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Version 04 als eigenes Repository

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Erster Commit des Strangs "Optimierte Entscheidungsfindung mit Python"
(Version 04). Die Historie der 71 Commits bis zur Trennung bleibt im
uebergeordneten Repository OR_mit_Python liegen, das ab jetzt nur noch
Version_03 (eingefroren) verwaltet und Version_04/ ignoriert.

Bewusst kein "git subtree split": Der Pfad Version_04/ existiert erst seit
der Verzeichnistrennung, ein Split braechte daher nur 7 der 41 einschlaegigen
Commits - eine Teilhistorie, die vollstaendig aussieht und es nicht ist.

Stand: 5 Teile, 23 Kapitel, 5 Anhaenge, 292 Abschnitte, 703 Querverweise,
325 Indexmarken, 73 Beispielprogramme, 32 SVGs, 4 Plotly-Figuren,
25 Notebooks, PDF mit 715 Seiten.

Zusaetzlich in diesem Commit:

* pyproject.toml mit Abhaengigkeitsgruppen finance, large-scale, api,
  figures, dev, empfehlungen. Die abgedruckte requirements.txt bleibt
  unveraendert daneben bestehen. ortools steht in der Grundausstattung,
  highspy erst in [large-scale] - so kann der HiGHS-Symbolkonflikt bei der
  schlanken Installation gar nicht erst auftreten.

* Dabei zwei Funde: graphviz wird von erzeuge_architektur_diagramme.py
  importiert, fehlt aber in requirements.txt (jetzt in [figures]); pymoo
  steht in requirements.txt, wird aber von keinem Programm importiert,
  sondern nur im Kapitel Metaheuristiken empfohlen (jetzt in
  [empfehlungen]).

* NEUER_TITEL.md nach Kritik_und_Verbesserungsvorschlaege/ verschoben - es
  ist die Vorlage des Titelblatts, kein Bestandteil des Werks. Die beiden
  Fundstellen in PROGRESS.md und erzeuge_titelseite.py nachgezogen.

* PROGRESS.md nannte noch den Untertitel der ersten Fassung; auf den
  tatsaechlichen aus erzeuge_titelseite.py korrigiert.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
This commit is contained in:
dschlueter 2026-09-08 01:20:09 +02:00
commit b7af2f1d9a
468 changed files with 262141 additions and 0 deletions
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<!-- Title: d22 Pages: 1 -->
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viewBox="7.00 7.00 352.00 241.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<title>d22</title>
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<g id="node1" class="node">
<title>primal</title>
<path fill="#eef2ff" stroke="#4338ca" stroke-width="2" d="M302.3,-225.31C302.3,-225.31 34.12,-225.31 34.12,-225.31 28.12,-225.31 22.12,-219.31 22.12,-213.31 22.12,-213.31 22.12,-153.03 22.12,-153.03 22.12,-147.03 28.12,-141.03 34.12,-141.03 34.12,-141.03 302.3,-141.03 302.3,-141.03 308.3,-141.03 314.3,-147.03 314.3,-153.03 314.3,-153.03 314.3,-213.31 314.3,-213.31 314.3,-219.31 308.3,-225.31 302.3,-225.31"/>
<text xml:space="preserve" text-anchor="start" x="35.09" y="-205.32" font-family="DejaVu Sans" font-weight="bold" font-size="13.00" fill="#4338ca">PRIMALES PROBLEM &#160;(Unternehmer)</text>
<text xml:space="preserve" text-anchor="start" x="35.09" y="-181.17" font-family="DejaVu Sans" font-size="10.00" fill="#1a1a2e">Maximiere Gewinn aus Produkten</text>
<text xml:space="preserve" text-anchor="start" x="35.09" y="-171.17" font-family="DejaVu Sans" font-size="10.00" fill="#1a1a2e">Zielfunktion: &#160;&#160;max &#160;cᵀx</text>
<text xml:space="preserve" text-anchor="start" x="35.09" y="-161.17" font-family="DejaVu Sans" font-size="10.00" fill="#1a1a2e">Restriktionen: &#160;A x ≤ b</text>
<text xml:space="preserve" text-anchor="start" x="35.09" y="-151.17" font-family="DejaVu Sans" font-size="10.00" fill="#1a1a2e">Variablen: &#160;x ≥ 0 &#160;(Produktionsmengen)</text>
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<g id="node2" class="node">
<title>dual</title>
<path fill="#ecfeff" stroke="#0891b2" stroke-width="2" d="M324.42,-84.28C324.42,-84.28 12,-84.28 12,-84.28 6,-84.28 0,-78.28 0,-72.28 0,-72.28 0,-12 0,-12 0,-6 6,0 12,0 12,0 324.42,0 324.42,0 330.42,0 336.42,-6 336.42,-12 336.42,-12 336.42,-72.28 336.42,-72.28 336.42,-78.28 330.42,-84.28 324.42,-84.28"/>
<text xml:space="preserve" text-anchor="start" x="12.96" y="-64.29" font-family="DejaVu Sans" font-weight="bold" font-size="13.00" fill="#0891b2">DUALES PROBLEM &#160;(Ressourcen&#45;Bewerter)</text>
<text xml:space="preserve" text-anchor="start" x="12.96" y="-40.14" font-family="DejaVu Sans" font-size="10.00" fill="#1a1a2e">Minimiere Bewertung der Ressourcen</text>
<text xml:space="preserve" text-anchor="start" x="12.96" y="-30.14" font-family="DejaVu Sans" font-size="10.00" fill="#1a1a2e">Zielfunktion: &#160;&#160;min &#160;bᵀy</text>
<text xml:space="preserve" text-anchor="start" x="12.96" y="-20.14" font-family="DejaVu Sans" font-size="10.00" fill="#1a1a2e">Restriktionen: &#160;Aᵀy ≥ c</text>
<text xml:space="preserve" text-anchor="start" x="12.96" y="-10.14" font-family="DejaVu Sans" font-size="10.00" fill="#1a1a2e">Variablen: &#160;y ≥ 0 &#160;(Schattenpreise)</text>
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<g id="edge1" class="edge">
<title>primal&#45;&gt;dual</title>
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<text xml:space="preserve" text-anchor="middle" x="193.71" y="-109.53" font-family="DejaVu Sans" font-size="10.00" fill="#7c3aed"> &#160;Dualität &#160;</text>
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<!-- Title: d09 Pages: 1 -->
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<title>d09</title>
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<g id="node1" class="node">
<title>store</title>
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<text xml:space="preserve" text-anchor="start" x="111.96" y="-278.85" font-family="DejaVu Sans" font-weight="bold" font-size="13.00" fill="#4338ca">CONSTRAINT STORE</text>
<text xml:space="preserve" text-anchor="start" x="81.59" y="-254.7" font-family="DejaVu Sans" font-size="10.00" fill="#1a1a2e">Domain x₁ ∈ {1, 2, 3, 4}, &#160;x₂ ∈ {2, 3, 4, 5}</text>
<text xml:space="preserve" text-anchor="start" x="81.59" y="-244.7" font-family="DejaVu Sans" font-size="10.00" fill="#1a1a2e">Constraint: x₁ + x₂ = 7</text>
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<g id="node2" class="node">
<title>prop</title>
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<text xml:space="preserve" text-anchor="start" x="39.96" y="-171.57" font-family="DejaVu Sans" font-weight="bold" font-size="13.00" fill="#0891b2">CONSTRAINT PROPAGATION &#160;(Filterung)</text>
<text xml:space="preserve" text-anchor="start" x="39.96" y="-147.42" font-family="DejaVu Sans" font-size="10.00" fill="#1a1a2e">• x₁ = 1 ⇒ x₂ = 6 &#160;(nicht in Domain!)</text>
