diff --git a/background/allocation.html b/background/allocation.html
index 066a943c4..86d837ae5 100644
--- a/background/allocation.html
+++ b/background/allocation.html
@@ -601,7 +601,7 @@ <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="../python/examples.ipynb#model-with-allocation-user-demand">here</a>:</p>
-<div id="6ca2c809" class="cell" data-execution_count="1">
+<div id="ac27b236" class="cell" data-execution_count="1">
 <details class="code-fold">
 <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>
@@ -624,39 +624,39 @@ <h2 data-number="4.4" class="anchored" data-anchor-id="example"><span class="hea
 <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>
 </details>
 <div class="cell-output cell-output-stdout">
-<pre><code>Min F[(Basin #12, UserDemand #13)]² + F[(Basin #5, UserDemand #6)]² + F[(Basin #2, UserDemand #3)]²
+<pre><code>Min F[(Basin #2, UserDemand #3)]² + F[(Basin #12, UserDemand #13)]² + F[(Basin #5, UserDemand #6)]²
 Subject to
- flow_conservation[TabulatedRatingCurve #7] : -F[(TabulatedRatingCurve #7, FractionalFlow #9)] - F[(TabulatedRatingCurve #7, FractionalFlow #8)] + F[(Basin #5, TabulatedRatingCurve #7)] - F_flow_buffer_in[TabulatedRatingCurve #7] + F_flow_buffer_out[TabulatedRatingCurve #7] = 0
- flow_conservation[FractionalFlow #9] : F[(TabulatedRatingCurve #7, FractionalFlow #9)] - F[(FractionalFlow #9, Basin #12)] = 0
+ flow_conservation[Basin #5] : F[(LinearResistance #4, Basin #5)] - F[(Basin #5, LinearResistance #4)] + F[(UserDemand #6, Basin #5)] - F[(Basin #5, UserDemand #6)] - F[(Basin #5, TabulatedRatingCurve #7)] = 0
  flow_conservation[FractionalFlow #8] : F[(TabulatedRatingCurve #7, FractionalFlow #8)] - F[(FractionalFlow #8, Terminal #10)] = 0
+ flow_conservation[Basin #2] : -F[(Basin #2, UserDemand #3)] - F[(Basin #2, LinearResistance #4)] + F[(LinearResistance #4, Basin #2)] + F[(FlowBoundary #1, Basin #2)] + F[(UserDemand #3, Basin #2)] = 0
+ flow_conservation[TabulatedRatingCurve #7] : F[(Basin #5, TabulatedRatingCurve #7)] - F[(TabulatedRatingCurve #7, FractionalFlow #8)] - F[(TabulatedRatingCurve #7, FractionalFlow #9)] - F_flow_buffer_in[TabulatedRatingCurve #7] + F_flow_buffer_out[TabulatedRatingCurve #7] = 0
+ flow_conservation[LinearResistance #4] : -F[(LinearResistance #4, Basin #5)] + F[(Basin #5, LinearResistance #4)] + F[(Basin #2, LinearResistance #4)] - F[(LinearResistance #4, Basin #2)] = 0
  flow_conservation[Basin #12] : F[(FractionalFlow #9, Basin #12)] - F[(Basin #12, UserDemand #13)] = 0
+ flow_conservation[FractionalFlow #9] : -F[(FractionalFlow #9, Basin #12)] + F[(TabulatedRatingCurve #7, FractionalFlow #9)] = 0
  flow_conservation[Terminal #10] : F[(UserDemand #13, Terminal #10)] + F[(FractionalFlow #8, Terminal #10)] = 0
- flow_conservation[LinearResistance #4] : -F[(LinearResistance #4, Basin #5)] + F[(Basin #5, LinearResistance #4)] + F[(Basin #2, LinearResistance #4)] - F[(LinearResistance #4, Basin #2)] = 0
- flow_conservation[Basin #2] : F[(UserDemand #3, Basin #2)] + F[(FlowBoundary #1, Basin #2)] - F[(Basin #2, UserDemand #3)] - F[(Basin #2, LinearResistance #4)] + F[(LinearResistance #4, Basin #2)] = 0
