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Implement initial plant capacity

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This commit is contained in:
Alinson S. Xavier
2023-02-23 10:34:15 -06:00
parent 1f3a3c9317
commit 256b863c34
11 changed files with 138 additions and 95 deletions
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15
docs/src/format.md
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@@ -110,13 +110,14 @@ The **plants** section describes the available types of reverse manufacturing pl
Each type of plant is associated with a set of potential locations where it can be built. Each location is represented by a dictionary with the following keys:
| Key | Description |
| :------------------- | -------------------------------------------------------------------------------- |
| `latitude (deg)` | The latitude of the location, in degrees. |
| `longitude (deg)` | The longitude of the location, in degrees. |
| `disposal` | A dictionary describing what products can be disposed locally at the plant. |
| `storage` | A dictionary describing the plant's storage. |
| `capacities (tonne)` | A dictionary describing what plant sizes are allowed, and their characteristics. |
| Key | Description |
| :------------------------- | -------------------------------------------------------------------------------- |
| `latitude (deg)` | The latitude of the location, in degrees. |
| `longitude (deg)` | The longitude of the location, in degrees. |
| `disposal` | A dictionary describing what products can be disposed locally at the plant. |
| `storage` | A dictionary describing the plant's storage. |
| `capacities (tonne)` | A dictionary describing what plant sizes are allowed, and their characteristics. |
| `initial capacity (tonne)` | Capacity already available at this location. Optional. |
The `storage` dictionary should contain the following keys:

25
docs/src/model.md
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@@ -25,9 +25,10 @@ In this page, we describe the precise mathematical optimization model used by RE
| $c^\text{open}_{pt}$ | Cost of opening plant $p$ at time $t$, at minimum capacity | $ |
| $c^\text{p-disp}_{pmt}$ | Cost of disposing recovered material $m$ at plant $p$ during time $t$ | \$/tonne/km |
| $c^\text{store}_{pt}$ | Cost of storing primary material at plant $p$ at time $t$ | \$/tonne |
| $c^\text{var}_{pt}$ | Variable cost of processing primary material at plant $p$ at time $t$ | \$/tonne |
| $c^\text{proc}_{pt}$ | Variable cost of processing primary material at plant $p$ at time $t$ | \$/tonne |
| $m^\text{max}_p$ | Maximum capacity of plant $p$ | tonne |
| $m^\text{min}_p$ | Minimum capacity of plant $p$ | tonne |
| $m^\text{init}_p$ | Initial capacity of plant $p$ | tonne |
| $m^\text{p-disp}_{pmt}$ | Maximum amount of recovered material $m$ that plant $p$ can dispose of during time $t$ | tonne |
| $m^\text{store}_p$ | Maximum amount of primary material that plant $p$ can store for later processing. | tonne |
@@ -72,7 +73,7 @@ RELOG minimizes the overall capital, production and transportation costs:
\sum_{t \in T} \sum_{p \in P} \left[
c^\text{open}_{pt} u_{pt} +
c^\text{f-base}_{pt} x_{pt} +
\sum_{i=1}^t c^\text{f-exp}_{pt} w_{pi} +
c^\text{f-exp}_{pt} \left( \sum_{i=0}^t w_{pi} \right) +
c^{\text{exp}}_{pt} w_{pt}
\right] + \\
&
@@ -138,7 +139,7 @@ In the fifth line, we have acquisition and disposal cost at the collection cente
```math
\begin{align*}
& z^{\text{proc}}_{pt} \leq m^\text{min}_p x_p + \sum_{i=1}^t w_p
& z^{\text{proc}}_{pt} \leq m^\text{min}_p x_p + \sum_{i=0}^t w_p
& \forall p \in P, t \in T
\end{align*}
```
@@ -156,7 +157,7 @@ In the fifth line, we have acquisition and disposal cost at the collection cente
```math
\begin{align*}
& \sum_{i=1}^t w_p \leq m^\text{max}_p x_p
& \sum_{i=0}^t w_p \leq \left( m^\text{max}_p - m^\text{min}_p \right) x_p
& \forall p \in P, t \in T
\end{align*}
```
@@ -184,9 +185,19 @@ In the fifth line, we have acquisition and disposal cost at the collection cente
```math
\begin{align*}
& x_{pt} = x_{p,t-1} + u_{pt}
& \forall p \in P, t \in T \setminus \{1\} \\
& x_{p,1} = u_{p,1}
& \forall p \in P
& \forall p \in P, t \in T \\
\end{align*}
```
- Boundary constants:
```math
\begin{align*}
& x_{p,0} = \begin{cases}
0 & \text{ if } m^\text{init}_p = 0 \\
1 & \text{ otherwise }
\end{cases} \\
& w_{p,0} = \max\left\{0, m^\text{init}_p - m^\text{min}_p \right\}
\end{align*}
```