<text xml:space="preserve" text-anchor="start" x="39.96" y="-137.42" font-family="DejaVu Sans" font-size="10.00" fill="#1a1a2e"> &#160;⟶ entferne 1 aus Domain(x₁)</text>
<text xml:space="preserve" text-anchor="start" x="39.96" y="-127.42" font-family="DejaVu Sans" font-size="10.00" fill="#1a1a2e">• Reduziert: x₁ ∈ {2, 3, 4}, x₂ ∈ {3, 4, 5}</text>
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<g id="edge1" class="edge">
<title>store&#45;&gt;prop</title>
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<polygon fill="#334155" stroke="#334155" stroke-width="2" points="188.61,-204.33 185.46,-195.33 182.31,-204.33 188.61,-204.33"/>
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<title>sat</title>
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<text xml:space="preserve" text-anchor="start" x="12.96" y="-54.29" font-family="DejaVu Sans" font-weight="bold" font-size="13.00" fill="#7c3aed">SAT&#45;SEARCH &amp; CONFLICT LEARNING &#160;(Nogoods)</text>
<text xml:space="preserve" text-anchor="start" x="12.96" y="-30.14" font-family="DejaVu Sans" font-size="10.00" fill="#1a1a2e">• Bei Widerspruch lernt der SAT&#45;Core eine Klausel</text>
<text xml:space="preserve" text-anchor="start" x="12.96" y="-20.14" font-family="DejaVu Sans" font-size="10.00" fill="#1a1a2e"> &#160;(„diese Belegung nie wieder prüfen“)</text>
<text xml:space="preserve" text-anchor="start" x="12.96" y="-10.14" font-family="DejaVu Sans" font-size="10.00" fill="#1a1a2e">• Non&#45;chronological Backtracking</text>
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<g id="edge2" class="edge">
<title>prop&#45;&gt;sat</title>
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<?xml version="1.0" encoding="UTF-8" standalone="no"?>
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<!-- Title: d13 Pages: 1 -->
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viewBox="7.00 7.00 561.00 170.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<title>d13</title>
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<text xml:space="preserve" text-anchor="start" x="132.96" y="-126.29" font-family="DejaVu Sans" font-weight="bold" font-size="13.00" fill="#ffffff">ANSÄTZE FÜR UNBEKANNTE ZUKUNFT</text>
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<text xml:space="preserve" text-anchor="start" x="46.33" y="-93.69" font-family="DejaVu Sans" font-weight="bold" font-size="11.00" fill="#4338ca">MONTE CARLO</text>
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<text xml:space="preserve" text-anchor="start" x="177.21" y="-93.69" font-family="DejaVu Sans" font-weight="bold" font-size="11.00" fill="#0891b2">STOCHASTISCHES RECOURSE</text>
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<text xml:space="preserve" text-anchor="start" x="375.96" y="-93.69" font-family="DejaVu Sans" font-weight="bold" font-size="11.00" fill="#059669">ROBUSTE OPTIMIERUNG</text>
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<text xml:space="preserve" text-anchor="start" x="21.96" y="-61.19" font-family="DejaVu Sans" font-size="11.00" fill="#1a1a2e">• Simuliert Szenarien</text>
<text xml:space="preserve" text-anchor="start" x="21.96" y="-47.69" font-family="DejaVu Sans" font-size="11.00" fill="#1a1a2e">• Misst Verlustverteilung</text>
<text xml:space="preserve" text-anchor="start" x="21.96" y="-34.19" font-family="DejaVu Sans" font-size="11.00" fill="#1a1a2e">• Reine Evaluierung,</text>
<text xml:space="preserve" text-anchor="start" x="36.21" y="-20.69" font-family="DejaVu Sans" font-size="11.00" fill="#1a1a2e"> &#160;keine Optimierung</text>
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<text xml:space="preserve" text-anchor="start" x="177.21" y="-61.19" font-family="DejaVu Sans" font-size="11.00" fill="#1a1a2e">• Entscheidet Stufe 1</text>
<text xml:space="preserve" text-anchor="start" x="177.21" y="-47.69" font-family="DejaVu Sans" font-size="11.00" fill="#1a1a2e">• Passt in Stufe 2 an</text>
<text xml:space="preserve" text-anchor="start" x="177.21" y="-34.19" font-family="DejaVu Sans" font-size="11.00" fill="#1a1a2e">• Optimiert Erwartungswert</text>
<text xml:space="preserve" text-anchor="start" x="197.46" y="-20.69" font-family="DejaVu Sans" font-size="11.00" fill="#1a1a2e"> &#160;über alle Szenarien</text>
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<text xml:space="preserve" text-anchor="start" x="375.96" y="-61.19" font-family="DejaVu Sans" font-size="11.00" fill="#1a1a2e">• Sucht den Worst&#45;Case</text>
<text xml:space="preserve" text-anchor="start" x="375.96" y="-47.69" font-family="DejaVu Sans" font-size="11.00" fill="#1a1a2e">• Keine Verteilungs&#45;</text>
<text xml:space="preserve" text-anchor="start" x="396.96" y="-34.19" font-family="DejaVu Sans" font-size="11.00" fill="#1a1a2e"> &#160;annahme nötig</text>
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OR_HTML_04/bilder_04/kap10_zustandskette.png Normal file
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<path fill="#eef2ff" stroke="#4338ca" stroke-width="2" d="M92.67,-74.28C92.67,-74.28 12,-74.28 12,-74.28 6,-74.28 0,-68.28 0,-62.28 0,-62.28 0,-12 0,-12 0,-6 6,0 12,0 12,0 92.67,0 92.67,0 98.67,0 104.67,-6 104.67,-12 104.67,-12 104.67,-62.28 104.67,-62.28 104.67,-68.28 98.67,-74.28 92.67,-74.28"/>
<text xml:space="preserve" text-anchor="start" x="12.96" y="-54.29" font-family="DejaVu Sans" font-weight="bold" font-size="13.00" fill="#4338ca">Zustand S₀</text>
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<text xml:space="preserve" text-anchor="start" x="405.3" y="-25.14" font-family="DejaVu Sans" font-size="10.00" fill="#ffffff">t = T</text>
<text xml:space="preserve" text-anchor="start" x="405.3" y="-15.14" font-family="DejaVu Sans" font-size="10.00" fill="#ffffff">alles verkauft</text>
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<text xml:space="preserve" text-anchor="start" x="89.83" y="-258.85" font-family="DejaVu Sans" font-weight="bold" font-size="13.00" fill="#e11d48">STICHPROBEN&#45;KOVARIANZ &#160;S</text>
<text xml:space="preserve" text-anchor="start" x="89.83" y="-234.7" font-family="DejaVu Sans" font-size="10.00" fill="#1a1a2e">• T &lt; N: singulär (Rang &lt; N)</text>
<text xml:space="preserve" text-anchor="start" x="89.83" y="-224.7" font-family="DejaVu Sans" font-size="10.00" fill="#1a1a2e">• T ≈ N: instabil, Eigenwerte streuen</text>
<text xml:space="preserve" text-anchor="start" x="89.83" y="-214.7" font-family="DejaVu Sans" font-size="10.00" fill="#1a1a2e">• kleine Eigenwerte unterschätzt</text>
