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Allow user to specify product acquisition costs

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feature/CapEx
Alinson S. Xavier 3 years ago
parent 2f0228e9ca
commit 78128bd79b
Signed by: isoron
GPG Key ID: 0DA8E4B9E1109DCA
15 changed files with 484 additions and 557 deletions
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1
CHANGELOG.md
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@ -14,6 +14,7 @@ All notable changes to this project will be documented in this file.
## [Unreleased]
### Added
- Allow disposal at collection centers
- Allow user to specify product acquisition costs
### Changed
- Switch from Cbc/Clp to HiGHS

2
docs/make.jl
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@ -15,5 +15,3 @@ function make()
)
)
end
make()

293
docs/src/format.md
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@ -10,21 +10,21 @@ RELOG accepts as input a JSON file with three sections: `parameters`, `products`
The **parameters** section describes details about the simulation itself.
| Key | Description
|:--------------------------|:---------------|
|`time horizon (years)` | Number of years in the simulation.
|`building period (years)` | List of years in which we are allowed to open new plants. For example, if this parameter is set to `[1,2,3]`, we can only open plants during the first three years. By default, this equals `[1]`; that is, plants can only be opened during the first year. |
|`distance metric` | Metric used to compute distances between pairs of locations. Valid options are: `"Euclidean"`, for the straight-line distance between points; or `"driving"` for an approximated driving distance. If not specified, defaults to `"Euclidean"`.
| Key | Description |
| :------------------------ | :----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| `time horizon (years)` | Number of years in the simulation. |
| `building period (years)` | List of years in which we are allowed to open new plants. For example, if this parameter is set to `[1,2,3]`, we can only open plants during the first three years. By default, this equals `[1]`; that is, plants can only be opened during the first year. |
| `distance metric` | Metric used to compute distances between pairs of locations. Valid options are: `"Euclidean"`, for the straight-line distance between points; or `"driving"` for an approximated driving distance. If not specified, defaults to `"Euclidean"`. |
#### Example
```json
{
"parameters": {
"time horizon (years)": 2,
"building period (years)": [1],
"distance metric": "driving",
}
"parameters": {
"time horizon (years)": 2,
"building period (years)": [1],
"distance metric": "driving"
}
}
```
@ -32,65 +32,67 @@ The **parameters** section describes details about the simulation itself.
The **products** section describes all products and subproducts in the simulation. The field `instance["Products"]` is a dictionary mapping the name of the product to a dictionary which describes its characteristics. Each product description contains the following keys:
| Key | Description
|:--------------------------------------|:---------------|
|`transportation cost ($/km/tonne)` | The cost to transport this product. Must be a time series.
|`transportation energy (J/km/tonne)` | The energy required to transport this product. Must be a time series. Optional.
|`transportation emissions (tonne/km/tonne)` | A dictionary mapping the name of each greenhouse gas, produced to transport one tonne of this product along one kilometer, to the amount of gas produced (in tonnes). Must be a time series. Optional.
|`initial amounts` | A dictionary mapping the name of each location to its description (see below). If this product is not initially available, this key may be omitted. Must be a time series.
| `disposal limit (tonne)` | Total amount of product that can be disposed of across all collection centers. If omitted, all product must be processed. This parameter has no effect on product disposal at plants.
| `disposal cost ($/tonne)` | Cost of disposing one tonne of this product at a collection center. If omitted, defaults to zero. This parameter has no effect on product disposal costs at plants.
| Key | Description |
| :------------------------------------------ | :----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| `transportation cost ($/km/tonne)` | The cost to transport this product. Must be a time series. |
| `transportation energy (J/km/tonne)` | The energy required to transport this product. Must be a time series. Optional. |
| `transportation emissions (tonne/km/tonne)` | A dictionary mapping the name of each greenhouse gas, produced to transport one tonne of this product along one kilometer, to the amount of gas produced (in tonnes). Must be a time series. Optional. |
| `initial amounts` | A dictionary mapping the name of each location to its description (see below). If this product is not initially available, this key may be omitted. Must be a time series. |
| `disposal limit (tonne)` | Total amount of product that can be disposed of across all collection centers. If omitted, all product must be processed. This parameter has no effect on product disposal at plants. |
| `disposal cost ($/tonne)` | Cost of disposing one tonne of this product at a collection center. If omitted, defaults to zero. This parameter has no effect on product disposal costs at plants. |
| `acquisition cost ($/tonne)` | Cost of acquiring one tonne of this product at a collection center. If omitted, defaults to zero. |
Each product may have some amount available at the beginning of each time period. In this case, the key `initial amounts` maps to a dictionary with the following keys:
| Key | Description
|:------------------------|:---------------|
| `latitude (deg)` | The latitude of the location.
| `longitude (deg)` | The longitude of the location.
| `amount (tonne)` | The amount of the product initially available at the location. Must be a time series.
