Allow user to specify product acquisition costs

Author: iSoron

CHANGELOG.md

@@ -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

docs/make.jl

@@ -15,5 +15,3 @@ function make()
         )
     )
 end
-
-make()

docs/src/format.md

@@ -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*}
 ```

docs/src/model.md

@@ -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"

relog-web/src/casebuilder/ProductBlock.js

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

relog-web/src/casebuilder/defaults.js

@@ -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) => {

relog-web/src/casebuilder/export.js

@@ -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],
   },