<text xml:space="preserve" text-anchor="start" x="89.83" y="-204.7" font-family="DejaVu Sans" font-size="10.00" fill="#1a1a2e"> &#160;⟶ Solver nutzt Scheinkorrelationen</text>
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<text xml:space="preserve" text-anchor="start" x="12.96" y="-10.14" font-family="DejaVu Sans" font-size="10.00" fill="#1a1a2e">unverzerrt, hohes Rauschen</text>
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<!-- Title: d19 Pages: 1 -->
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<title>s1</title>
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<text xml:space="preserve" text-anchor="start" x="128.96" y="-473.41" font-family="DejaVu Sans" font-weight="bold" font-size="13.00" fill="#d97706">1 · HISTORISCHE DATENPIPELINE</text>
<text xml:space="preserve" text-anchor="start" x="128.96" y="-449.26" font-family="DejaVu Sans" font-size="10.00" fill="#1a1a2e">Automatischer Download bereinigter</text>
<text xml:space="preserve" text-anchor="start" x="128.96" y="-439.26" font-family="DejaVu Sans" font-size="10.00" fill="#1a1a2e">Kursdaten über 5 Jahre</text>
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<title>s2</title>
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<text xml:space="preserve" text-anchor="start" x="12.96" y="-366.13" font-family="DejaVu Sans" font-weight="bold" font-size="13.00" fill="#4338ca">2 · FAKTOR&#45;SCORING&#45;MODELL</text>
<text xml:space="preserve" text-anchor="start" x="12.96" y="-341.98" font-family="DejaVu Sans" font-size="10.00" fill="#1a1a2e">12−1M Momentum</text>
<text xml:space="preserve" text-anchor="start" x="12.96" y="-331.98" font-family="DejaVu Sans" font-size="10.00" fill="#1a1a2e">als Rendite&#45;Signal μₜ</text>
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<text xml:space="preserve" text-anchor="start" x="287.33" y="-366.13" font-family="DejaVu Sans" font-weight="bold" font-size="13.00" fill="#0891b2">3 · ROBUSTE KOVARIANZ</text>
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<text xml:space="preserve" text-anchor="start" x="116.21" y="-258.85" font-family="DejaVu Sans" font-weight="bold" font-size="13.00" fill="#7c3aed">4 · OR&#45;OPTIMIERUNGSKERN (CVXPY)</text>
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<text xml:space="preserve" text-anchor="start" x="106.08" y="-151.57" font-family="DejaVu Sans" font-weight="bold" font-size="13.00" fill="#0891b2">5 · REBALANCING &amp; ORDER&#45;EXECUTION</text>
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<text xml:space="preserve" text-anchor="start" x="111.33" y="-20.14" font-family="DejaVu Sans" font-size="10.00" fill="#ffffff">Sharpe, Max Drawdown, CAGR</text>
<text xml:space="preserve" text-anchor="start" x="111.33" y="-10.14" font-family="DejaVu Sans" font-size="10.00" fill="#ffffff">vs. S&amp;P 500 (SPY)</text>
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<path fill="none" stroke="#cbd5e1" stroke-dasharray="5,2" d="M100.31,-36.24C149.22,-40.68 224.08,-47.48 276.49,-52.24"/>
<polygon fill="#cbd5e1" stroke="#cbd5e1" points="275.86,-55.69 286.14,-53.11 276.5,-48.72 275.86,-55.69"/>
<text xml:space="preserve" text-anchor="middle" x="193.91" y="-52.03" font-family="DejaVu Sans" font-size="9.00" fill="#94a3b8">0 / 10, 4 € &#160;(ungenutzt)</text>
</g>
<!-- Kunde_2 -->
<g id="node5" class="node">
<title>Kunde_2</title>
<path fill="#eef2ff" stroke="#4338ca" stroke-width="2" d="M613.12,-57.34C613.12,-57.34 533.83,-57.34 533.83,-57.34 527.83,-57.34 521.83,-51.34 521.83,-45.34 521.83,-45.34 521.83,-18.13 521.83,-18.13 521.83,-12.13 527.83,-6.13 533.83,-6.13 533.83,-6.13 613.12,-6.13 613.12,-6.13 619.12,-6.13 625.12,-12.13 625.12,-18.13 625.12,-18.13 625.12,-45.34 625.12,-45.34 625.12,-51.34 619.12,-57.34 613.12,-57.34"/>
<text xml:space="preserve" text-anchor="middle" x="573.47" y="-41.36" font-family="DejaVu Sans" font-size="10.00">Kunde 2</text>
<text xml:space="preserve" text-anchor="middle" x="573.47" y="-28.61" font-family="DejaVu Sans" font-size="10.00">Bedarf &#45;15</text>
<text xml:space="preserve" text-anchor="middle" x="573.47" y="-15.86" font-family="DejaVu Sans" font-size="10.00">Knotenpreis &#45;3 €</text>
</g>
<!-- Werk_B&#45;&gt;Kunde_2 -->
<g id="edge4" class="edge">
<title>Werk_B&#45;&gt;Kunde_2</title>
<path fill="none" stroke="#b45309" stroke-width="4" d="M100.44,-22.29C166.16,-10.96 285.65,5.56 387.83,-2.49 427.11,-5.58 470.66,-12.32 505.6,-18.55"/>
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<text xml:space="preserve" text-anchor="middle" x="338.06" y="-5.19" font-family="DejaVu Sans" font-size="9.00" fill="#b45309">10 / 10, 6 € &#160;⟵ voll</text>
</g>
<!-- Umschlag&#45;&gt;Kunde_1 -->
<g id="edge5" class="edge">
<title>Umschlag&#45;&gt;Kunde_1</title>
<path fill="none" stroke="#0891b2" stroke-width="2.5" d="M388.56,-73.22C423.4,-84.11 470.35,-98.8 508.09,-110.6"/>
<polygon fill="#0891b2" stroke="#0891b2" stroke-width="2.5" points="506.83,-113.87 517.41,-113.52 508.91,-107.19 506.83,-113.87"/>
<text xml:space="preserve" text-anchor="middle" x="454.83" y="-103.48" font-family="DejaVu Sans" font-size="9.00" fill="#334155">10 / 20, 1 €</text>
</g>
<!-- Umschlag&#45;&gt;Kunde_2 -->
<g id="edge6" class="edge">
<title>Umschlag&#45;&gt;Kunde_2</title>
<path fill="none" stroke="#0891b2" stroke-width="2.5" d="M388.56,-52.22C423.24,-48.36 469.94,-43.16 507.6,-38.96"/>
<polygon fill="#0891b2" stroke="#0891b2" stroke-width="2.5" points="507.71,-42.47 517.26,-37.89 506.94,-35.52 507.71,-42.47"/>
<text xml:space="preserve" text-anchor="middle" x="454.83" y="-50.53" font-family="DejaVu Sans" font-size="9.00" fill="#334155">5 / 10, 3 €</text>
</g>
</g>
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<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<!-- Generated by graphviz version 14.1.2 (20260126.1125)
-->
<!-- Pages: 1 -->
<svg width="581pt" height="301pt"
viewBox="0.00 0.00 581.00 301.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 296.63)">
<text xml:space="preserve" text-anchor="middle" x="286.68" y="-277.23" font-family="DejaVu Sans" font-size="12.00">Branch&#45;and&#45;Bound: 5 gelöste LPs statt aller ganzzahligen Punkte</text>
<text xml:space="preserve" text-anchor="middle" x="286.68" y="-262.98" font-family="DejaVu Sans" font-size="12.00">max 5x₁ + 4x₂ &#160;u.d.N. &#160;6x₁+4x₂ ≤ 24, &#160;x₁+2x₂ ≤ 6</text>
<!-- P₀ -->
<g id="node1" class="node">
<title>P₀</title>
