Docs: rename m^base to m^min

docs/index.html

@@ -136,7 +136,7 @@
         <div class="col-md-9" role="main">
 
 <h1 id="relog-reverse-logistics-optimization">RELOG: Reverse Logistics Optimization</h1>
-<p><strong>RELOG</strong> is a supply chain optimization package focusing on reverse logistics and reverse manufacturing. The package uses Mixed-Integer Linear Programming to determine where to build recycling plants, what size should these plants have and which customers should be served by which plants. The package supports custom reverse logistics pipelines, with multiple types of plants, multiple types of product and multiple time periods.</p>
+<p><strong>RELOG</strong> is an open-source supply chain optimization package focusing on reverse logistics and reverse manufacturing. The package uses Mixed-Integer Linear Programming to determine where to build recycling plants, what size should these plants have and which customers should be served by which plants. The package supports custom reverse logistics pipelines, with multiple types of plants, multiple types of product and multiple time periods.</p>
 <h3 id="table-of-contents">Table of Contents</h3>
 <ul>
 <li><a href="usage/">Usage</a></li>
@@ -282,5 +282,5 @@ POSSIBILITY OF SUCH DAMAGE.
 
 <!--
 MkDocs version : 1.1.2
-Build Date UTC : 2020-08-21 20:55:30.655918+00:00
+Build Date UTC : 2020-08-21 22:27:01.041378+00:00
 -->

docs/model/index.html

@@ -130,6 +130,7 @@
                 <li class="third-level"><a href="#decision-variables">Decision variables</a></li>
                 <li class="third-level"><a href="#objective-function">Objective function</a></li>
                 <li class="third-level"><a href="#constraints">Constraints</a></li>
+                <li class="third-level"><a href="#complete-optimization-model">Complete optimization model</a></li>
     </ul>
 </div></div>
         <div class="col-md-9" role="main">
@@ -142,7 +143,7 @@
 <li>$L$ - Set of locations holding the original material to be recycled</li>
 <li>$M$ - Set of materials recovered during the reverse manufacturing process</li>
 <li>$P$ - Set of potential plants to open</li>
-<li>$T={1, \ldots, t^{max}}$ - Set of time periods</li>
+<li>$T = { 1, \ldots, t^{max} } $ - Set of time periods</li>
 </ul>
 <h3 id="constants">Constants</h3>
 <p><strong>Plants:</strong></p>
@@ -160,7 +161,7 @@
 <p><strong>Products:</strong></p>
 <ul>
 <li>$\alpha_{pm}$ - Amount of material $m$ recovered by plant $t$ for each tonne of original material (<code>tonne/tonne</code>)</li>
-<li>$m^\text{initial}_{lt}$ - Amount of original material to be recycled at location $l$ during time $t$ (tonne)</li>
+<li>$m^\text{initial}_{lt}$ - Amount of original material to be recycled at location $l$ during time $t$ (<code>tonne</code>)</li>
 </ul>
 <p><strong>Transportation:</strong></p>
 <ul>
@@ -213,7 +214,7 @@ In the third line, we have the disposal costs.</p>
 </ul>
 <p>
 <script type="math/tex; mode=display">\begin{align}
-    & \sum_{l \in L} y_{lpt} \leq m^\text{base}_p x_p + \sum_{i=1}^t w_p
+    & \sum_{l \in L} y_{lpt} \leq m^\text{min}_p x_p + \sum_{i=1}^t w_p
         & \forall p \in P, t \in T
 \end{align}</script>
 </p>
@@ -270,9 +271,53 @@ In the third line, we have the disposal costs.</p>
         & \forall p \in P, t \in T \\
     & y_{lpt} \geq 0
         & \forall l \in L, p \in P, t \in T \\
-    & m^\text{disp}_{pmt} \geq z_{mpt} \geq 0
-        & \forall m \in M, p \in P, t \in T \\
+    & m^\text{disp}_{mpt} \geq z_{mpt} \geq 0
+        & \forall m \in M, p \in P, t \in T
 \end{align}</script>
+</p>
+<h3 id="complete-optimization-model">Complete optimization model</h3>
+<p>
+<script type="math/tex; mode=display">\begin{align*}
+    \text{minimize} \;\; &
+        \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{exp}}_{pt} w_{pt}
+            \right] + \\
+    &
+        \sum_{t \in T} \sum_{l \in L} \sum_{p \in P} \left[
+            c^{\text{tr}}_t d_{lp} + c^{\text{var}}_{pt}
+        \right]  y_{lpt} + \\
+    &
+        \sum_{t \in T} \sum_{p \in P} \sum_{m \in M} c^{\text{disp}}_{pmt} z_{pmt} \\
+    \text{subject to } & \sum_{p \in P} y_{lpt} = m^\text{initial}_{lt} 
+        & \forall l \in L, t \in T \\
+    & \sum_{l \in L} y_{lpt} \leq m^\text{min}_p x_p + \sum_{i=1}^t w_p
+        & \forall p \in P, t \in T \\
+    & \sum_{i=1}^t w_p \leq m^\text{max}_p x_p
+        & \forall p \in P, t \in T \\
+    & q_{mpt} = \alpha_{pm} \sum_{l \in L} y_{lpt}
+        & \forall m \in M, p \in P, t \in T \\
+    & q_{mpt} = z_{mpt}
+        & \forall m \in M, p \in P, t \in T \\
+    & 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 \\
+    & q_{mpt} \geq 0
+        & \forall m \in M, p \in P, t \in T \\
+    & u_{pt} \in \{0,1\}
+        & \forall p \in P, t \in T \\
+    & w_{pt} \geq 0
+        & \forall p \in P, t \in T \\
+    & x_{pt} \in \{0,1\}
+        & \forall p \in P, t \in T \\
+    & y_{lpt} \geq 0
+        & \forall l \in L, p \in P, t \in T \\
+    & m^\text{disp}_{mpt} \geq z_{mpt} \geq 0
+        & \forall m \in M, p \in P, t \in T
+\end{align*}</script>
 </p></div>
         
         

src/docs/model.md

@@ -81,7 +81,7 @@ In the third line, we have the disposal costs.
 * Plants have a limited capacity:
 
 \begin{align}
-    & \sum_{l \in L} y_{lpt} \leq m^\text{base}_p x_p + \sum_{i=1}^t w_p
+    & \sum_{l \in L} y_{lpt} \leq m^\text{min}_p x_p + \sum_{i=1}^t w_p
         & \forall p \in P, t \in T
 \end{align}
 
@@ -151,7 +151,7 @@ In the third line, we have the disposal costs.
         \sum_{t \in T} \sum_{p \in P} \sum_{m \in M} c^{\text{disp}}_{pmt} z_{pmt} \\
     \text{subject to } & \sum_{p \in P} y_{lpt} = m^\text{initial}_{lt} 
         & \forall l \in L, t \in T \\
-    & \sum_{l \in L} y_{lpt} \leq m^\text{base}_p x_p + \sum_{i=1}^t w_p
+    & \sum_{l \in L} y_{lpt} \leq m^\text{min}_p x_p + \sum_{i=1}^t w_p
         & \forall p \in P, t \in T \\
     & \sum_{i=1}^t w_p \leq m^\text{max}_p x_p
         & \forall p \in P, t \in T \\