- flow_conservation[Basin #5] : F[(LinearResistance #4, Basin #5)] - F[(Basin #5, LinearResistance #4)] + F[(UserDemand #6, Basin #5)] - F[(Basin #5, TabulatedRatingCurve #7)] - F[(Basin #5, UserDemand #6)] = 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 #13] : F[(UserDemand #13, Terminal #10)] ≤ 0
  source_user[UserDemand #6] : F[(UserDemand #6, Basin #5)] ≤ 0
- fractional_flow[(TabulatedRatingCurve #7, FractionalFlow #8)] : F[(TabulatedRatingCurve #7, FractionalFlow #8)] - 0.6 F[(Basin #5, TabulatedRatingCurve #7)] ≤ 0
- fractional_flow[(TabulatedRatingCurve #7, FractionalFlow #9)] : F[(TabulatedRatingCurve #7, FractionalFlow #9)] - 0.4 F[(Basin #5, TabulatedRatingCurve #7)] ≤ 0
+ source_user[UserDemand #3] : F[(UserDemand #3, Basin #2)] ≤ 0
+ fractional_flow[(TabulatedRatingCurve #7, FractionalFlow #8)] : -0.6 F[(Basin #5, TabulatedRatingCurve #7)] + F[(TabulatedRatingCurve #7, FractionalFlow #8)] ≤ 0
+ fractional_flow[(TabulatedRatingCurve #7, FractionalFlow #9)] : -0.4 F[(Basin #5, TabulatedRatingCurve #7)] + F[(TabulatedRatingCurve #7, FractionalFlow #9)] ≤ 0
  flow_buffer_outflow[TabulatedRatingCurve #7] : F_flow_buffer_out[TabulatedRatingCurve #7] ≤ 0
  F[(LinearResistance #4, Basin #5)] ≥ 0
  F[(Basin #5, LinearResistance #4)] ≥ 0
- F[(TabulatedRatingCurve #7, FractionalFlow #9)] ≥ 0
- F[(UserDemand #13, Terminal #10)] ≥ 0
- F[(UserDemand #3, Basin #2)] ≥ 0
- F[(TabulatedRatingCurve #7, FractionalFlow #8)] ≥ 0
+ F[(Basin #2, UserDemand #3)] ≥ 0
  F[(UserDemand #6, Basin #5)] ≥ 0
- F[(Basin #5, TabulatedRatingCurve #7)] ≥ 0
  F[(FractionalFlow #9, Basin #12)] ≥ 0
  F[(Basin #12, UserDemand #13)] ≥ 0
- F[(FractionalFlow #8, Terminal #10)] ≥ 0
+ F[(UserDemand #13, Terminal #10)] ≥ 0
  F[(Basin #5, UserDemand #6)] ≥ 0
- F[(FlowBoundary #1, Basin #2)] ≥ 0
- F[(Basin #2, UserDemand #3)] ≥ 0
+ F[(Basin #5, TabulatedRatingCurve #7)] ≥ 0
  F[(Basin #2, LinearResistance #4)] ≥ 0
  F[(LinearResistance #4, Basin #2)] ≥ 0
+ F[(TabulatedRatingCurve #7, FractionalFlow #8)] ≥ 0
+ F[(FlowBoundary #1, Basin #2)] ≥ 0
+ F[(UserDemand #3, Basin #2)] ≥ 0
+ F[(TabulatedRatingCurve #7, FractionalFlow #9)] ≥ 0
+ F[(FractionalFlow #8, Terminal #10)] ≥ 0
  F_flow_buffer_in[TabulatedRatingCurve #7] ≥ 0
  F_flow_buffer_out[TabulatedRatingCurve #7] ≥ 0
 </code></pre>
diff --git a/background/equations.html b/background/equations.html
index 6093df73c..b09e2ef2e 100644
--- a/background/equations.html
+++ b/background/equations.html
@@ -463,7 +463,7 @@ <h2 data-number="2.1" class="anchored" data-anchor-id="sec-reduction_factor"><sp
     \end{cases}
 \end{align}\]</span></p>
 <p>Here <span class="math inline">\(p &gt; 0\)</span> is the threshold value which determines the interval <span class="math inline">\([0,p]\)</span> of the smooth transition between <span class="math inline">\(0\)</span> and <span class="math inline">\(1\)</span>, see the plot below.</p>
-<div id="4cdaba12" class="cell" data-execution_count="1">
+<div id="81f13c82" class="cell" data-execution_count="1">
 <details class="code-fold">
 <summary>Code</summary>
 <div class="sourceCode cell-code" id="cb1"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="im">import</span> numpy <span class="im">as</span> np</span>
diff --git a/background/validation.html b/background/validation.html
index 8d75bddd3..9ebdb647c 100644
--- a/background/validation.html
+++ b/background/validation.html
@@ -298,7 +298,7 @@ <h1 class="title">Validation</h1>
