|`time horizon (years)` | Number of years in the simulation.
|`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. |
| `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"`.
| `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
#### Example
```json
```json
{
{
"parameters": {
"parameters": {
"time horizon (years)": 2,
"time horizon (years)": 2,
"building period (years)": [1],
"building period (years)": [1],
"distance metric": "driving",
"distance metric": "driving"
}
}
}
}
```
```
@ -32,22 +32,23 @@ 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:
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:
|`transportation cost ($/km/tonne)` | The cost to transport this product. Must be a time series.
| `transportation cost ($/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 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.
| `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.
| `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 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 ($/tonne)` | Cost of disposing one tonne of this product at a collection center. If omitted, defaults to zero. This parameter has no effect on product disposal costs at plants.
| `disposal cost ($/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:
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:
@ -98,46 +100,45 @@ 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:
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:
| `input` | The name of the product that this plant takes as input. Only one input is accepted per plant.
| `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.
| `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.
|`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.
|`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).
| `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:
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:
| `cost ($/tonne)` | The cost to dispose of the product. Must be a time series.
| `cost ($/tonne)` | The cost to dispose of the product. Must be a time series. |
| `limit (tonne)` | The maximum amount that can be disposed of. If an unlimited amount can be disposed, this key may be omitted. Must be a time series.
| `limit (tonne)` | The maximum amount that can be disposed of. If an unlimited amount can be disposed, this key may be omitted. Must be a time series. |
The keys in the `capacities (tonne)` dictionary should be the amounts (in tonnes). The values are dictionaries with the following keys:
The keys in the `capacities (tonne)` dictionary should be the amounts (in tonnes). The values are dictionaries with the following keys:
| `opening cost ($)`| The cost to open a plant of this size.
| `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.
| `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.
| `variable operating cost ($/tonne)` | The cost that the plant incurs to process each tonne of input. Must be a time series. |
#### Example
#### Example
@ -152,7 +153,7 @@ The keys in the `capacities (tonne)` dictionary should be the amounts (in tonnes
},
},
"energy (GJ/tonne)": [0.12, 0.11],
"energy (GJ/tonne)": [0.12, 0.11],
"emissions (tonne/tonne)": {
"emissions (tonne/tonne)": {
"CO2": [0.052, 0.050],
"CO2": [0.052, 0.05],
"CH4": [0.003, 0.002]
"CH4": [0.003, 0.002]
},
},
"locations": {
"locations": {
@ -167,13 +168,13 @@ The keys in the `capacities (tonne)` dictionary should be the amounts (in tonnes
},
},
"storage": {
"storage": {
"cost ($/tonne)": [5.0, 5.3],
"cost ($/tonne)": [5.0, 5.3],
"limit (tonne)": 100.0,
"limit (tonne)": 100.0
},
},
"capacities (tonne)": {
"capacities (tonne)": {
"100": {
"100": {
"opening cost ($)": [500, 530],
"opening cost ($)": [500, 530],
"fixed operating cost ($)": [300.0, 310.0],
"fixed operating cost ($)": [300.0, 310.0],
"variable operating cost ($/tonne)": [5.0, 5.2],
"variable operating cost ($/tonne)": [5.0, 5.2]
},
},
"500": {
"500": {
"opening cost ($)": [750, 760],
"opening cost ($)": [750, 760],
@ -191,6 +192,7 @@ The keys in the `capacities (tonne)` dictionary should be the amounts (in tonnes
### Geographic database
### 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:
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
```json
{
{
"initial amounts": {
"initial amounts": {
@ -198,35 +200,38 @@ Instead of specifying locations using latitudes and longitudes, it is also possi
"latitude (deg)": 37.27182,
"latitude (deg)": 37.27182,
"longitude (deg)": -119.2704,
"longitude (deg)": -119.2704,
"amount (tonne)": [934.56, 934.56]
"amount (tonne)": [934.56, 934.56]
},
}
}
}
}
}
```
```
is is possible to write:
is is possible to write:
```json
```json
{
{
"initial amounts": {
"initial amounts": {
"C1": {
"C1": {
"location": "us-state:CA",
"location": "us-state:CA",
"amount (tonne)": [934.56, 934.56]
"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:
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:
`us-state`| List of states of the United States. | `us-state:IL` (State of Illinois)
| `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)
| `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
### Current limitations
* Each plant can only be opened exactly once. After open, the plant remains open until the end of the simulation.
- 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.
- 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.
- 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.
- 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.
- Accurate driving distances are only available for the continental United States.
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 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 second line, we have storage and variable processing costs.
In the third line, we have transportation 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
### 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:
- Amount received equals amount processed plus stored. Furthermore, all primary material should be processed by the end of the simulation.
```math
```math
\begin{align*}
\begin{align*}
@ -117,7 +134,7 @@ In the fourth line, we have the disposal costs.
\end{align*}
\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
```math
\begin{align*}
\begin{align*}
@ -126,7 +143,7 @@ In the fourth line, we have the disposal costs.
\end{align*}
\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
```math
\begin{align*}
\begin{align*}
@ -135,7 +152,7 @@ In the fourth line, we have the disposal costs.
\end{align*}
\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
```math
\begin{align*}
\begin{align*}
@ -144,7 +161,7 @@ In the fourth line, we have the disposal costs.
\end{align*}
\end{align*}
```
```
* Amount of recovered material is proportional to amount processed:
- Amount of recovered material is proportional to amount processed:
```math
```math
\begin{align*}
\begin{align*}
@ -153,16 +170,16 @@ In the fourth line, we have the disposal costs.
\end{align*}
\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
```math
\begin{align*}
\begin{align*}
& q_{mpt} = z_{mpt}
& q_{mpt} = z^{\text{p-disp}}_{mpt}
& \forall m \in M, p \in P, t \in T
& \forall m \in M, p \in P, t \in T
\end{align*}
\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
```math
\begin{align*}
\begin{align*}
@ -173,8 +190,7 @@ In the fourth line, we have the disposal costs.
\end{align*}
\end{align*}
```
```
- Variable bounds:
* Variable bounds:
```math
```math
\begin{align*}
\begin{align*}
@ -188,9 +204,11 @@ In the fourth line, we have the disposal costs.