| Key | Description |
| :---------------- | :------------------------------------------------------------------------------------ |
| `latitude (deg)` | The latitude of the location. |
| `longitude (deg)` | The longitude of the location. |
| `amount (tonne)` | The amount of the product initially available at the location. Must be a time series. |
#### Example
```json
{
"products": {
"P1": {
"initial amounts": {
"C1": {
"latitude (deg)": 7.0,
"longitude (deg)": 7.0,
"amount (tonne)": [934.56, 934.56]
},
"C2": {
"latitude (deg)": 7.0,
"longitude (deg)": 19.0,
"amount (tonne)": [198.95, 198.95]
},
"C3": {
"latitude (deg)": 84.0,
"longitude (deg)": 76.0,
"amount (tonne)": [212.97, 212.97]
}
},
"transportation cost ($/km/tonne)": [0.015, 0.015],
"transportation energy (J/km/tonne)": [0.12, 0.11],
"transportation emissions (tonne/km/tonne)": {
"CO2": [0.052, 0.050],
"CH4": [0.003, 0.002]
},
"disposal cost ($/tonne)": [-10.0, -12.0],
"disposal limit (tonne)": [1.0, 1.0],
},
"P2": {
"transportation cost ($/km/tonne)": [0.022, 0.020]
"products": {
"P1": {
"initial amounts": {
"C1": {
"latitude (deg)": 7.0,
"longitude (deg)": 7.0,
"amount (tonne)": [934.56, 934.56]
},
"P3": {
"transportation cost ($/km/tonne)": [0.0125, 0.0125]
"C2": {
"latitude (deg)": 7.0,
"longitude (deg)": 19.0,
"amount (tonne)": [198.95, 198.95]
},
"P4": {
"transportation cost ($/km/tonne)": [0.0175, 0.0175]
"C3": {
"latitude (deg)": 84.0,
"longitude (deg)": 76.0,
"amount (tonne)": [212.97, 212.97]
}
},
"transportation cost ($/km/tonne)": [0.015, 0.015],
"transportation energy (J/km/tonne)": [0.12, 0.11],
"transportation emissions (tonne/km/tonne)": {
"CO2": [0.052, 0.05],
"CH4": [0.003, 0.002]
},
"disposal cost ($/tonne)": [-10.0, -12.0],
"disposal limit (tonne)": [1.0, 1.0],
"acquisition cost ($/tonne)": [1.0, 1.0]
},
"P2": {
"transportation cost ($/km/tonne)": [0.022, 0.02]
},
"P3": {
"transportation cost ($/km/tonne)": [0.0125, 0.0125]
},
"P4": {
"transportation cost ($/km/tonne)": [0.0175, 0.0175]
}
}
}
```
@ -98,135 +100,138 @@ Each product may have some amount available at the beginning of each time period
The **plants** section describes the available types of reverse manufacturing plants, their potential locations and associated costs, as well as their inputs and outputs. The field `instance["Plants"]` is a dictionary mapping the name of the plant to a dictionary with the following keys:
| Key | Description
|:------------------------|:---------------|
| `input` | The name of the product that this plant takes as input. Only one input is accepted per plant.
| `outputs (tonne/tonne)` | A dictionary specifying how many tonnes of each product is produced for each tonnes of input. For example, if the plant outputs 0.5 tonnes of P2 and 0.25 tonnes of P3 for each tonnes of P1 provided, then this entry should be `{"P2": 0.5, "P3": 0.25}`. If the plant does not output anything, this key may be omitted.
|`energy (GJ/tonne)` | The energy required to process 1 tonne of the input. Must be a time series. Optional.
|`emissions (tonne/tonne)` | A dictionary mapping the name of each greenhouse gas, produced to process each tonne of input, to the amount of gas produced (in tonne). Must be a time series. Optional.
| `locations` | A dictionary mapping the name of the location to a dictionary which describes the site characteristics (see below).
| Key | Description |
| :------------------------ | :-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| `input` | The name of the product that this plant takes as input. Only one input is accepted per plant. |
| `outputs (tonne/tonne)` | A dictionary specifying how many tonnes of each product is produced for each tonnes of input. For example, if the plant outputs 0.5 tonnes of P2 and 0.25 tonnes of P3 for each tonnes of P1 provided, then this entry should be `{"P2": 0.5, "P3": 0.25}`. If the plant does not output anything, this key may be omitted. |
| `energy (GJ/tonne)` | The energy required to process 1 tonne of the input. Must be a time series. Optional. |
| `emissions (tonne/tonne)` | A dictionary mapping the name of each greenhouse gas, produced to process each tonne of input, to the amount of gas produced (in tonne). Must be a time series. Optional. |
| `locations` | A dictionary mapping the name of the location to a dictionary which describes the site characteristics (see below). |
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. |
The `storage` dictionary should contain the following keys:
| Key | Description
|:------------------------|:---------------|
| `cost ($/tonne)` | The cost to store a tonne of input product for one time period. Must be a time series.
| `limit (tonne)` | The maximum amount of input product this plant can have in storage at any given time.
| Key | Description |
| :--------------- | :------------------------------------------------------------------------------------- |
| `cost ($/tonne)` | The cost to store a tonne of input product for one time period. Must be a time series. |
| `limit (tonne)` | The maximum amount of input product this plant can have in storage at any given time. |
The keys in the `disposal` dictionary should be the names of the products. The values are dictionaries with the following keys:
| Key | Description
|:------------------------|:---------------|
| `cost ($/tonne)` | The cost to dispose of the product. Must be a time series.
| `limit (tonne)` | The maximum amount that can be disposed of. If an unlimited amount can be disposed, this key may be omitted. Must be a time series.
| Key | Description |
| :--------------- | :---------------------------------------------------------------------------------------------------------------------------------- |
| `cost ($/tonne)` | The cost to dispose of the product. Must be a time series. |
| `limit (tonne)` | The maximum amount that can be disposed of. If an unlimited amount can be disposed, this key may be omitted. Must be a time series. |
The keys in the `capacities (tonne)` dictionary should be the amounts (in tonnes). The values are dictionaries with the following keys:
| Key | Description
|:--------------------------------------|:---------------|
| `opening cost ($)` | The cost to open a plant of this size.
| `fixed operating cost ($)` | The cost to keep the plant open, even if the plant doesn't process anything. Must be a time series.
| `variable operating cost ($/tonne)` | The cost that the plant incurs to process each tonne of input. Must be a time series.