 <section id="connectivity" class="level1" data-number="1">
 <h1 data-number="1"><span class="header-section-number">1</span> Connectivity</h1>
 <p>In the table below, each column shows which node types are allowed to be downstream (or ‘down-control’) of the node type at the top of the column.</p>
-<div id="b5873113" class="cell" data-execution_count="1">
+<div id="16a92ed1" class="cell" data-execution_count="1">
 <details class="code-fold">
 <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>
@@ -648,7 +648,7 @@ <h1 data-number="1"><span class="header-section-number">1</span> Connectivity</h
 <section id="neighbor-amounts" class="level1" data-number="2">
 <h1 data-number="2"><span class="header-section-number">2</span> Neighbor amounts</h1>
 <p>The table below shows for each node type between which bounds the amount of in- and outneighbors must be, for both flow and control edges.</p>
-<div id="c9ffa6e7" class="cell" data-execution_count="2">
+<div id="96a79a8a" class="cell" data-execution_count="2">
 <details class="code-fold">
 <summary>Code</summary>
 <div class="sourceCode cell-code" id="cb2"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a>flow_in_min <span class="op">=</span> <span class="fu">Vector</span><span class="dt">{String}</span>()</span>
diff --git a/guides/examples_files/figure-html/cell-71-output-1.png b/guides/examples_files/figure-html/cell-71-output-1.png
index 2e273a56f..42dfff946 100644
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diff --git a/reference/test-models.html b/reference/test-models.html
index 3547e4be2..6dc0691ed 100644
--- a/reference/test-models.html
+++ b/reference/test-models.html
@@ -325,7 +325,7 @@ <h1 class="title">Test models</h1>
 
 
 <p>Ribasim developers use the following models in their testbench and in order to test new features.</p>
-<div id="8b27bafd" class="cell" data-execution_count="1">
+<div id="bd5b1336" class="cell" data-execution_count="1">
 <details class="code-fold">
 <summary>Code</summary>
 <div class="sourceCode cell-code" id="cb1"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="im">import</span> ribasim_testmodels</span>
diff --git a/search.json b/search.json
index 02eb3d682..8d78b49e3 100644
--- a/search.json
+++ b/search.json
@@ -304,7 +304,7 @@
     "href": "background/allocation.html#example",
     "title": "Allocation",
     "section": "4.4 Example",
-    "text": "4.4 Example\nThe following is an example of an optimization problem for the example shown here:\n\n\nCode\nusing Ribasim\nusing Ribasim: NodeID\nusing SQLite\nusing ComponentArrays: ComponentVector\n\ntoml_path = normpath(@__DIR__, \"../../generated_testmodels/allocation_example/ribasim.toml\")\np = Ribasim.Model(toml_path).integrator.p\nu = ComponentVector(; storage = zeros(length(p.basin.node_id)))\n\nallocation_model = p.allocation.allocation_models[1]\nt = 0.0\npriority_idx = 1\n\nRibasim.set_flow!(p.graph, NodeID(:FlowBoundary, 1), NodeID(:Basin, 2), 1.0)\nRibasim.set_objective_priority!(allocation_model, p, u, t, priority_idx)\nRibasim.set_initial_values!