<path fill="#eef2ff" stroke="#4338ca" stroke-width="2" d="M356.91,-256.13C356.91,-256.13 216.88,-256.13 216.88,-256.13 210.88,-256.13 204.88,-250.13 204.88,-244.13 204.88,-244.13 204.88,-216.92 204.88,-216.92 204.88,-210.92 210.88,-204.92 216.88,-204.92 216.88,-204.92 356.91,-204.92 356.91,-204.92 362.91,-204.92 368.91,-210.92 368.91,-216.92 368.91,-216.92 368.91,-244.13 368.91,-244.13 368.91,-250.13 362.91,-256.13 356.91,-256.13"/>
<text xml:space="preserve" text-anchor="middle" x="286.89" y="-240.15" font-family="DejaVu Sans" font-size="10.00">P₀</text>
<text xml:space="preserve" text-anchor="middle" x="286.89" y="-227.4" font-family="DejaVu Sans" font-size="10.00">x = (3; 1,5), Schranke Z ≤ 21</text>
<text xml:space="preserve" text-anchor="middle" x="286.89" y="-214.65" font-family="DejaVu Sans" font-size="10.00">x2 gebrochen — verzweigen</text>
</g>
<!-- A -->
<g id="node2" class="node">
<title>A</title>
<path fill="#ecfeff" stroke="#0891b2" stroke-width="2" d="M270.41,-153.67C270.41,-153.67 109.38,-153.67 109.38,-153.67 103.38,-153.67 97.37,-147.67 97.37,-141.67 97.37,-141.67 97.37,-114.46 97.37,-114.46 97.37,-108.46 103.37,-102.46 109.37,-102.46 109.37,-102.46 270.41,-102.46 270.41,-102.46 276.41,-102.46 282.41,-108.46 282.41,-114.46 282.41,-114.46 282.41,-141.67 282.41,-141.67 282.41,-147.67 276.41,-153.67 270.41,-153.67"/>
<text xml:space="preserve" text-anchor="middle" x="189.89" y="-137.69" font-family="DejaVu Sans" font-size="10.00">A</text>
<text xml:space="preserve" text-anchor="middle" x="189.89" y="-124.94" font-family="DejaVu Sans" font-size="10.00">x = (3,33; 1), Schranke Z ≤ 20,67</text>
<text xml:space="preserve" text-anchor="middle" x="189.89" y="-112.19" font-family="DejaVu Sans" font-size="10.00">x1 gebrochen — verzweigen</text>
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<g id="edge1" class="edge">
<title>P₀&#45;&gt;A</title>
<path fill="none" stroke="#5c6380" d="M262.42,-204.17C250.24,-191.56 235.36,-176.15 222.26,-162.58"/>
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<text xml:space="preserve" text-anchor="middle" x="256.68" y="-176.37" font-family="DejaVu Sans" font-size="9.00">x2 ≤ 1</text>
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<g id="node5" class="node">
<title>B</title>
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<text xml:space="preserve" text-anchor="middle" x="382.89" y="-137.69" font-family="DejaVu Sans" font-size="10.00">B</text>
<text xml:space="preserve" text-anchor="middle" x="382.89" y="-124.94" font-family="DejaVu Sans" font-size="10.00">Z = 18 ≤ Incumbent 20</text>
<text xml:space="preserve" text-anchor="middle" x="382.89" y="-112.19" font-family="DejaVu Sans" font-size="10.00">→ gekappt</text>
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<g id="edge4" class="edge">
<title>P₀&#45;&gt;B</title>
<path fill="none" stroke="#5c6380" d="M311.12,-204.17C323.17,-191.56 337.9,-176.15 350.87,-162.58"/>
<polygon fill="#5c6380" stroke="#5c6380" points="353.25,-165.15 357.63,-155.5 348.19,-160.31 353.25,-165.15"/>
<text xml:space="preserve" text-anchor="middle" x="353.15" y="-176.37" font-family="DejaVu Sans" font-size="9.00">x2 ≥ 2</text>
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<!-- A1 -->
<g id="node3" class="node">
<title>A1</title>
<path fill="#ecfdf5" stroke="#059669" stroke-width="2" d="M161.79,-51.21C161.79,-51.21 12,-51.21 12,-51.21 6,-51.21 0,-45.21 0,-39.21 0,-39.21 0,-12 0,-12 0,-6 6,0 12,0 12,0 161.79,0 161.79,0 167.79,0 173.79,-6 173.79,-12 173.79,-12 173.79,-39.21 173.79,-39.21 173.79,-45.21 167.79,-51.21 161.79,-51.21"/>
<text xml:space="preserve" text-anchor="middle" x="86.89" y="-35.23" font-family="DejaVu Sans" font-size="10.00">A1</text>
<text xml:space="preserve" text-anchor="middle" x="86.89" y="-22.48" font-family="DejaVu Sans" font-size="10.00">x = (3; 1), Z = 19</text>
<text xml:space="preserve" text-anchor="middle" x="86.89" y="-9.73" font-family="DejaVu Sans" font-size="10.00">ganzzahlig — neuer Incumbent</text>
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<g id="edge2" class="edge">
<title>A&#45;&gt;A1</title>
<path fill="none" stroke="#5c6380" d="M163.9,-101.71C150.85,-88.98 134.87,-73.4 120.86,-59.74"/>
<polygon fill="#5c6380" stroke="#5c6380" points="123.56,-57.48 113.96,-53 118.68,-62.49 123.56,-57.48"/>
<text xml:space="preserve" text-anchor="middle" x="156.86" y="-73.91" font-family="DejaVu Sans" font-size="9.00">x1 ≤ 3</text>
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<g id="node4" class="node">
<title>A2</title>
<path fill="#ecfdf5" stroke="#059669" stroke-width="2" d="M367.79,-51.21C367.79,-51.21 218,-51.21 218,-51.21 212,-51.21 206,-45.21 206,-39.21 206,-39.21 206,-12 206,-12 206,-6 212,0 218,0 218,0 367.79,0 367.79,0 373.79,0 379.79,-6 379.79,-12 379.79,-12 379.79,-39.21 379.79,-39.21 379.79,-45.21 373.79,-51.21 367.79,-51.21"/>
<text xml:space="preserve" text-anchor="middle" x="292.89" y="-35.23" font-family="DejaVu Sans" font-size="10.00">A2</text>
<text xml:space="preserve" text-anchor="middle" x="292.89" y="-22.48" font-family="DejaVu Sans" font-size="10.00">x = (4; 0), Z = 20</text>
<text xml:space="preserve" text-anchor="middle" x="292.89" y="-9.73" font-family="DejaVu Sans" font-size="10.00">ganzzahlig — neuer Incumbent</text>
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<g id="edge3" class="edge">
<title>A&#45;&gt;A2</title>
<path fill="none" stroke="#5c6380" d="M215.89,-101.71C228.94,-88.98 244.92,-73.4 258.93,-59.74"/>
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<text xml:space="preserve" text-anchor="middle" x="259.86" y="-73.91" font-family="DejaVu Sans" font-size="9.00">x1 ≥ 4</text>
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<g id="node6" class="node">
<title>ergebnis</title>
<polygon fill="#f8fafc" stroke="#94a3b8" points="567.36,-248.53 400.44,-248.53 400.44,-212.53 573.36,-212.53 573.36,-242.53 567.36,-248.53"/>
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<text xml:space="preserve" text-anchor="middle" x="486.89" y="-227.4" font-family="DejaVu Sans" font-size="10.00">Optimum: x* = (4; 0), Z* = 20</text>
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</g>
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<?xml version="1.0" encoding="UTF-8" standalone="no"?>
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<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 364.66)">
<text xml:space="preserve" text-anchor="middle" x="350.58" y="-344.31" font-family="DejaVu Sans" font-size="13.00">Die Schichten von or_kern.py — alle Pfeile zeigen nach innen</text>
<!-- io -->
<g id="node1" class="node">
<title>io</title>
