)": 1000.0,
"penalty ($/tonne)": 50.0
},
"CH4": {
"limit (tonne)": null,
"penalty ($/tonne)": 1200.0
},
"N2O": {
"limit (tonne)": 10.0,
"penalty ($/tonne)": 15000.0
}
}
}
```

44
docs/src/problem.md
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@@ -55,20 +55,22 @@ The mathematical model employed by RELOG is based on three main components:
| $K^\text{cap}_{p}$ | Capacity of plant $p$, if the plant is open | tonne |
| $K^\text{disp-limit}_{mt}$ | Maximum amount of material $m$ that can be disposed of (globally) at time $t$ | tonne |
| $K^\text{disp-limit}_{mut}$ | Maximum amount of material $m$ that can be disposed of at plant/center $u$ at time $t$ | tonne |
| $K^\text{em-limit}_{gt}$ | Maximum amount of greenhouse gas $g$ allowed to be emitted (globally) at time $t$ | tonne |
| $K^\text{em-plant}_{gpt}$ | Amount of greenhouse gas $g$ released by plant $p$ at time $t$ for each tonne of input material processed | tonne/tonne |
| $K^\text{em-tr}_{gmt}$ | Amount of greenhouse gas $g$ released by transporting 1 tonne of material $m$ over one km at time $t$ | tonne/km-tonne |
| $K^\text{mix}_{pmt}$ | If plant $p$ receives one tonne of input material at time $t$, then $K^\text{mix}_{pmt}$ is the amount of product $m$ in this mix. Must be between zero and one, and the sum of these amounts must equal to one. | tonne |
| $K^\text{out-fix}_{cmt}$ | Fixed amount of material $m$ collected at center $m$ at time $t$ | \$/tonne |
| $K^\text{out-var-len}_{cm}$ | Length of the $K^\text{out-var}_{c,m,*}$ vector. | -- |
| $K^\text{out-var}_{c,m,i}$ | Factor used to calculate variable amount of material $m$ collected at center $m$. See `eq_z_collected` for more details. | -- |
| $K^\text{output}_{pmt}$ | Amount of material $m$ produced by plant $p$ at time $t$ for each tonne of input material processed | tonne |
| $K^\text{plant-em}_{gpt}$ | Amount of greenhouse gas $g$ released by plant $p$ at time $t$ for each tonne of input material processed | tonne/tonne |
| $K^\text{tr-em}_{gmt}$ | Amount of greenhouse gas $g$ released by transporting 1 tonne of material $m$ over one km at time $t$ | tonne/km-tonne |
| $R^\text{tr}_{mt}$ | Cost to send material $m$ at time $t$ | \$/km-tonne |
| $R^\text{collect}_{cmt}$ | Cost of collecting material $m$ at center $c$ at time $t$ | \$/tonne |
| $R^\text{disp}_{umt}$ | Cost to dispose of material at plant/center $u$ at time $t$ | \$/tonne |
| $R^\text{em}_{gt}$ | Penalty cost per tonne of greenhouse gas $g$ emitted at time $t$ | \$/tonne |
| $R^\text{fix}_{ut}$ | Fixed operating cost for plant/center $u$ at time $t$ | \$ |
| $R^\text{open}_{pt}$ | Cost to open plant $p$ at time $t$ | \$ |
| $R^\text{rev}_{ct}$ | Revenue for selling the input product of center $c$ at this center at time $t$ | \$/tonne |
| $R^\text{tr}_{mt}$ | Cost to send material $m$ at time $t$ | \$/km-tonne |
| $R^\text{var}_{pt}$ | Cost to process one tonne of input material at plant $p$ at time $t$ | \$/tonne |
| $K^\text{out-fix}_{cmt}$ | Fixed amount of material $m$ collected at center $m$ at time $t$ | \$/tonne |
