diff --git a/concept/allocation.html b/concept/allocation.html
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@@ -583,7 +583,7 @@ <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>
-<div id="84cf3327" class="cell" data-execution_count="1">
+<div id="c3b8cd6e" 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>
@@ -609,24 +609,24 @@ <h2 data-number="4.4" class="anchored" data-anchor-id="example"><span class="hea
 <pre><code>Min F[(Basin #5, UserDemand #6)]² + F[(Basin #2, UserDemand #3)]²
 Subject to
  flow_conservation[Terminal #1] : F[(TabulatedRatingCurve #7, Terminal #1)] = 0
+ flow_conservation[Basin #2] : -F[(Basin #2, LinearResistance #4)] + F[(LinearResistance #4, Basin #2)] + F[(FlowBoundary #1, Basin #2)] + F[(UserDemand #3, Basin #2)] - F[(Basin #2, UserDemand #3)] = 0
+ flow_conservation[Basin #5] : -F[(Basin #5, UserDemand #6)] - F[(Basin #5, TabulatedRatingCurve #7)] + F[(LinearResistance #4, Basin #5)] - F[(Basin #5, LinearResistance #4)] + F[(UserDemand #6, Basin #5)] = 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[Basin #2] : -F[(Basin #2, LinearResistance #4)] + F[(LinearResistance #4, Basin #2)] + F[(UserDemand #3, Basin #2)] + F[(FlowBoundary #1, Basin #2)] - F[(Basin #2, UserDemand #3)] = 0
- flow_conservation[Basin #5] : F[(UserDemand #6, Basin #5)] + F[(LinearResistance #4, Basin #5)] - F[(Basin #5, LinearResistance #4)] - F[(Basin #5, UserDemand #6)] - F[(Basin #5, TabulatedRatingCurve #7)] = 0
- flow_conservation[TabulatedRatingCurve #7] : F[(Basin #5, TabulatedRatingCurve #7)] - F[(TabulatedRatingCurve #7, Terminal #1)] = 0
+ flow_conservation[TabulatedRatingCurve #7] : -F[(TabulatedRatingCurve #7, Terminal #1)] + 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
+ source_user[UserDemand #3] : F[(UserDemand #3, Basin #2)] ≤ 0
+ F[(Basin #5, UserDemand #6)] ≥ 0
+ F[(TabulatedRatingCurve #7, Terminal #1)] ≥ 0
  F[(Basin #2, LinearResistance #4)] ≥ 0
  F[(LinearResistance #4, Basin #2)] ≥ 0
- F[(UserDemand #6, Basin #5)] ≥ 0
- F[(LinearResistance #4, Basin #5)] ≥ 0
- F[(Basin #5, LinearResistance #4)] ≥ 0
- F[(Basin #5, UserDemand #6)] ≥ 0
- F[(UserDemand #3, Basin #2)] ≥ 0
  F[(FlowBoundary #1, Basin #2)] ≥ 0
- F[(Basin #2, UserDemand #3)] ≥ 0
  F[(Basin #5, TabulatedRatingCurve #7)] ≥ 0
- F[(TabulatedRatingCurve #7, Terminal #1)] ≥ 0
+ F[(UserDemand #3, Basin #2)] ≥ 0
+ F[(Basin #2, UserDemand #3)] ≥ 0
+ F[(LinearResistance #4, Basin #5)] ≥ 0
+ F[(Basin #5, LinearResistance #4)] ≥ 0
+ F[(UserDemand #6, Basin #5)] ≥ 0
 </code></pre>
 </div>
 </div>
diff --git a/guide/examples.html b/guide/examples.html
index 4d25ebc8b..9d2a8e123 100644
--- a/guide/examples.html
+++ b/guide/examples.html
@@ -493,7 +493,7 @@ <h1 data-number="1"><span class="header-section-number">1</span> Basic model wit
 <div class="cell-output cell-output-display">
 <div>
 <figure class="figure">
-<p><img src="examples_files/figure-html/cell-19-output-1.png" width="727" height="445" class="figure-img"></p>
+<p><img src="examples_files/figure-html/cell-19-output-1.png" width="727" height="444" class="figure-img"></p>
 </figure>
 </div>
 </div>
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diff --git a/reference/node/basin.html b/reference/node/basin.html
index 8d9780662..ea5d0ca96 100644
--- a/reference/node/basin.html
+++ b/reference/node/basin.html
@@ -820,7 +820,7 @@ <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="adf81c04" class="cell" data-execution_count="1">
+<div id="64ccce78" 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/reference/node/discrete-control.html b/reference/node/discrete-control.html
index bf041ae4f..d9d5ab218 100644
--- a/reference/node/discrete-control.html
+++ b/reference/node/discrete-control.html
@@ -377,7 +377,7 @@ <h1 class="title">DiscreteControl</h1>
 
 
 <p>Set parameters of other nodes based on model state conditions (e.g.&nbsp;Basin level). The table below shows which parameters are controllable for a given node type.</p>
-<div id="5d9b229f" class="cell" data-execution_count="1">
+<div id="c1493172" 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>