<path fill="#fffbeb" stroke="#b45309" stroke-width="2" d="M248.04,-237.7C248.04,-237.7 12,-237.7 12,-237.7 6,-237.7 0,-231.7 0,-225.7 0,-225.7 0,-198.49 0,-198.49 0,-192.49 6,-186.49 12,-186.49 12,-186.49 248.04,-186.49 248.04,-186.49 254.04,-186.49 260.04,-192.49 260.04,-198.49 260.04,-198.49 260.04,-225.7 260.04,-225.7 260.04,-231.7 254.04,-237.7 248.04,-237.7"/>
<text xml:space="preserve" text-anchor="middle" x="130.02" y="-221.72" font-family="DejaVu Sans" font-size="10.00">Ein&#45; und Ausgabe</text>
<text xml:space="preserve" text-anchor="middle" x="130.02" y="-208.97" font-family="DejaVu Sans" font-size="10.00">lade_produktionsproblem() · schreibe_ergebnis()</text>
<text xml:space="preserve" text-anchor="middle" x="130.02" y="-196.22" font-family="DejaVu Sans" font-size="10.00">Excel, CSV — die Wirklichkeit des Anwenders</text>
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<!-- dom -->
<g id="node5" class="node">
<title>dom</title>
<path fill="#eef2ff" stroke="#4338ca" stroke-width="2" d="M465.04,-139.24C465.04,-139.24 271,-139.24 271,-139.24 265,-139.24 259,-133.24 259,-127.24 259,-127.24 259,-100.03 259,-100.03 259,-94.03 265,-88.03 271,-88.03 271,-88.03 465.04,-88.03 465.04,-88.03 471.04,-88.03 477.04,-94.03 477.04,-100.03 477.04,-100.03 477.04,-127.24 477.04,-127.24 477.04,-133.24 471.04,-139.24 465.04,-139.24"/>
<text xml:space="preserve" text-anchor="middle" x="368.02" y="-123.26" font-family="DejaVu Sans" font-size="10.00">Domäne</text>
<text xml:space="preserve" text-anchor="middle" x="368.02" y="-110.51" font-family="DejaVu Sans" font-size="10.00">Produkt · Produktionsproblem</text>
<text xml:space="preserve" text-anchor="middle" x="368.02" y="-97.76" font-family="DejaVu Sans" font-size="10.00">validiert (Pydantic), kennt keinen Solver</text>
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<!-- io&#45;&gt;dom -->
<g id="edge1" class="edge">
<title>io&#45;&gt;dom</title>
<path fill="none" stroke="#5c6380" d="M153.56,-185.74C166.52,-171.78 180.02,-157.24 180.02,-157.24 180.02,-157.24 210.63,-150.3 247.15,-142.03"/>
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<text xml:space="preserve" text-anchor="middle" x="235.52" y="-159.94" font-family="DejaVu Sans" font-size="9.00">liest ein, schreibt zurück</text>
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<g id="node2" class="node">
<title>bau</title>
<path fill="#f5f3ff" stroke="#7c3aed" stroke-width="2" d="M432.04,-336.16C432.04,-336.16 256,-336.16 256,-336.16 250,-336.16 244,-330.16 244,-324.16 244,-324.16 244,-296.95 244,-296.95 244,-290.95 250,-284.95 256,-284.95 256,-284.95 432.04,-284.95 432.04,-284.95 438.04,-284.95 444.04,-290.95 444.04,-296.95 444.04,-296.95 444.04,-324.16 444.04,-324.16 444.04,-330.16 438.04,-336.16 432.04,-336.16"/>
<text xml:space="preserve" text-anchor="middle" x="344.02" y="-320.18" font-family="DejaVu Sans" font-size="10.00">Modellbauer — austauschbar</text>
<text xml:space="preserve" text-anchor="middle" x="344.02" y="-307.43" font-family="DejaVu Sans" font-size="10.00">loese_mit_glop() · loese_mit_scipy()</text>
<text xml:space="preserve" text-anchor="middle" x="344.02" y="-294.68" font-family="DejaVu Sans" font-size="10.00">je Solver einer, gleiche Signatur</text>
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<!-- erg -->
<g id="node4" class="node">
<title>erg</title>
<path fill="#ecfeff" stroke="#0891b2" stroke-width="2" d="M588.66,-237.7C588.66,-237.7 437.38,-237.7 437.38,-237.7 431.38,-237.7 425.38,-231.7 425.38,-225.7 425.38,-225.7 425.38,-198.49 425.38,-198.49 425.38,-192.49 431.38,-186.49 437.38,-186.49 437.38,-186.49 588.66,-186.49 588.66,-186.49 594.66,-186.49 600.66,-192.49 600.66,-198.49 600.66,-198.49 600.66,-225.7 600.66,-225.7 600.66,-231.7 594.66,-237.7 588.66,-237.7"/>
<text xml:space="preserve" text-anchor="middle" x="513.02" y="-221.72" font-family="DejaVu Sans" font-size="10.00">Ergebnis — solverunabhängig</text>
<text xml:space="preserve" text-anchor="middle" x="513.02" y="-208.97" font-family="DejaVu Sans" font-size="10.00">SolverStatus · Loesung</text>
<text xml:space="preserve" text-anchor="middle" x="513.02" y="-196.22" font-family="DejaVu Sans" font-size="10.00">fünf Bibliotheken, eine Sprache</text>
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<g id="edge3" class="edge">
<title>bau&#45;&gt;erg</title>
<path fill="none" stroke="#5c6380" d="M388.87,-283.96C410.25,-271.76 436.01,-257.05 458.51,-244.21"/>
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<text xml:space="preserve" text-anchor="middle" x="446.34" y="-258.4" font-family="DejaVu Sans" font-size="9.00">liefert</text>
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<text xml:space="preserve" text-anchor="middle" x="244.04" y="-528.69" font-family="DejaVu Sans" font-size="13.00">Optimierungsdienst: warum die Antwort 202 lautet, nicht 200</text>
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<text xml:space="preserve" text-anchor="middle" x="317.64" y="-120.76" font-family="DejaVu Sans" font-size="10.00">Hintergrundrechnung</text>
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<text xml:space="preserve" text-anchor="start" x="207.77" y="-33.84" font-family="DejaVu Sans" font-size="9.00">Eine Optimierung dauert Sekunden bis Minuten.</text>
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<text xml:space="preserve" text-anchor="middle" x="365.89" y="-507.4" font-family="DejaVu Sans" font-size="13.00">Welches Werkzeug passt zu meinem Problem? (Teil II)</text>
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<title>f1&#45;&gt;f2</title>
<path fill="none" stroke="#5c6380" d="M513.35,-448.6C497.2,-434.96 475.99,-417.04 458.13,-401.95"/>
<polygon fill="#5c6380" stroke="#5c6380" points="460.72,-399.55 450.82,-395.77 456.2,-404.9 460.72,-399.55"/>
<text xml:space="preserve" text-anchor="middle" x="493.75" y="-417.94" font-family="DejaVu Sans" font-size="9.00">nein</text>
</g>
<!-- routing -->
<g id="node6" class="node">
<title>routing</title>
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<text xml:space="preserve" text-anchor="middle" x="653.52" y="-374.11" font-family="DejaVu Sans" font-size="10.00">OR&#45;Tools Routing</text>
<text xml:space="preserve" text-anchor="middle" x="653.52" y="-361.36" font-family="DejaVu Sans" font-size="10.00">(Kapitel Graphen)</text>
</g>
<!-- f1&#45;&gt;routing -->
<g id="edge1" class="edge">
<title>f1&#45;&gt;routing</title>
<path fill="none" stroke="#5c6380" d="M563.47,-448.6C580.84,-433.8 604.13,-413.96 622.66,-398.16"/>
<polygon fill="#5c6380" stroke="#5c6380" points="624.84,-400.9 630.18,-391.75 620.3,-395.57 624.84,-400.9"/>
<text xml:space="preserve" text-anchor="middle" x="603.22" y="-417.94" font-family="DejaVu Sans" font-size="9.00">ja</text>