(allocation_model, p, u, t)\n\nprintln(p.allocation.allocation_models[1].problem)\n\n\nMin F[(Basin #12, UserDemand #13)]² + F[(Basin #5, UserDemand #6)]² + F[(Basin #2, UserDemand #3)]²\nSubject to\n flow_conservation[TabulatedRatingCurve #7] : -F[(TabulatedRatingCurve #7, FractionalFlow #9)] - F[(TabulatedRatingCurve #7, FractionalFlow #8)] + F[(Basin #5, TabulatedRatingCurve #7)] - F_flow_buffer_in[TabulatedRatingCurve #7] + F_flow_buffer_out[TabulatedRatingCurve #7] = 0\n flow_conservation[FractionalFlow #9] : F[(TabulatedRatingCurve #7, FractionalFlow #9)] - F[(FractionalFlow #9, Basin #12)] = 0\n flow_conservation[FractionalFlow #8] : F[(TabulatedRatingCurve #7, FractionalFlow #8)] - F[(FractionalFlow #8, Terminal #10)] = 0\n flow_conservation[Basin #12] : F[(FractionalFlow #9, Basin #12)] - F[(Basin #12, UserDemand #13)] = 0\n flow_conservation[Terminal #10] : F[(UserDemand #13, Terminal #10)] + F[(FractionalFlow #8, Terminal #10)] = 0\n flow_conservation[LinearResistance #4] : -F[(LinearResistance #4, Basin #5)] + F[(Basin #5, LinearResistance #4)] + F[(Basin #2, LinearResistance #4)] - F[(LinearResistance #4, Basin #2)] = 0\n flow_conservation[Basin #2] : F[(UserDemand #3, Basin #2)] + F[(FlowBoundary #1, Basin #2)] - F[(Basin #2, UserDemand #3)] - F[(Basin #2, LinearResistance #4)] + F[(LinearResistance #4, Basin #2)] = 0\n flow_conservation[Basin #5] : F[(LinearResistance #4, Basin #5)] - F[(Basin #5, LinearResistance #4)] + F[(UserDemand #6, Basin #5)] - F[(Basin #5, TabulatedRatingCurve #7)] - F[(Basin #5, UserDemand #6)] = 0\n source[(FlowBoundary #1, Basin #2)] : F[(FlowBoundary #1, Basin #2)] ≤ 172800\n source_user[UserDemand #3] : F[(UserDemand #3, Basin #2)] ≤ 0\n source_user[UserDemand #13] : F[(UserDemand #13, Terminal #10)] ≤ 0\n source_user[UserDemand #6] : F[(UserDemand #6, Basin #5)] ≤ 0\n fractional_flow[(TabulatedRatingCurve #7, FractionalFlow #8)] : F[(TabulatedRatingCurve #7, FractionalFlow #8)] - 0.6 F[(Basin #5, TabulatedRatingCurve #7)] ≤ 0\n fractional_flow[(TabulatedRatingCurve #7, FractionalFlow #9)] : F[(TabulatedRatingCurve #7, FractionalFlow #9)] - 0.4 F[(Basin #5, TabulatedRatingCurve #7)] ≤ 0\n flow_buffer_outflow[TabulatedRatingCurve #7] : F_flow_buffer_out[TabulatedRatingCurve #7] ≤ 0\n F[(LinearResistance #4, Basin #5)] ≥ 0\n F[(Basin #5, LinearResistance #4)] ≥ 0\n F[(TabulatedRatingCurve #7, FractionalFlow #9)] ≥ 0\n F[(UserDemand #13, Terminal #10)] ≥ 0\n F[(UserDemand #3, Basin #2)] ≥ 0\n F[(TabulatedRatingCurve #7, FractionalFlow #8)] ≥ 0\n F[(UserDemand #6, Basin #5)] ≥ 0\n F[(Basin #5, TabulatedRatingCurve #7)] ≥ 0\n F[(FractionalFlow #9, Basin #12)] ≥ 0\n F[(Basin #12, UserDemand #13)] ≥ 0\n F[(FractionalFlow #8, Terminal #10)] ≥ 0\n F[(Basin #5, UserDemand #6)] ≥ 0\n F[(FlowBoundary #1, Basin #2)] ≥ 0\n F[(Basin #2, UserDemand #3)] ≥ 0\n F[(Basin #2, LinearResistance #4)] ≥ 0\n F[(LinearResistance #4, Basin #2)] ≥ 0\n F_flow_buffer_in[TabulatedRatingCurve #7] ≥ 0\n F_flow_buffer_out[TabulatedRatingCurve #7] ≥ 0",