| Key | Description |
| :---------------------------------- | :-------------------------------------------------------------------------------------------------- |
| `opening cost ($)` | The cost to open a plant of this size. |
| `fixed operating cost ($)` | The cost to keep the plant open, even if the plant doesn't process anything. Must be a time series. |
| `variable operating cost ($/tonne)` | The cost that the plant incurs to process each tonne of input. Must be a time series. |
#### Example
```json
{
"plants": {
"F1": {
"input": "P1",
"outputs (tonne/tonne)": {
"P2": 0.2,
"P3": 0.5
},
"energy (GJ/tonne)": [0.12, 0.11],
"emissions (tonne/tonne)": {
"CO2": [0.052, 0.050],
"CH4": [0.003, 0.002]
"plants": {
"F1": {
"input": "P1",
"outputs (tonne/tonne)": {
"P2": 0.2,
"P3": 0.5
},
"energy (GJ/tonne)": [0.12, 0.11],
"emissions (tonne/tonne)": {
"CO2": [0.052, 0.05],
"CH4": [0.003, 0.002]
},
"locations": {
"L1": {
"latitude (deg)": 0.0,
"longitude (deg)": 0.0,
"disposal": {
"P2": {
"cost ($/tonne)": [-10.0, -12.0],
"limit (tonne)": [1.0, 1.0]
}
},
"storage": {
"cost ($/tonne)": [5.0, 5.3],
"limit (tonne)": 100.0
},
"capacities (tonne)": {
"100": {
"opening cost ($)": [500, 530],
"fixed operating cost ($)": [300.0, 310.0],
"variable operating cost ($/tonne)": [5.0, 5.2]
},
"locations": {
"L1": {
"latitude (deg)": 0.0,
"longitude (deg)": 0.0,
"disposal": {
"P2": {
"cost ($/tonne)": [-10.0, -12.0],
"limit (tonne)": [1.0, 1.0]
}
},
"storage": {
"cost ($/tonne)": [5.0, 5.3],
"limit (tonne)": 100.0,
},
"capacities (tonne)": {
"100": {
"opening cost ($)": [500, 530],
"fixed operating cost ($)": [300.0, 310.0],
"variable operating cost ($/tonne)": [5.0, 5.2],
},
"500": {
"opening cost ($)": [750, 760],
"fixed operating cost ($)": [400.0, 450.0],
"variable operating cost ($/tonne)": [5.0, 5.2]
}
}
}
"500": {
"opening cost ($)": [750, 760],
"fixed operating cost ($)": [400.0, 450.0],
"variable operating cost ($/tonne)": [5.0, 5.2]
}
}
}
}
}
}
}
```
### Geographic database
Instead of specifying locations using latitudes and longitudes, it is also possible to specify them using unique identifiers, such as the name of a US state, or the county FIPS code. This works anywhere `latitude (deg)` and `longitude (deg)` are expected. For example, instead of:
```json
{
"initial amounts": {
"C1": {
"latitude (deg)": 37.27182,
"longitude (deg)": -119.2704,
"amount (tonne)": [934.56, 934.56]
},
"initial amounts": {
"C1": {
"latitude (deg)": 37.27182,
"longitude (deg)": -119.2704,
"amount (tonne)": [934.56, 934.56]
}
}
}
```
is is possible to write:
```json
{
"initial amounts": {
"C1": {
"location": "us-state:CA",
"amount (tonne)": [934.56, 934.56]
},
"initial amounts": {
"C1": {
"location": "us-state:CA",
"amount (tonne)": [934.56, 934.56]
}
}
}
```
Location names follow the format `db:id`, where `db` is the name of the database and `id` is the identifier for a specific location. RELOG currently includes the following databases:
Database | Description | Examples
:--------|:------------|:---------
`us-state`| List of states of the United States. | `us-state:IL` (State of Illinois)
`2018-us-county` | List of United States counties, as of 2018. IDs are 5-digit FIPS codes. | `2018-us-county:17043` (DuPage county in Illinois)
| Database | Description | Examples |
| :--------------- | :---------------------------------------------------------------------- | :------------------------------------------------- |
| `us-state` | List of states of the United States. | `us-state:IL` (State of Illinois) |
| `2018-us-county` | List of United States counties, as of 2018. IDs are 5-digit FIPS codes. | `2018-us-county:17043` (DuPage county in Illinois) |
### Current limitations
* Each plant can only be opened exactly once. After open, the plant remains open until the end of the simulation.
* Plants can be expanded at any time, even long after they are open.
* All material available at the beginning of a time period must be entirely processed by the end of that time period. It is not possible to store unprocessed materials from one time period to the next.
* Up to two plant sizes are currently supported. Variable operating costs must be the same for all plant sizes.
* Accurate driving distances are only available for the continental United States.
- Each plant can only be opened exactly once. After open, the plant remains open until the end of the simulation.
- Plants can be expanded at any time, even long after they are open.
- All material available at the beginning of a time period must be entirely processed by the end of that time period. It is not possible to store unprocessed materials from one time period to the next.
- Up to two plant sizes are currently supported. Variable operating costs must be the same for all plant sizes.
- Accurate driving distances are only available for the continental United States.
## Output Data Format (JSON)

130
docs/src/model.md
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@ -6,59 +6,61 @@ In this page, we describe the precise mathematical optimization model used by RE
### Sets
Symbol | Description
:-------|:------------
$L$ | Set of locations holding the original material to be recycled
$M$ | Set of materials recovered during the reverse manufacturing process
$P$ | Set of potential plants to open
$T = \{ 1, \ldots, t^{max} \}$ | Set of time periods
| Symbol | Description |
| :----------------------------- | :-------------------------------------------------------------------- |
| $L$ | Set of collection centers holding the primary material to be recycled |
| $M$ | Set of materials recovered during the reverse manufacturing process |
| $P$ | Set of potential plants to open |
| $T = \{ 1, \ldots, t^{max} \}$ | Set of time periods |
### Constants
#### Plants
Symbol | Description | Unit
:-------|:------------|:---
$c^\text{disp}_{pmt}$ | Cost of disposing one tonne of material $m$ at plant $p$ during time $t$ | \$/tonne/km
$c^\text{exp}_{pt}$ | Cost of adding one tonne of capacity to plant $p$ at time $t$ | \$/tonne
$c^\text{open}_{pt}$ | Cost of opening plant $p$ at time $t$, at minimum capacity | $
