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Docs: rename m^base to m^min

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Alinson S. Xavier
2020-08-21 17:27:06 -05:00
parent 8ea50128b8
commit 21eed29cec
5 changed files with 55 additions and 10 deletions
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55
docs/model/index.html
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@@ -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>