</g>
<!-- f3 -->
<g id="node3" class="node">
<title>f3</title>
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<text xml:space="preserve" text-anchor="middle" x="264.52" y="-261.35" font-family="DejaVu Sans" font-size="10.00">Zielfunktion und alle</text>
<text xml:space="preserve" text-anchor="middle" x="264.52" y="-248.6" font-family="DejaVu Sans" font-size="10.00">Nebenbedingungen linear?</text>
</g>
<!-- f2&#45;&gt;f3 -->
<g id="edge4" class="edge">
<title>f2&#45;&gt;f3</title>
<path fill="none" stroke="#5c6380" d="M390.93,-347.71C366.19,-330.38 331.63,-306.14 304.89,-287.4"/>
<polygon fill="#5c6380" stroke="#5c6380" points="307.23,-284.76 297.03,-281.89 303.21,-290.5 307.23,-284.76"/>
<text xml:space="preserve" text-anchor="middle" x="367.42" y="-317.93" font-family="DejaVu Sans" font-size="9.00">nein</text>
</g>
<!-- f4 -->
<g id="node4" class="node">
<title>f4</title>
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<text xml:space="preserve" text-anchor="middle" x="581.52" y="-267.73" font-family="DejaVu Sans" font-size="10.00">Logische Regeln</text>
<text xml:space="preserve" text-anchor="middle" x="581.52" y="-254.98" font-family="DejaVu Sans" font-size="10.00">(wenn&#45;dann, entweder&#45;oder)</text>
<text xml:space="preserve" text-anchor="middle" x="581.52" y="-242.23" font-family="DejaVu Sans" font-size="10.00">oder Zeitplanung?</text>
</g>
<!-- f2&#45;&gt;f4 -->
<g id="edge3" class="edge">
<title>f2&#45;&gt;f4</title>
<path fill="none" stroke="#5c6380" d="M454.31,-347.71C476.01,-332.6 505.23,-312.24 530.19,-294.85"/>
<polygon fill="#5c6380" stroke="#5c6380" points="532.08,-297.8 538.29,-289.22 528.08,-292.06 532.08,-297.8"/>
<text xml:space="preserve" text-anchor="middle" x="501" y="-317.93" font-family="DejaVu Sans" font-size="9.00">ja</text>
</g>
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<g id="node5" class="node">
<title>f5</title>
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<text xml:space="preserve" text-anchor="middle" x="134.52" y="-126.09" font-family="DejaVu Sans" font-size="10.00">Nur Fluss oder</text>
<text xml:space="preserve" text-anchor="middle" x="134.52" y="-113.34" font-family="DejaVu Sans" font-size="10.00">Zuordnung im Netzwerk?</text>
</g>
<!-- f3&#45;&gt;f5 -->
<g id="edge7" class="edge">
<title>f3&#45;&gt;f5</title>
<path fill="none" stroke="#5c6380" d="M241.58,-233.58C220.32,-211.79 188.55,-179.22 165.14,-155.22"/>
<polygon fill="#5c6380" stroke="#5c6380" points="167.78,-152.92 158.29,-148.21 162.77,-157.81 167.78,-152.92"/>
<text xml:space="preserve" text-anchor="middle" x="211.05" y="-181.17" font-family="DejaVu Sans" font-size="9.00">ja</text>
</g>
<!-- teil3 -->
<g id="node11" class="node">
<title>teil3</title>
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<text xml:space="preserve" text-anchor="middle" x="342.52" y="-119.72" font-family="DejaVu Sans" font-size="10.00">weiter in Teil III</text>
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<g id="edge8" class="edge">
<title>f3&#45;&gt;teil3</title>
<path fill="none" stroke="#5c6380" d="M279.19,-232.03C292.65,-209.05 312.53,-175.07 326.42,-151.35"/>
<polygon fill="#5c6380" stroke="#5c6380" points="329.36,-153.26 331.39,-142.86 323.31,-149.72 329.36,-153.26"/>
<text xml:space="preserve" text-anchor="middle" x="324.81" y="-181.17" font-family="DejaVu Sans" font-size="9.00">nein</text>
</g>
<!-- cpsat -->
<g id="node7" class="node">
<title>cpsat</title>
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<text xml:space="preserve" text-anchor="middle" x="492.52" y="-126.09" font-family="DejaVu Sans" font-size="10.00">CP&#45;SAT</text>
<text xml:space="preserve" text-anchor="middle" x="492.52" y="-113.34" font-family="DejaVu Sans" font-size="10.00">(Kapitel CP&#45;SAT)</text>
</g>
<!-- f4&#45;&gt;cpsat -->
<g id="edge5" class="edge">
<title>f4&#45;&gt;cpsat</title>
<path fill="none" stroke="#5c6380" d="M558.6,-222.78C543.99,-200.91 525.3,-172.91 511.52,-152.29"/>
<polygon fill="#5c6380" stroke="#5c6380" points="514.5,-150.44 506.03,-144.07 508.67,-154.33 514.5,-150.44"/>
<text xml:space="preserve" text-anchor="middle" x="546.1" y="-181.17" font-family="DejaVu Sans" font-size="9.00">ja</text>
</g>
<!-- milp -->
<g id="node8" class="node">
<title>milp</title>
<path fill="#ecfeff" stroke="#0891b2" stroke-width="2" d="M685.54,-142.07C685.54,-142.07 581.5,-142.07 581.5,-142.07 575.5,-142.07 569.5,-136.07 569.5,-130.07 569.5,-130.07 569.5,-115.61 569.5,-115.61 569.5,-109.61 575.5,-103.61 581.5,-103.61 581.5,-103.61 685.54,-103.61 685.54,-103.61 691.54,-103.61 697.54,-109.61 697.54,-115.61 697.54,-115.61 697.54,-130.07 697.54,-130.07 697.54,-136.07 691.54,-142.07 685.54,-142.07"/>
<text xml:space="preserve" text-anchor="middle" x="633.52" y="-126.09" font-family="DejaVu Sans" font-size="10.00">MILP: HiGHS / CP&#45;SAT</text>
<text xml:space="preserve" text-anchor="middle" x="633.52" y="-113.34" font-family="DejaVu Sans" font-size="10.00">(Kapitel MILP)</text>
</g>
<!-- f4&#45;&gt;milp -->
<g id="edge6" class="edge">
<title>f4&#45;&gt;milp</title>
<path fill="none" stroke="#5c6380" d="M595.87,-220.33C604.1,-199.24 614.29,-173.11 622,-153.37"/>
<polygon fill="#5c6380" stroke="#5c6380" points="625.18,-154.85 625.55,-144.26 618.66,-152.3 625.18,-154.85"/>
<text xml:space="preserve" text-anchor="middle" x="642.97" y="-192.42" font-family="DejaVu Sans" font-size="9.00">nein</text>
<text xml:space="preserve" text-anchor="middle" x="642.97" y="-181.17" font-family="DejaVu Sans" font-size="9.00">(Fixkosten,</text>
<text xml:space="preserve" text-anchor="middle" x="642.97" y="-169.92" font-family="DejaVu Sans" font-size="9.00">Kardinalität)</text>
</g>
<!-- netz -->
<g id="node9" class="node">
<title>netz</title>
<path fill="#ecfdf5" stroke="#059669" stroke-width="2" d="M116.29,-51.21C116.29,-51.21 16.75,-51.21 16.75,-51.21 10.75,-51.21 4.75,-45.21 4.75,-39.21 4.75,-39.21 4.75,-12 4.75,-12 4.75,-6 10.75,0 16.75,0 16.75,0 116.29,0 116.29,0 122.29,0 128.29,-6 128.29,-12 128.29,-12 128.29,-39.21 128.29,-39.21 128.29,-45.21 122.29,-51.21 116.29,-51.21"/>
<text xml:space="preserve" text-anchor="middle" x="66.52" y="-35.23" font-family="DejaVu Sans" font-size="10.00">Spezialalgorithmus:</text>
<text xml:space="preserve" text-anchor="middle" x="66.52" y="-22.48" font-family="DejaVu Sans" font-size="10.00">Min&#45;Cost&#45;Flow,</text>
<text xml:space="preserve" text-anchor="middle" x="66.52" y="-9.73" font-family="DejaVu Sans" font-size="10.00">Ungarische Methode</text>