$c^\text{f-base}_{pt}$ | Fixed cost of keeping plant $p$ open during time period $t$ | $
$c^\text{f-exp}_{pt}$ | Increase in fixed cost for each additional tonne of capacity | \$/tonne
$c^\text{var}_{pt}$ | Variable cost of processing one tonne of input at plant $p$ at time $t$ | \$/tonne
$c^\text{store}_{pt}$ | Cost of storing one tonne of original material at plant $p$ at time $t$ | \$/tonne
$m^\text{min}_p$ | Minimum capacity of plant $p$ | tonne
$m^\text{max}_p$ | Maximum capacity of plant $p$ | tonne
$m^\text{disp}_{pmt}$ | Maximum amount of material $m$ that plant $p$ can dispose of during time $t$ | tonne
$m^\text{store}_p$ | Maximum amount of original material that plant $p$ can store for later processing. | tonne
| Symbol | Description | Unit |
| :---------------------- | :------------------------------------------------------------------------------------- | :---------- |
| $c^\text{exp}_{pt}$ | Cost of adding one tonne of capacity to plant $p$ at time $t$ | \$/tonne |
| $c^\text{f-base}_{pt}$ | Fixed cost of keeping plant $p$ open during time period $t$ | $ |
| $c^\text{f-exp}_{pt}$ | Increase in fixed cost for each additional tonne of capacity | \$/tonne |
| $c^\text{open}_{pt}$ | 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 |
| $m^\text{max}_p$ | Maximum capacity of plant $p$ | tonne |
| $m^\text{min}_p$ | Minimum 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 |
#### Products
Symbol | Description | Unit
:-------|:------------|:---
$\alpha_{pm}$ | Amount of material $m$ recovered by plant $t$ for each tonne of original material | tonne/tonne
$m^\text{initial}_{lt}$ | Amount of original material to be recycled at location $l$ during time $t$ | tonne
| Symbol | Description | Unit |
| :---------------------- | :------------------------------------------------------------------------------------------------------- | :---------- |
| $\alpha_{pm}$ | Amount of material $m$ recovered by plant $t$ for each tonne of primary material | tonne/tonne |
| $c^\text{acq}_{lt}$ | Cost of acquiring primary material at collection center $l$ during time $t$ | \$/tonne |
| $c^\text{c-disp}_{lt}$ | Cost of disposing primary material at collection center $l$ during time $t$ | \$/tonne |
| $m^\text{c-disp}_{t}$ | Maximum amount of primary material that can be disposed of across all collection centers during time $t$ | tonne |
| $m^\text{initial}_{lt}$ | Amount of primary material available to be recycled at collection center $l$ during time $t$ | tonne |
#### Transportation
Symbol | Description | Unit
:-------|:------------|:---
$c^\text{tr}_{t}$ | Transportation cost during time $t$ | \$/tonne/km
$d_{lp}$ | Distance between plant $p$ and location $l$ | km
| Symbol | Description | Unit |
| :---------------- | :--------------------------------------------------- | :---------- |
| $c^\text{tr}_{t}$ | Cost to transport primary material during time $t$ | \$/tonne/km |
| $d_{lp}$ | Distance between plant $p$ and collection center $l$ | km |
### Decision variables
Symbol | Description | Unit
:-------|:------------|:---
$q_{mpt}$ | Amount of material $m$ recovered by plant $p$ during time $t$ | tonne
$u_{pt}$ | Binary variable that equals 1 if plant $p$ starts operating at time $t$ | Boolean
$w_{pt}$ | Extra capacity (amount above the minimum) added to plant $p$ during time $t$ | tonne
$x_{pt}$ | Binary variable that equals 1 if plant $p$ is operational at time $t$ | Boolean
$y_{lpt}$ | Amount of product sent from location $l$ to plant $p$ during time $t$ | tonne
$z^{\text{disp}}_{mpt}$ | Amount of material $m$ disposed of by plant $p$ during time $t$ | tonne
$z^{\text{store}}_{pt}$ | Amount of original material in storage at plant $p$ by the end of time period $t$ | tonne
$z^{\text{proc}}_{mpt}$ | Amount of original material processed by plant $p$ during time period $t$ | tonne
| Symbol | Description | Unit |
| :------------------------ | :-------------------------------------------------------------------------------------- | :------ |
| $q_{mpt}$ | Amount of material $m$ recovered by plant $p$ during time $t$ | tonne |
| $u_{pt}$ | Binary variable that equals 1 if plant $p$ starts operating at time $t$ | Boolean |
| $w_{pt}$ | Extra capacity (amount above the minimum) added to plant $p$ during time $t$ | tonne |
| $x_{pt}$ | Binary variable that equals 1 if plant $p$ is operational at time $t$ | Boolean |
| $y_{lpt}$ | Amount of primary material sent from collection center $l$ to plant $p$ during time $t$ | tonne |
| $z^{\text{p-disp}}_{mpt}$ | Amount of recovered material $m$ disposed of by plant $p$ during time $t$ | tonne |
| $z^{\text{c-disp}}_{lt}$ | Amount of primary material disposed of at collection center $l$ during time $t$ | tonne |
| $z^{\text{store}}_{pt}$ | Amount of primary material in storage at plant $p$ by the end of time period $t$ | tonne |
| $z^{\text{proc}}_{mpt}$ | Amount of primary material processed by plant $p$ during time period $t$ | tonne |
### Objective function
@ -73,37 +75,52 @@ RELOG minimizes the overall capital, production and transportation costs:
\sum_{i=1}^t c^\text{f-exp}_{pt} w_{pi} +
c^{\text{exp}}_{pt} w_{pt}
\right] + \\
&
&
\sum_{t \in T} \sum_{p \in P} \left[
c^{\text{store}}_{pt} z^{\text{store}}_{pt} +
c^{\text{proc}}_{pt} z^{\text{proc}}_{pt}
\right] + \\
&
\sum_{t \in T} \sum_{l \in L} \sum_{p \in P}
c^{\text{tr}}_t d_{lp} y_{lpt}
c^{\text{tr}}_t d_{lp} y_{lpt} +
\\
&
\sum_{t \in T} \sum_{p \in P} \sum_{m \in M} c^{\text{disp}}_{pmt} z_{pmt}
\sum_{t \in T} \sum_{p \in P} \sum_{m \in M} c^{\text{p-disp}}_{pmt} z_{pmt} +
\\
&
\sum_{t \in T} \sum_{l \in L} c^\text{acq}_{lt} \left(
m^\text{initial}_{lt} - z^{\text{c-disp}}_{lt}
\right) + c^\text{c-disp}_{lt} z^{\text{c-disp}}_{lt}
\end{align*}
```
In the first line, we have (i) opening costs, if plant starts operating at time $t$, (ii) fixed operating costs, if plant is operational, (iii) additional fixed operating costs coming from expansion performed in all previous time periods up to the current one, and finally (iv) the expansion costs during the current time period.
In the second line, we have storage and variable processing costs.
In the third line, we have transportation costs.