+    "text": "4.4 Example\nThe following is an example of an optimization problem for the example shown here:\n\n\nCode\nusing Ribasim\nusing Ribasim: NodeID\nusing SQLite\nusing ComponentArrays: ComponentVector\n\ntoml_path = normpath(@__DIR__, \"../../generated_testmodels/allocation_example/ribasim.toml\")\np = Ribasim.Model(toml_path).integrator.p\nu = ComponentVector(; storage = zeros(length(p.basin.node_id)))\n\nallocation_model = p.allocation.allocation_models[1]\nt = 0.0\npriority_idx = 1\n\nRibasim.set_flow!(p.graph, NodeID(:FlowBoundary, 1), NodeID(:Basin, 2), 1.0)\nRibasim.set_objective_priority!(allocation_model, p, u, t, priority_idx)\nRibasim.set_initial_values!(allocation_model, p, u, t)\n\nprintln(p.allocation.allocation_models[1].problem)\n\n\nMin F[(Basin #2, UserDemand #3)]² + F[(Basin #12, UserDemand #13)]² + F[(Basin #5, UserDemand #6)]²\nSubject to\n flow_conservation[Basin #5] : F[(LinearResistance #4, Basin #5)] - F[(Basin #5, LinearResistance #4)] + F[(UserDemand #6, Basin #5)] - F[(Basin #5, UserDemand #6)] - F[(Basin #5, TabulatedRatingCurve #7)] = 0\n flow_conservation[FractionalFlow #8] : F[(TabulatedRatingCurve #7, FractionalFlow #8)] - F[(FractionalFlow #8, Terminal #10)] = 0\n flow_conservation[Basin #2] : -F[(Basin #2, UserDemand #3)] - F[(Basin #2, LinearResistance #4)] + F[(LinearResistance #4, Basin #2)] + F[(FlowBoundary #1, Basin #2)] + F[(UserDemand #3, Basin #2)] = 0\n flow_conservation[TabulatedRatingCurve #7] : F[(Basin #5, TabulatedRatingCurve #7)] - F[(TabulatedRatingCurve #7, FractionalFlow #8)] - F[(TabulatedRatingCurve #7, FractionalFlow #9)] - F_flow_buffer_in[TabulatedRatingCurve #7] + F_flow_buffer_out[TabulatedRatingCurve #7] = 0\n flow_conservation[LinearResistance #4] : -F[(LinearResistance #4, Basin #5)] + F[(Basin #5, LinearResistance #4)] + F[(Basin #2, LinearResistance #4)] - F[(LinearResistance #4, Basin #2)] = 0\n flow_conservation[Basin #12] : F[(FractionalFlow #9, Basin #12)] - F[(Basin #12, UserDemand #13)] = 0\n flow_conservation[FractionalFlow #9] : -F[(FractionalFlow #9, Basin #12)] + F[(TabulatedRatingCurve #7, FractionalFlow #9)] = 0\n flow_conservation[Terminal #10] : F[(UserDemand #13, Terminal #10)] + F[(FractionalFlow #8, Terminal #10)] = 0\n source[(FlowBoundary #1, Basin #2)] : F[(FlowBoundary #1, Basin #2)] ≤ 172800\n source_user[UserDemand #13] : F[(UserDemand #13, Terminal #10)] ≤ 0\n source_user[UserDemand #6] : F[(UserDemand #6, Basin #5)] ≤ 0\n source_user[UserDemand #3] : F[(UserDemand #3, Basin #2)] ≤ 0\n fractional_flow[(TabulatedRatingCurve #7, FractionalFlow #8)] : -0.6 F[(Basin #5, TabulatedRatingCurve #7)] + F[(TabulatedRatingCurve #7, FractionalFlow #8)] ≤ 0\n fractional_flow[(TabulatedRatingCurve #7, FractionalFlow #9)] : -0.4 F[(Basin #5, TabulatedRatingCurve #7)] + F[(TabulatedRatingCurve #7, FractionalFlow #9)] ≤ 0\n flow_buffer_outflow[TabulatedRatingCurve #7] : F_flow_buffer_out[TabulatedRatingCurve #7] ≤ 0\n F[(LinearResistance #4, Basin #5)] ≥ 0\n F[(Basin #5, LinearResistance #4)] ≥ 0\n F[(Basin #2, UserDemand #3)] ≥ 0\n F[(UserDemand #6, Basin #5)] ≥ 0\n F[(FractionalFlow #9, Basin #12)] ≥ 0\n F[(Basin #12, UserDemand #13)] ≥ 0\n F[(UserDemand #13, Terminal #10)] ≥ 0\n F[(Basin #5, UserDemand #6)] ≥ 0\n F[(Basin #5, TabulatedRatingCurve #7)] ≥ 0\n F[(Basin #2, LinearResistance #4)] ≥ 0\n F[(LinearResistance #4, Basin #2)] ≥ 0\n F[(TabulatedRatingCurve #7, FractionalFlow #8)] ≥ 0\n F[(FlowBoundary #1, Basin #2)] ≥ 0\n F[(UserDemand #3, Basin #2)] ≥ 0\n F[(TabulatedRatingCurve #7, FractionalFlow #9)] ≥ 0\n F[(FractionalFlow #8, Terminal #10)] ≥ 0\n F_flow_buffer_in[TabulatedRatingCurve #7] ≥ 0\n F_flow_buffer_out[TabulatedRatingCurve #7] ≥ 0",
     "crumbs": [
       "Background",
       "Implementation",