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<!-- f5&#45;&gt;netz -->
<g id="edge9" class="edge">
<title>f5&#45;&gt;netz</title>
<path fill="none" stroke="#5c6380" d="M117.36,-97.81C109.4,-86.66 99.78,-73.19 91.07,-60.99"/>
<polygon fill="#5c6380" stroke="#5c6380" points="94.16,-59.3 85.51,-53.19 88.47,-63.37 94.16,-59.3"/>
<text xml:space="preserve" text-anchor="middle" x="106.31" y="-69.91" font-family="DejaVu Sans" font-size="9.00">ja</text>
</g>
<!-- lp -->
<g id="node10" class="node">
<title>lp</title>
<path fill="#eef2ff" stroke="#4338ca" stroke-width="2" d="M242.04,-51.21C242.04,-51.21 165,-51.21 165,-51.21 159,-51.21 153,-45.21 153,-39.21 153,-39.21 153,-12 153,-12 153,-6 159,0 165,0 165,0 242.04,0 242.04,0 248.04,0 254.04,-6 254.04,-12 254.04,-12 254.04,-39.21 254.04,-39.21 254.04,-45.21 248.04,-51.21 242.04,-51.21"/>
<text xml:space="preserve" text-anchor="middle" x="203.52" y="-35.23" font-family="DejaVu Sans" font-size="10.00">LP: scipy.linprog</text>
<text xml:space="preserve" text-anchor="middle" x="203.52" y="-22.48" font-family="DejaVu Sans" font-size="10.00">oder highspy</text>
<text xml:space="preserve" text-anchor="middle" x="203.52" y="-9.73" font-family="DejaVu Sans" font-size="10.00">(Kapitel LP)</text>
</g>
<!-- f5&#45;&gt;lp -->
<g id="edge10" class="edge">
<title>f5&#45;&gt;lp</title>
<path fill="none" stroke="#5c6380" d="M151.93,-97.81C160.01,-86.66 169.77,-73.19 178.61,-60.99"/>
<polygon fill="#5c6380" stroke="#5c6380" points="181.23,-63.34 184.26,-53.19 175.56,-59.23 181.23,-63.34"/>
<text xml:space="preserve" text-anchor="middle" x="182.9" y="-69.91" font-family="DejaVu Sans" font-size="9.00">nein</text>
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<text xml:space="preserve" text-anchor="middle" x="490.89" y="-383.39" font-family="DejaVu Sans" font-size="13.00">Welches Werkzeug passt zu meinem Problem? (Teil III)</text>
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<g id="node1" class="node">
<title>g1</title>
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<text xml:space="preserve" text-anchor="middle" x="510.89" y="-350.11" font-family="DejaVu Sans" font-size="10.00">Sind die Daten sicher</text>
<text xml:space="preserve" text-anchor="middle" x="510.89" y="-337.36" font-family="DejaVu Sans" font-size="10.00">bekannt?</text>
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<g id="node2" class="node">
<title>g2</title>
<polygon fill="#eef2ff" stroke="#4338ca" stroke-width="1.6" points="370.89,-275.23 259.62,-234.1 370.89,-192.97 482.16,-234.1 370.89,-275.23"/>
<text xml:space="preserve" text-anchor="middle" x="370.89" y="-243.72" font-family="DejaVu Sans" font-size="10.00">Entscheidung fällt in</text>
<text xml:space="preserve" text-anchor="middle" x="370.89" y="-230.97" font-family="DejaVu Sans" font-size="10.00">mehreren Stufen</text>
<text xml:space="preserve" text-anchor="middle" x="370.89" y="-218.22" font-family="DejaVu Sans" font-size="10.00">über die Zeit?</text>
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<g id="edge2" class="edge">
<title>g1&#45;&gt;g2</title>
<path fill="none" stroke="#5c6380" d="M483.9,-324.5C464.33,-309.02 437.44,-287.74 414.8,-269.83"/>
<polygon fill="#5c6380" stroke="#5c6380" points="417.23,-267.3 407.22,-263.84 412.89,-272.79 417.23,-267.3"/>
<text xml:space="preserve" text-anchor="middle" x="463.18" y="-293.93" font-family="DejaVu Sans" font-size="9.00">nein</text>
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<g id="node4" class="node">
<title>g4</title>
<polygon fill="#eef2ff" stroke="#4338ca" stroke-width="1.6" points="651.89,-275.23 506.88,-234.1 651.89,-192.97 796.91,-234.1 651.89,-275.23"/>
<text xml:space="preserve" text-anchor="middle" x="651.89" y="-243.72" font-family="DejaVu Sans" font-size="10.00">Zielfunktion konvex?</text>
<text xml:space="preserve" text-anchor="middle" x="651.89" y="-230.97" font-family="DejaVu Sans" font-size="10.00">(Quadrate, Normen,</text>
<text xml:space="preserve" text-anchor="middle" x="651.89" y="-218.22" font-family="DejaVu Sans" font-size="10.00">log/exp konvex kombiniert)</text>
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<g id="edge1" class="edge">
<title>g1&#45;&gt;g4</title>
<path fill="none" stroke="#5c6380" d="M538.08,-324.5C556.93,-309.7 582.53,-289.59 604.67,-272.2"/>
<polygon fill="#5c6380" stroke="#5c6380" points="606.71,-275.05 612.41,-266.12 602.38,-269.54 606.71,-275.05"/>
<text xml:space="preserve" text-anchor="middle" x="580.92" y="-293.93" font-family="DejaVu Sans" font-size="9.00">ja</text>
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<g id="node3" class="node">
<title>g3</title>
<polygon fill="#eef2ff" stroke="#4338ca" stroke-width="1.6" points="155.89,-149.72 40.88,-121.34 155.89,-92.96 270.91,-121.34 155.89,-149.72"/>
<text xml:space="preserve" text-anchor="middle" x="155.89" y="-124.59" font-family="DejaVu Sans" font-size="10.00">Wahrscheinlichkeiten</text>
<text xml:space="preserve" text-anchor="middle" x="155.89" y="-111.84" font-family="DejaVu Sans" font-size="10.00">bekannt?</text>
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<g id="edge4" class="edge">
<title>g2&#45;&gt;g3</title>
<path fill="none" stroke="#5c6380" d="M324.77,-209.34C288.68,-190.75 238.71,-165 202.5,-146.35"/>
<polygon fill="#5c6380" stroke="#5c6380" points="204.51,-143.45 194.02,-141.98 201.3,-149.67 204.51,-143.45"/>
<text xml:space="preserve" text-anchor="middle" x="266.7" y="-168.42" font-family="DejaVu Sans" font-size="9.00">nein</text>
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<!-- dp -->
<g id="node6" class="node">
<title>dp</title>
<path fill="#fffbeb" stroke="#b45309" stroke-width="2" d="M452.16,-140.57C452.16,-140.57 307.62,-140.57 307.62,-140.57 301.62,-140.57 295.62,-134.57 295.62,-128.57 295.62,-128.57 295.62,-114.11 295.62,-114.11 295.62,-108.11 301.62,-102.11 307.62,-102.11 307.62,-102.11 452.16,-102.11 452.16,-102.11 458.16,-102.11 464.16,-108.11 464.16,-114.11 464.16,-114.11 464.16,-128.57 464.16,-128.57 464.16,-134.57 458.16,-140.57 452.16,-140.57"/>
<text xml:space="preserve" text-anchor="middle" x="379.89" y="-124.59" font-family="DejaVu Sans" font-size="10.00">Dynamische Programmierung</text>
<text xml:space="preserve" text-anchor="middle" x="379.89" y="-111.84" font-family="DejaVu Sans" font-size="10.00">(Bellman)</text>
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<g id="edge3" class="edge">
<title>g2&#45;&gt;dp</title>
<path fill="none" stroke="#5c6380" d="M374.12,-193.43C375.21,-179.97 376.41,-165.17 377.44,-152.57"/>