In the fourth line, we have the disposal costs.
In the fourth line, we have disposal costs at the plants.
In the fifth line, we have acquisition and disposal cost at the collection centers.
### Constraints
* All original materials must be sent to a plant:
- All primary material must either be sent to a plant for processing or disposed of at the collection center:
```math
\begin{align*}
& \sum_{p \in P} y_{lpt} = m^\text{initial}_{lt}
& \sum_{p \in P} y_{lpt} + z^{\text{c-disp}}_{lt} = m^\text{initial}_{lt}
& \forall l \in L, t \in T
\end{align*}
```
* Amount received equals amount processed plus stored. Furthermore, all original material should be processed by the end of the simulation.
- There is a limit on how much primary material can be disposed of at the collection centers:
```math
\begin{align*}
& \sum_{l \in L} z^{\text{c-disp}}_{lt} \leq m^\text{c-disp}_{t}
& t \in T
\end{align*}
```
- Amount received equals amount processed plus stored. Furthermore, all primary material should be processed by the end of the simulation.
```math
\begin{align*}
@ -117,7 +134,7 @@ In the fourth line, we have the disposal costs.
\end{align*}
```
* Plants have a limited processing capacity. Furthermore, if a plant is closed, it has zero processing capacity:
- Plants have a limited processing capacity. Furthermore, if a plant is closed, it has zero processing capacity:
```math
\begin{align*}
@ -126,7 +143,7 @@ In the fourth line, we have the disposal costs.
\end{align*}
```
* Plants have limited storage capacity. Furthermore, if a plant is closed, is has zero storage capacity:
- Plants have limited storage capacity. Furthermore, if a plant is closed, is has zero storage capacity:
```math
\begin{align*}
@ -135,7 +152,7 @@ In the fourth line, we have the disposal costs.
\end{align*}
```
* Plants can only be expanded up to their maximum capacity. Furthermore, if a plant is closed, it cannot be expanded:
- Plants can only be expanded up to their maximum capacity. Furthermore, if a plant is closed, it cannot be expanded:
```math
\begin{align*}
@ -144,7 +161,7 @@ In the fourth line, we have the disposal costs.
\end{align*}
```
* Amount of recovered material is proportional to amount processed:
- Amount of recovered material is proportional to amount processed:
```math
\begin{align*}
@ -153,16 +170,16 @@ In the fourth line, we have the disposal costs.
\end{align*}
```
* Because we only consider a single type of plant, all recovered material must be immediately disposed of. In RELOG's full model, recovered materials may be sent to another plant for further processing.
- Because we only consider a single type of plant, all recovered material must be immediately disposed of. In RELOG's full model, recovered materials may be sent to another plant for further processing.
```math
\begin{align*}
& q_{mpt} = z_{mpt}
& q_{mpt} = z^{\text{p-disp}}_{mpt}
& \forall m \in M, p \in P, t \in T
\end{align*}
```
* A plant is operational at time $t$ if it was operational at time $t-1$ or it was built at time $t$. This constraint also prevents a plant from being built multiple times.
- A plant is operational at time $t$ if it was operational at time $t-1$ or it was built at time $t$. This constraint also prevents a plant from being built multiple times.
```math
\begin{align*}
@ -173,8 +190,7 @@ In the fourth line, we have the disposal costs.
\end{align*}
```
* Variable bounds:
- Variable bounds:
```math
\begin{align*}
@ -188,9 +204,11 @@ In the fourth line, we have the disposal costs.
& \forall p \in P, t \in T \\
& y_{lpt} \geq 0
& \forall l \in L, p \in P, t \in T \\
& z^{\text{c-disp}}_{lt} \geq 0
& l \in L, t \in T \\
& z^{\text{store}}_{pt} \geq 0
& p \in P, t \in T \\
& z^{\text{disp}}_{mpt}, z^{\text{proc}}_{mpt} \geq 0
& z^{\text{p-disp}}_{mpt}, z^{\text{proc}}_{mpt} \geq 0
& \forall m \in M, p \in P, t \in T
\end{align*}
```

10
relog-web/src/casebuilder/ProductBlock.js
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@ -118,9 +118,17 @@ const ProductBlock = (props) => {
/>
<h1 style={{ display: nCenters == 0 ? "none" : "block" }}>
Disposal
Acquisition & disposal
</h1>
<div style={{ display: nCenters == 0 ? "none" : "block" }}>
<TextInputRow
label="Acquisition cost"
unit="$/tonne"
tooltip="Cost of acquiring one tonne of this product at a collection center."