diff --git a/reference/test-models.html b/reference/test-models.html
index fcaf6c29d..e29cc1807 100644
--- a/reference/test-models.html
+++ b/reference/test-models.html
@@ -337,7 +337,7 @@ <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="6668eedd" class="cell" data-execution_count="1">
+<div id="3cb2401c" 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/reference/validation.html b/reference/validation.html
index 801e52828..74fa7b668 100644
--- a/reference/validation.html
+++ b/reference/validation.html
@@ -347,7 +347,7 @@ <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="490328b0" class="cell" data-execution_count="1">
+<div id="ec2e3d70" 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>
@@ -663,7 +663,7 @@ <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="e3130947" class="cell" data-execution_count="2">
+<div id="088a3b19" 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/search.json b/search.json
index 13ab24813..3c30f092b 100644
--- a/search.json
+++ b/search.json
@@ -187,7 +187,7 @@
     "href": "concept/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, p), NodeID(:Basin, 2, p), 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 #5, UserDemand #6)]² + F[(Basin #2, UserDemand #3)]²\nSubject to\n flow_conservation[Terminal #1] : F[(TabulatedRatingCurve #7, Terminal #1)] = 0\n 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\n flow_conservation[Basin #2] : -F[(Basin #2, LinearResistance #4)] + F[(LinearResistance #4, Basin #2)] + F[(UserDemand #3, Basin #2)] + F[(FlowBoundary #1, Basin #2)] - F[(Basin #2, UserDemand #3)] = 0\n flow_conservation[Basin #5] : F[(UserDemand #6, Basin #5)] + F[(LinearResistance #4, Basin #5)] - F[(Basin #5, LinearResistance #4)] - F[(Basin #5, UserDemand #6)] - F[(Basin #5, TabulatedRatingCurve #7)] = 0\n flow_conservation[TabulatedRatingCurve #7] : F[(Basin #5, TabulatedRatingCurve #7)] - F[(TabulatedRatingCurve #7, Terminal #1)] = 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 #6] : F[(UserDemand #6, Basin #5)] ≤ 0\n F[(Basin #2, LinearResistance #4)] ≥ 0\n F[(LinearResistance #4, Basin #2)] ≥ 0\n F[(UserDemand #6, Basin #5)] ≥ 0\n F[(LinearResistance #4, Basin #5)] ≥ 0\n F[(Basin #5, LinearResistance #4)] ≥ 0\n F[(Basin #5, UserDemand #6)] ≥ 0\n F[(UserDemand #3, Basin #2)] ≥ 0\n F[(FlowBoundary #1, Basin #2)] ≥ 0\n F[(Basin #2, UserDemand #3)] ≥ 0\n F[(Basin #5, TabulatedRatingCurve #7)] ≥ 0\n F[(TabulatedRatingCurve #7, Terminal #1)] ≥ 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, p), NodeID(:Basin, 2, p), 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 #5, UserDemand #6)]² + F[(Basin #2, UserDemand #3)]²\nSubject to\n flow_conservation[Terminal #1] : F[(TabulatedRatingCurve #7, Terminal #1)] = 0\n flow_conservation[Basin #2] : -F[(Basin #2, LinearResistance #4)] + F[(LinearResistance #4, Basin #2)] + F[(FlowBoundary #1, Basin #2)] + F[(UserDemand #3, Basin #2)] - F[(Basin #2, UserDemand #3)] = 0\n flow_conservation[Basin #5] : -F[(Basin #5, UserDemand #6)] - F[(Basin #5, TabulatedRatingCurve #7)] + F[(LinearResistance #4, Basin #5)] - F[(Basin #5, LinearResistance #4)] + F[(UserDemand #6, Basin #5)] = 0\n 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\n flow_conservation[TabulatedRatingCurve #7] : -F[(TabulatedRatingCurve #7, Terminal #1)] + F[(Basin #5, TabulatedRatingCurve #7)] = 0\n source[(FlowBoundary #1, Basin #2)] : F[(FlowBoundary #1, Basin #2)] ≤ 172800\n source_user[UserDemand #6] : F[(UserDemand #6, Basin #5)] ≤ 0\n source_user[UserDemand #3] : F[(UserDemand #3, Basin #2)] ≤ 0\n F[(Basin #5, UserDemand #6)] ≥ 0\n F[(TabulatedRatingCurve #7, Terminal #1)] ≥ 0\n F[(Basin #2, LinearResistance #4)] ≥ 0\n F[(LinearResistance #4, Basin #2)] ≥ 0\n F[(FlowBoundary #1, Basin #2)] ≥ 0\n F[(Basin #5, TabulatedRatingCurve #7)] ≥ 0\n F[(UserDemand #3, Basin #2)] ≥ 0\n F[(Basin #2, UserDemand #3)] ≥ 0\n F[(LinearResistance #4, Basin #5)] ≥ 0\n F[(Basin #5, LinearResistance #4)] ≥ 0\n F[(UserDemand #6, Basin #5)] ≥ 0",
     "crumbs": [
       "Concepts",
       "Implementation",