<polygon fill="#5c6380" stroke="#5c6380" points="380.91,-153.05 378.23,-142.8 373.93,-152.48 380.91,-153.05"/>
<text xml:space="preserve" text-anchor="middle" x="379.95" y="-168.42" font-family="DejaVu Sans" font-size="9.00">ja</text>
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<g id="node7" class="node">
<title>stoch</title>
<path fill="#f5f3ff" stroke="#7c3aed" stroke-width="2" d="M137.79,-38.46C137.79,-38.46 12,-38.46 12,-38.46 6,-38.46 0,-32.46 0,-26.46 0,-26.46 0,-12 0,-12 0,-6 6,0 12,0 12,0 137.79,0 137.79,0 143.79,0 149.79,-6 149.79,-12 149.79,-12 149.79,-26.46 149.79,-26.46 149.79,-32.46 143.79,-38.46 137.79,-38.46"/>
<text xml:space="preserve" text-anchor="middle" x="74.89" y="-22.48" font-family="DejaVu Sans" font-size="10.00">Zweistufige stochastische</text>
<text xml:space="preserve" text-anchor="middle" x="74.89" y="-9.73" font-family="DejaVu Sans" font-size="10.00">Optimierung, Szenarien</text>
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<!-- g3&#45;&gt;stoch -->
<g id="edge5" class="edge">
<title>g3&#45;&gt;stoch</title>
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<polygon fill="#5c6380" stroke="#5c6380" points="100.21,-45.95 91.2,-40.38 94.76,-50.35 100.21,-45.95"/>
<text xml:space="preserve" text-anchor="middle" x="123.99" y="-62.79" font-family="DejaVu Sans" font-size="9.00">ja</text>
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<g id="node8" class="node">
<title>robust</title>
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<text xml:space="preserve" text-anchor="middle" x="237.89" y="-22.48" font-family="DejaVu Sans" font-size="10.00">Robuste Optimierung</text>
<text xml:space="preserve" text-anchor="middle" x="237.89" y="-9.73" font-family="DejaVu Sans" font-size="10.00">(Worst Case)</text>
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<g id="edge6" class="edge">
<title>g3&#45;&gt;robust</title>
<path fill="none" stroke="#5c6380" d="M174.91,-97.12C186.94,-82.44 202.54,-63.39 215.21,-47.93"/>
<polygon fill="#5c6380" stroke="#5c6380" points="217.69,-50.42 221.32,-40.47 212.28,-45.98 217.69,-50.42"/>
<text xml:space="preserve" text-anchor="middle" x="246.16" y="-68.41" font-family="DejaVu Sans" font-size="9.00">nein,</text>
<text xml:space="preserve" text-anchor="middle" x="246.16" y="-57.16" font-family="DejaVu Sans" font-size="9.00">nur Bandbreiten</text>
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<g id="node5" class="node">
<title>g5</title>
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<text xml:space="preserve" text-anchor="middle" x="646.89" y="-124.59" font-family="DejaVu Sans" font-size="10.00">Quadratisch mit</text>
<text xml:space="preserve" text-anchor="middle" x="646.89" y="-111.84" font-family="DejaVu Sans" font-size="10.00">linearen Nebenbedingungen?</text>
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<g id="edge7" class="edge">
<title>g4&#45;&gt;g5</title>
<path fill="none" stroke="#5c6380" d="M650.08,-192.8C649.61,-182.57 649.12,-171.61 648.66,-161.44"/>
<polygon fill="#5c6380" stroke="#5c6380" points="652.16,-161.32 648.21,-151.48 645.17,-161.63 652.16,-161.32"/>
<text xml:space="preserve" text-anchor="middle" x="653" y="-168.42" font-family="DejaVu Sans" font-size="9.00">ja</text>
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<!-- nichtkonvex -->
<g id="node11" class="node">
<title>nichtkonvex</title>
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<text xml:space="preserve" text-anchor="middle" x="903.89" y="-130.97" font-family="DejaVu Sans" font-size="10.00">scipy.optimize.minimize</text>
<text xml:space="preserve" text-anchor="middle" x="903.89" y="-118.22" font-family="DejaVu Sans" font-size="10.00">mit mehreren Startpunkten</text>
<text xml:space="preserve" text-anchor="middle" x="903.89" y="-105.47" font-family="DejaVu Sans" font-size="10.00">— nur lokales Optimum!</text>
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<g id="edge8" class="edge">
<title>g4&#45;&gt;nichtkonvex</title>
<path fill="none" stroke="#5c6380" d="M708.45,-208.24C746.01,-191.73 795.56,-169.96 835.36,-152.46"/>
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<text xml:space="preserve" text-anchor="middle" x="810.22" y="-168.42" font-family="DejaVu Sans" font-size="9.00">nein</text>
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<g id="node9" class="node">
<title>qp</title>
<path fill="#ecfeff" stroke="#0891b2" stroke-width="2" d="M611.91,-38.46C611.91,-38.46 531.88,-38.46 531.88,-38.46 525.88,-38.46 519.88,-32.46 519.88,-26.46 519.88,-26.46 519.88,-12 519.88,-12 519.88,-6 525.88,0 531.88,0 531.88,0 611.91,0 611.91,0 617.91,0 623.91,-6 623.91,-12 623.91,-12 623.91,-26.46 623.91,-26.46 623.91,-32.46 617.91,-38.46 611.91,-38.46"/>
<text xml:space="preserve" text-anchor="middle" x="571.89" y="-22.48" font-family="DejaVu Sans" font-size="10.00">QP über CVXPY</text>
<text xml:space="preserve" text-anchor="middle" x="571.89" y="-9.73" font-family="DejaVu Sans" font-size="10.00">(OSQP, Clarabel)</text>
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<g id="edge9" class="edge">
<title>g5&#45;&gt;qp</title>
<path fill="none" stroke="#5c6380" d="M628.36,-95.59C617.68,-81.34 604.22,-63.38 593.13,-48.57"/>
<polygon fill="#5c6380" stroke="#5c6380" points="595.93,-46.47 587.13,-40.57 590.33,-50.67 595.93,-46.47"/>
<text xml:space="preserve" text-anchor="middle" x="617.64" y="-62.79" font-family="DejaVu Sans" font-size="9.00">ja</text>
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<g id="node10" class="node">
<title>konvex</title>
<path fill="#ecfdf5" stroke="#059669" stroke-width="2" d="M782.91,-38.46C782.91,-38.46 660.88,-38.46 660.88,-38.46 654.88,-38.46 648.88,-32.46 648.88,-26.46 648.88,-26.46 648.88,-12 648.88,-12 648.88,-6 654.88,0 660.88,0 660.88,0 782.91,0 782.91,0 788.91,0 794.91,-6 794.91,-12 794.91,-12 794.91,-26.46 794.91,-26.46 794.91,-32.46 788.91,-38.46 782.91,-38.46"/>
<text xml:space="preserve" text-anchor="middle" x="721.89" y="-22.48" font-family="DejaVu Sans" font-size="10.00">CVXPY</text>
<text xml:space="preserve" text-anchor="middle" x="721.89" y="-9.73" font-family="DejaVu Sans" font-size="10.00">— prüft Konvexität selbst</text>
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<g id="edge10" class="edge">
<title>g5&#45;&gt;konvex</title>
<path fill="none" stroke="#5c6380" d="M665.43,-95.59C676.11,-81.34 689.57,-63.38 700.66,-48.57"/>
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<text xml:space="preserve" text-anchor="middle" x="705.25" y="-62.79" font-family="DejaVu Sans" font-size="9.00">nein</text>
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