value={props.value["acquisition cost ($/tonne)"]}
onChange={(v) => onChange("acquisition cost ($/tonne)", v)}
validate="floatList"
/>
<TextInputRow
label="Disposal cost"
unit="$/tonne"

1
relog-web/src/casebuilder/defaults.js
Unescape View File

@ -1,5 +1,6 @@
export const defaultProduct = {
"initial amounts": {},
"acquisition cost ($/tonne)": "0",
"disposal cost ($/tonne)": "0",
"disposal limit (tonne)": "0",
"disposal limit (%)": "",

27
relog-web/src/casebuilder/export.js
Unescape View File

@ -139,12 +139,14 @@ export const exportProduct = (original, parameters) => {
);
// Copy cost time series (with inflation)
["disposal cost ($/tonne)", "transportation cost ($/km/tonne)"].forEach(
(key) => {
const v = exportValue(original[key], T, R);
if (v.length > 0) result[key] = v;
}
);
[
"disposal cost ($/tonne)",
"acquisition cost ($/tonne)",
"transportation cost ($/km/tonne)",
].forEach((key) => {
const v = exportValue(original[key], T, R);
if (v.length > 0) result[key] = v;
});
// Copy dictionaries
["transportation emissions (tonne/km/tonne)"].forEach((key) => {
@ -344,16 +346,19 @@ export const importProduct = (original) => {
const [R, T] = computeInflationAndTimeHorizon(original, [
"transportation cost ($/km/tonne)",
"disposal cost ($/tonne)",
"acquisition cost ($/tonne)",
]);
parameters["inflation rate (%)"] = String((R - 1) * 100);
parameters["time horizon (years)"] = String(T);
// Import cost lists
["transportation cost ($/km/tonne)", "disposal cost ($/tonne)"].forEach(
(key) => {
prod[key] = importList(original[key], R);
}
);
[
"transportation cost ($/km/tonne)",
"disposal cost ($/tonne)",
"acquisition cost ($/tonne)",
].forEach((key) => {
prod[key] = importList(original[key], R);
});
// Import dicts
["transportation emissions (tonne/km/tonne)"].forEach((key) => {

6
relog-web/src/casebuilder/export.test.js
Unescape View File

@ -27,6 +27,7 @@ const sampleProductsOriginal = [
"amount (tonne)": [100, 200, 300],
},
},
"acquisition cost ($/tonne)": "4",
"disposal cost ($/tonne)": "50",
"disposal limit (tonne)": "30",
"disposal limit (%)": "",
@ -57,6 +58,7 @@ const sampleProductsOriginal = [
"amount (tonne)": [100, 200, 300],
},
},
"acquisition cost ($/tonne)": "4",
"disposal cost ($/tonne)": "50",
"disposal limit (tonne)": "",
"disposal limit (%)": "10",
@ -87,6 +89,7 @@ const sampleProductsOriginal = [
"amount (tonne)": [100, 200, 300],
},
},
"acquisition cost ($/tonne)": "4",
"disposal cost ($/tonne)": "50",
"disposal limit (tonne)": "",
"disposal limit (%)": "",
@ -118,6 +121,7 @@ const sampleProductsExported = [
"amount (tonne)": [100, 200, 300],
},
},
"acquisition cost ($/tonne)": [4, 8, 16],
"disposal cost ($/tonne)": [50, 100, 200],
"disposal limit (tonne)": [30, 30, 30],
"transportation cost ($/km/tonne)": [0, 0, 0],
@ -145,6 +149,7 @@ const sampleProductsExported = [
"amount (tonne)": [100, 200, 300],
},
},
"acquisition cost ($/tonne)": [4, 4, 4],
"disposal cost ($/tonne)": [50, 50, 50],
"disposal limit (tonne)": [30, 60, 90],
"transportation cost ($/km/tonne)": [5, 5, 5],
@ -172,6 +177,7 @@ const sampleProductsExported = [
"amount (tonne)": [100, 200, 300],
},
},
"acquisition cost ($/tonne)": [4, 4, 4],
"disposal cost ($/tonne)": [50, 50, 50],
"transportation cost ($/km/tonne)": [5, 5, 5],
},

6
src/instance/parse.jl
Unescape View File

@ -51,6 +51,7 @@ function parse(json)::Instance
emissions = Dict()
disposal_limit = zeros(T)
disposal_cost = zeros(T)
acquisition_cost = zeros(T)
if "transportation energy (J/km/tonne)" in keys(product_dict)
energy = product_dict["transportation energy (J/km/tonne)"]
@ -68,6 +69,10 @@ function parse(json)::Instance
disposal_cost = product_dict["disposal cost (\$/tonne)"]
end
if "acquisition cost (\$/tonne)" in keys(product_dict)
acquisition_cost = product_dict["acquisition cost (\$/tonne)"]
end
prod_centers = []
product = Product(
@ -77,6 +82,7 @@ function parse(json)::Instance
emissions,
disposal_limit,
disposal_cost,
acquisition_cost,
prod_centers,
)
push!(products, product)

1
src/instance/structs.jl
Unescape View File

@ -15,6 +15,7 @@ mutable struct Product
transportation_emissions::Dict{String,Vector{Float64}}
disposal_limit::Vector{Float64}
disposal_cost::Vector{Float64}
acquisition_cost::Vector{Float64}
collection_centers::Vector
end

10
src/model/build.jl
Unescape View File

@ -149,10 +149,16 @@ function create_objective_function!(model::JuMP.Model)
# Collection shipping node costs
for n in values(graph.collection_shipping_nodes), t = 1:T
# Disposal costs
# Acquisition costs
add_to_expression!(
obj,
n.location.product.acquisition_cost[t] * n.location.amount[t]
)
# Disposal costs -- in this case, we recover the acquisition cost.
add_to_expression!(
obj,
n.location.product.disposal_cost[t],
(n.location.product.disposal_cost[t] - n.location.product.acquisition_cost[t]),
model[:collection_dispose][n, t],
)
end

16
src/model/getsol.jl
Unescape View File

