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29 changes: 14 additions & 15 deletions concept/allocation.html
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Expand Up @@ -574,7 +574,7 @@ <h2 data-number="4.3" class="anchored" data-anchor-id="the-optimization-constrai
<section id="example" class="level2" data-number="4.4">
<h2 data-number="4.4" class="anchored" data-anchor-id="example"><span class="header-section-number">4.4</span> Example</h2>
<p>The following is an example of an optimization problem for the example shown <a href="../guide/examples.html#model-with-allocation-user-demand">here</a>:</p>
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<summary>Code</summary>
<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="im">using</span> <span class="bu">Ribasim</span></span>
Expand All @@ -590,34 +590,33 @@ <h2 data-number="4.4" class="anchored" data-anchor-id="example"><span class="hea
<span id="cb1-11"><a href="#cb1-11" aria-hidden="true" tabindex="-1"></a>t <span class="op">=</span> <span class="fl">0.0</span></span>
<span id="cb1-12"><a href="#cb1-12" aria-hidden="true" tabindex="-1"></a>priority_idx <span class="op">=</span> <span class="fl">1</span></span>
<span id="cb1-13"><a href="#cb1-13" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-14"><a href="#cb1-14" aria-hidden="true" tabindex="-1"></a>Ribasim.<span class="fu">set_flow!</span>(p.graph, <span class="fl">1</span>, <span class="fl">1.0</span>, u)</span>
<span id="cb1-15"><a href="#cb1-15" aria-hidden="true" tabindex="-1"></a>Ribasim.<span class="fu">set_objective_priority!</span>(allocation_model, p, u, t, priority_idx)</span>
<span id="cb1-16"><a href="#cb1-16" aria-hidden="true" tabindex="-1"></a>Ribasim.<span class="fu">set_initial_values!</span>(allocation_model, p, u, t)</span>
<span id="cb1-17"><a href="#cb1-17" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-18"><a href="#cb1-18" aria-hidden="true" tabindex="-1"></a><span class="fu">println</span>(p.allocation.allocation_models[<span class="fl">1</span>].problem)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<span id="cb1-14"><a href="#cb1-14" aria-hidden="true" tabindex="-1"></a>Ribasim.<span class="fu">set_objective_priority!</span>(allocation_model, p, u, t, priority_idx)</span>
<span id="cb1-15"><a href="#cb1-15" aria-hidden="true" tabindex="-1"></a>Ribasim.<span class="fu">set_initial_values!</span>(allocation_model, p, u, t)</span>
<span id="cb1-16"><a href="#cb1-16" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-17"><a href="#cb1-17" aria-hidden="true" tabindex="-1"></a><span class="fu">println</span>(p.allocation.allocation_models[<span class="fl">1</span>].problem)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</details>
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<pre><code>Min F[(Basin #2, UserDemand #3)]² + F[(Basin #5, UserDemand #6)]²
Subject to
flow_conservation[LinearResistance #4] : F[(Basin #2, LinearResistance #4)] - F[(LinearResistance #4, Basin #2)] - F[(LinearResistance #4, Basin #5)] + F[(Basin #5, LinearResistance #4)] = 0
flow_conservation[TabulatedRatingCurve #7] : F[(Basin #5, TabulatedRatingCurve #7)] - F[(TabulatedRatingCurve #7, Terminal #8)] = 0
flow_conservation[Basin #5] : F[(UserDemand #6, Basin #5)] - F[(Basin #5, UserDemand #6)] - F[(Basin #5, TabulatedRatingCurve #7)] + F[(LinearResistance #4, Basin #5)] - F[(Basin #5, LinearResistance #4)] = 0
flow_conservation[Terminal #8] : F[(TabulatedRatingCurve #7, Terminal #8)] = 0
flow_conservation[Basin #5] : -F[(Basin #5, TabulatedRatingCurve #7)] + F[(UserDemand #6, Basin #5)] - F[(Basin #5, UserDemand #6)] + F[(LinearResistance #4, Basin #5)] - F[(Basin #5, LinearResistance #4)] = 0
flow_conservation[Basin #2] : -F[(Basin #2, UserDemand #3)] + F[(UserDemand #3, Basin #2)] - F[(Basin #2, LinearResistance #4)] + F[(LinearResistance #4, Basin #2)] + F[(FlowBoundary #1, Basin #2)] = 0
flow_conservation[Basin #2] : F[(UserDemand #3, Basin #2)] - F[(Basin #2, LinearResistance #4)] + F[(LinearResistance #4, Basin #2)] - F[(Basin #2, UserDemand #3)] + F[(FlowBoundary #1, Basin #2)] = 0
flow_conservation[LinearResistance #4] : F[(Basin #2, LinearResistance #4)] - F[(LinearResistance #4, Basin #2)] - F[(LinearResistance #4, Basin #5)] + F[(Basin #5, LinearResistance #4)] = 0
flow_conservation[TabulatedRatingCurve #7] : -F[(TabulatedRatingCurve #7, Terminal #8)] + F[(Basin #5, TabulatedRatingCurve #7)] = 0
source[(FlowBoundary #1, Basin #2)] : F[(FlowBoundary #1, Basin #2)] ≤ 172800
source_user[UserDemand #3] : F[(UserDemand #3, Basin #2)] ≤ 0
source_user[UserDemand #6] : F[(UserDemand #6, Basin #5)] ≤ 0
F[(Basin #2, UserDemand #3)] ≥ 0
F[(Basin #5, TabulatedRatingCurve #7)] ≥ 0
source_user[UserDemand #3] : F[(UserDemand #3, Basin #2)] ≤ 0
F[(UserDemand #3, Basin #2)] ≥ 0
F[(UserDemand #6, Basin #5)] ≥ 0
F[(Basin #2, LinearResistance #4)] ≥ 0
F[(LinearResistance #4, Basin #2)] ≥ 0
F[(Basin #2, UserDemand #3)] ≥ 0
F[(TabulatedRatingCurve #7, Terminal #8)] ≥ 0
F[(Basin #5, UserDemand #6)] ≥ 0
F[(Basin #5, TabulatedRatingCurve #7)] ≥ 0
F[(FlowBoundary #1, Basin #2)] ≥ 0
F[(LinearResistance #4, Basin #5)] ≥ 0
F[(Basin #5, LinearResistance #4)] ≥ 0
F[(FlowBoundary #1, Basin #2)] ≥ 0
F[(TabulatedRatingCurve #7, Terminal #8)] ≥ 0
</code></pre>
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