| $K^\text{out-var}_{c,m,i}$ | Factor used to calculate variable amount of material $m$ collected at center $m$. See `eq_z_collected` for more details. | -- |
| $K^\text{out-var-len}_{cm}$ | Length of the $K^\text{out-var}_{c,m,*}$ vector. | -- |
## Decision variables
@@ -80,8 +82,8 @@ The mathematical model employed by RELOG is based on three main components:
| $z^{\text{disp}}_{umt}$ | `z_disp[u.name, m.name, t]` | Amount of product $m$ disposed of at plant/center $u$ at time $t$ | tonne |
| $z^{\text{input}}_{ut}$ | `z_input[u.name, t]` | Total plant/center input at time $t$ | tonne |
| $z^{\text{prod}}_{umt}$ | `z_prod[u.name, m.name, t]` | Amount of product $m$ produced by plant/center $u$ at time $t$ | tonne |
| $z^{\text{tr-em}}_{guvmt}$ | `z_tr_em[g.name, u.name, v.name, m.name, t]` | Amount of greenhouse gas $g$ released at time $t$ due to transportation of material $m$ from $u$ to $v$ | tonne |
| $z^{\text{plant-em}}_{gpt}$ | `z_plant_em[g.name, p.name, t]` | Amount of greenhouse gas $g$ released by plant $p$ at time $t$ | tonne |
| $z^{\text{em-tr}}_{guvmt}$ | `z_em_tr[g.name, u.name, v.name, m.name, t]` | Amount of greenhouse gas $g$ released at time $t$ due to transportation of material $m$ from $u$ to $v$ | tonne |
| $z^{\text{em-plant}}_{gpt}$ | `z_em_plant[g.name, p.name, t]` | Amount of greenhouse gas $g$ released by plant $p$ at time $t$ | tonne |
## Objective function
@@ -151,6 +153,13 @@ The goals is to minimize a linear objective function with the following terms:
\sum_{p \in P} \sum_{(u,m) \in E^-(p)} \sum_{t \in T} R^\text{var}_{pt} y_{upmt}
```
- Emissions penalty cost, incurred for each tonne of greenhouse gas emitted:
```math
\sum_{g \in G} \sum_{t \in T} R^\text{em}_{gt} \left(
\sum_{p \in P} z^{\text{em-plant}}_{gpt} + \sum_{(u,v,m) \in E} z^{\text{em-tr}}_{guvmt}
\right)
```
## Constraints
- Definition of plant input (`eq_z_input[p.name, t]`):
@@ -271,20 +280,29 @@ The goals is to minimize a linear objective function with the following terms:
\end{align*}
```
- Computation of transportation emissions
(`eq_tr_em[g.name, u.name, v.name, m.name, t`):
- Computation of transportation emissions (`eq_emission_tr[g.name, u.name, v.name, m.name, t`):
```math
\begin{align*}
& z^{\text{tr-em}}_{guvmt} = K^{\text{dist}}_{uv} K^\text{tr-em}_{gmt} y_{uvmt}
& z^{\text{em-tr}}_{guvmt} = K^{\text{dist}}_{uv} K^\text{em-tr}_{gmt} y_{uvmt}
& \forall g \in G, (u, v, m) \in E, t \in T
\end{align*}
```
- Computation of plant emissions (`eq_plant_em[g.name, p.name, t]`):
- Computation of plant emissions (`eq_emission_plant[g.name, p.name, t]`):
```math
\begin{align*}
& z^{\text{plant-em}}_{gpt} = \sum_{(u,m) \in E^-(p)} K^\text{plant-em}_{gpt} y_{upmt}
& z^{\text{em-plant}}_{gpt} = \sum_{(u,m) \in E^-(p)} K^\text{em-plant}_{gpt} y_{upmt}
& \forall g \in G, p \in P, t \in T
\end{align*}
```
- Global emissions limit (`eq_emission_limit[g.name, t]`):
```math
\begin{align*}
& \sum_{p \in P} z^{\text{em-plant}}_{gpt} + \sum_{(u,v,m) \in E} z^{\text{em-tr}}_{guvmt} \leq K^\text{em-limit}_{gt}
& \forall g \in G, t \in T
\end{align*}
```