@ -46,6 +46,22 @@ function get_solution(model::JuMP.Model; marginal_costs = true)
"Amount (tonne)" => n.location.amount,
"Dispose (tonne)" =>
[JuMP.value(model[:collection_dispose][n, t]) for t = 1:T],
"Acquisition cost (\$)" =>
[
(
n.location.amount[t] -
JuMP.value(model[:collection_dispose][n, t])
) * n.location.product.acquisition_cost[t]
for t = 1:T
],
"Disposal cost (\$)" =>
[
(
JuMP.value(model[:collection_dispose][n, t])
* n.location.product.disposal_cost[t]
)
for t = 1:T
]
)
if marginal_costs
location_dict["Marginal cost (\$/tonne)"] = [

6
src/reports/products.jl
Unescape View File

@ -15,6 +15,8 @@ function products_report(solution; marginal_costs = true)::DataFrame
df."amount (tonne)" = Float64[]
df."amount disposed (tonne)" = Float64[]
df."marginal cost (\$/tonne)" = Float64[]
df."acquisition cost (\$)" = Float64[]
df."disposal cost (\$)" = Float64[]
T = length(solution["Energy"]["Plants (GJ)"])
for (prod_name, prod_dict) in solution["Products"]
for (location_name, location_dict) in prod_dict
@ -24,6 +26,8 @@ function products_report(solution; marginal_costs = true)::DataFrame
longitude = round(location_dict["Longitude (deg)"], digits = 6)
amount = location_dict["Amount (tonne)"][year]
amount_disposed = location_dict["Dispose (tonne)"][year]
acquisition_cost = location_dict["Acquisition cost (\$)"][year]
disposal_cost = location_dict["Disposal cost (\$)"][year]
push!(
df,
[
@ -35,6 +39,8 @@ function products_report(solution; marginal_costs = true)::DataFrame
amount,
marginal_cost,
amount_disposed,
acquisition_cost,
disposal_cost,
],
)
end

530
test/fixtures/s1.json vendored
Unescape View File

@ -1,358 +1,206 @@
{
"parameters": {
"time horizon (years)": 2,
"distance metric": "driving"
},
"products": {
"P1": {
"transportation cost ($/km/tonne)": [
0.015,
0.015
],
"transportation energy (J/km/tonne)": [
0.12,
0.11
],
"transportation emissions (tonne/km/tonne)": {
"CO2": [
0.052,
0.050
],
"CH4": [
0.003,
0.002
]
},
"initial amounts": {
"C1": {
"latitude (deg)": 7.0,
"longitude (deg)": 7.0,
"amount (tonne)": [
934.56,
934.56
]
},
"C2": {
"latitude (deg)": 7.0,
"longitude (deg)": 19.0,
"amount (tonne)": [
198.95,
198.95
]
},
"C3": {
"latitude (deg)": 84.0,
"longitude (deg)": 76.0,
"amount (tonne)": [
212.97,
212.97
]
},
"C4": {
"latitude (deg)": 21.0,
"longitude (deg)": 16.0,
"amount (tonne)": [
352.19,
352.19
]
},
"C5": {
"latitude (deg)": 32.0,
"longitude (deg)": 92.0,
"amount (tonne)": [
510.33,
510.33
]
},
"C6": {
"latitude (deg)": 14.0,
"longitude (deg)": 62.0,
"amount (tonne)": [
471.66,
471.66
]
},
"C7": {
"latitude (deg)": 30.0,
"longitude (deg)": 83.0,
"amount (tonne)": [
785.21,
785.21
]
},
"C8": {
"latitude (deg)": 35.0,
"longitude (deg)": 40.0,
"amount (tonne)": [
706.17,
706.17
]
},
"C9": {
"latitude (deg)": 74.0,
"longitude (deg)": 52.0,
"amount (tonne)": [
30.08,
30.08
]
},
"C10": {
"latitude (deg)": 22.0,
"longitude (deg)": 54.0,
"amount (tonne)": [
536.52,
536.52
]
}
},
"disposal limit (tonne)": [
1.0,
1.0
],
"disposal cost ($/tonne)": [
-1000,
-1000
]
"parameters": {
"time horizon (years)": 2,
"distance metric": "driving"
},
"products": {
"P1": {
"transportation cost ($/km/tonne)": [0.015, 0.015],
"transportation energy (J/km/tonne)": [0.12, 0.11],
"transportation emissions (tonne/km/tonne)": {
"CO2": [0.052, 0.05],
"CH4": [0.003, 0.002]
},
"initial amounts": {
"C1": {
"latitude (deg)": 7.0,
"longitude (deg)": 7.0,
"amount (tonne)": [934.56, 934.56]
},
"C2": {
"latitude (deg)": 7.0,
"longitude (deg)": 19.0,
"amount (tonne)": [198.95, 198.95]
},
"C3": {
"latitude (deg)": 84.0,
"longitude (deg)": 76.0,
"amount (tonne)": [212.97, 212.97]
},
"C4": {
"latitude (deg)": 21.0,
"longitude (deg)": 16.0,
"amount (tonne)": [352.19, 352.19]
},
"P2": {
"transportation cost ($/km/tonne)": [
0.02,
0.02
]
"C5": {
"latitude (deg)": 32.0,
"longitude (deg)": 92.0,
"amount (tonne)": [510.33, 510.33]
},
"P3": {
"transportation cost ($/km/tonne)": [
0.0125,
0.0125
]
"C6": {
"latitude (deg)": 14.0,
"longitude (deg)": 62.0,
"amount (tonne)": [471.66, 471.66]
},
"P4": {
"transportation cost ($/km/tonne)": [
0.0175,
0.0175
]
"C7": {
"latitude (deg)": 30.0,
"longitude (deg)": 83.0,
"amount (tonne)": [785.21, 785.21]
},
"C8": {
"latitude (deg)": 35.0,
"longitude (deg)": 40.0,
"amount (tonne)": [706.17, 706.17]
},
"C9": {
"latitude (deg)": 74.0,
"longitude (deg)": 52.0,
"amount (tonne)": [30.08, 30.08]
},
"C10": {
"latitude (deg)": 22.0,
"longitude (deg)": 54.0,
"amount (tonne)": [536.52, 536.52]
}
},
"disposal limit (tonne)": [1.0, 1.0],
"disposal cost ($/tonne)": [-1000, -1000],
"acquisition cost ($/tonne)": [0.5, 0.5]
},
"plants": {
"F1": {
"input": "P1",
"outputs (tonne/tonne)": {
"P2": 0.2,
"P3": 0.5
"P2": {
"transportation cost ($/km/tonne)": [0.02, 0.02]
},
"P3": {
"transportation cost ($/km/tonne)": [0.0125, 0.0125]
},
"P4": {
"transportation cost ($/km/tonne)": [0.0175, 0.0175]
}
},
"plants": {
"F1": {
"input": "P1",
"outputs (tonne/tonne)": {
"P2": 0.2,
"P3": 0.5
},
"energy (GJ/tonne)": [0.12, 0.11],
"emissions (tonne/tonne)": {
"CO2": [0.052, 0.05],
"CH4": [0.003, 0.002]
},
"locations": {
"L1": {
"latitude (deg)": 0.0,
"longitude (deg)": 0.0,
"disposal": {
"P2": {
"cost ($/tonne)": [-10.0, -10.0],
"limit (tonne)": [1.0, 1.0]
},
"energy (GJ/tonne)": [
0.12,
0.11
],
"emissions (tonne/tonne)": {
"CO2": [
0.052,
0.050
],
"CH4": [
0.003,
0.002
]
"P3": {
"cost ($/tonne)": [-10.0, -10.0],
"limit (tonne)": [1.0, 1.0]
}
},
"capacities (tonne)": {
"250.0": {
"opening cost ($)": [500.0, 500.0],
"fixed operating cost ($)": [30.0, 30.0],
"variable operating cost ($/tonne)": [30.0, 30.0]
},
"locations": {
"L1": {
"latitude (deg)": 0.0,
"longitude (deg)": 0.0,
"disposal": {
"P2": {
"cost ($/tonne)": [
-10.0,
-10.0
],
"limit (tonne)": [
1.0,
1.0
]
},
"P3": {
"cost ($/tonne)": [
-10.0,
-10.0
],
"limit (tonne)": [
1.0,
1.0
]
}
},
"capacities (tonne)": {
"250.0": {
"opening cost ($)": [
500.0,
500.0
],
"fixed operating cost ($)": [
30.0,
30.0
],
"variable operating cost ($/tonne)": [
30.0,
30.0
]
},
"1000.0": {
"opening cost ($)": [
1250.0,
1250.0
],
"fixed operating cost ($)": [
30.0,
30.0
],
"variable operating cost ($/tonne)": [
30.0,
30.0
]
}
}
},
"L2": {
"latitude (deg)": 0.5,
"longitude (deg)": 0.5,
"capacities (tonne)": {
"0.0": {
"opening cost ($)": [
1000,
1000
],
"fixed operating cost ($)": [
50.0,
50.0
],
"variable operating cost ($/tonne)": [
50.0,
50.0
]
},
"10000.0": {
"opening cost ($)": [
10000,
10000
],
"fixed operating cost ($)": [
50.0,
50.0
],
"variable operating cost ($/tonne)": [
50.0,
50.0
]
}
}
}
"1000.0": {
"opening cost ($)": [1250.0, 1250.0],
"fixed operating cost ($)": [30.0, 30.0],
"variable operating cost ($/tonne)": [30.0, 30.0]
}
}
},
"F2": {
"input": "P2",
"outputs (tonne/tonne)": {
"P3": 0.05,
"P4": 0.80
"L2": {
"latitude (deg)": 0.5,
"longitude (deg)": 0.5,
"capacities (tonne)": {
"0.0": {
"opening cost ($)": [1000, 1000],
"fixed operating cost ($)": [50.0, 50.0],
"variable operating cost ($/tonne)": [50.0, 50.0]
},
"locations": {
"L3": {
"latitude (deg)": 25.0,
"longitude (deg)": 65.0,
"disposal": {
"P3": {
"cost ($/tonne)": [
100.0,
100.0
]
}
},
"capacities (tonne)": {
"1000.0": {
"opening cost ($)": [
3000,
3000
],
"fixed operating cost ($)": [
50.0,
50.0
],
"variable operating cost ($/tonne)": [
50.0,
50.0
]
}
}
},
"L4": {
"latitude (deg)": 0.75,
"longitude (deg)": 0.20,
"capacities (tonne)": {
"10000": {
"opening cost ($)": [
3000,
3000
],
"fixed operating cost ($)": [
50.0,
50.0
],
"variable operating cost ($/tonne)": [
50.0,
50.0
]
}
}
}
"10000.0": {
"opening cost ($)": [10000, 10000],
"fixed operating cost ($)": [50.0, 50.0],
"variable operating cost ($/tonne)": [50.0, 50.0]
}
},
"F3": {
"input": "P4",
"locations": {
"L5": {
"latitude (deg)": 100.0,
"longitude (deg)": 100.0,
"capacities (tonne)": {
"15000": {
"opening cost ($)": [
0.0,
0.0
],
"fixed operating cost ($)": [
0.0,
0.0
],
"variable operating cost ($/tonne)": [
-15.0,
-15.0
]
}
}
}
}
}
}
},
"F2": {
"input": "P2",
"outputs (tonne/tonne)": {
"P3": 0.05,
"P4": 0.8
},
"locations": {
"L3": {
"latitude (deg)": 25.0,
"longitude (deg)": 65.0,
"disposal": {
"P3": {
"cost ($/tonne)": [100.0, 100.0]
}
},
"capacities (tonne)": {
"1000.0": {
"opening cost ($)": [3000, 3000],
"fixed operating cost ($)": [50.0, 50.0],
"variable operating cost ($/tonne)": [50.0, 50.0]
}
}
},
"F4": {
"input": "P3",
"locations": {
"L6": {
"latitude (deg)": 50.0,
"longitude (deg)": 50.0,
"capacities (tonne)": {
"10000": {
"opening cost ($)": [
0.0,
0.0
],
"fixed operating cost ($)": [
0.0,
0.0
],
"variable operating cost ($/tonne)": [
-15.0,
-15.0
]
}
}
}
"L4": {
"latitude (deg)": 0.75,
"longitude (deg)": 0.2,
"capacities (tonne)": {
"10000": {
"opening cost ($)": [3000, 3000],
"fixed operating cost ($)": [50.0, 50.0],
"variable operating cost ($/tonne)": [50.0, 50.0]
}
}
}
}
},
"F3": {
"input": "P4",
"locations": {
"L5": {
"latitude (deg)": 100.0,
"longitude (deg)": 100.0,
"capacities (tonne)": {
"15000": {
"opening cost ($)": [0.0, 0.0],
"fixed operating cost ($)": [0.0, 0.0],
"variable operating cost ($/tonne)": [-15.0, -15.0]
}
}
}
}
},
"F4": {
"input": "P3",
"locations": {
"L6": {
"latitude (deg)": 50.0,
"longitude (deg)": 50.0,
"capacities (tonne)": {
"10000": {
"opening cost ($)": [0.0, 0.0],
"fixed operating cost ($)": [0.0, 0.0],
"variable operating cost ($/tonne)": [-15.0, -15.0]
}
}
}
}
}
}
}
}

2
test/src/instance/parse_test.jl
Unescape View File

@ -43,10 +43,12 @@ function instance_parse_test()
p1 = product_name_to_product["P1"]
@test p1.disposal_limit == [1.0, 1.0]
@test p1.disposal_cost == [-1000.0, -1000.0]
@test p1.acquisition_cost == [0.5, 0.5]
p2 = product_name_to_product["P2"]
@test p2.disposal_limit == [0.0, 0.0]
@test p2.disposal_cost == [0.0, 0.0]
@test p2.acquisition_cost == [0.0, 0.0]
p3 = product_name_to_product["P3"]
@test length(plant.output) == 2

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