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<!DOCTYPE html>
<head>
<meta charset="utf-8" />
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<title>Uncertain Optimization</title>
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<a class="navbar-brand" href="#!">Uncertain Optimization Complementary Material</a>
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<figure class="text-center mb-5">
<blockquote class="blockquote">
<p>Le doute n'est pas une condition agréable, mais la certitude est absurde.</p>
</blockquote>
<figcaption class="blockquote-footer">
<cite title="Source Title">Voltaire</cite>
</figcaption>
</figure>
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Language: Persian
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<div class="small mb-1">ISBN xxx-yyyy-zz-bbbbbb-t</div>
<h1 class="display-5 fw-bolder">Uncertain Optimization</h1>
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<span>Theory, Models, and Applications</span>
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<p class="text-justify font-weight-light">
In this book, various aspects of uncertainty in decision-making and mathematical models are investigated.
The book is organized in four chapters.
In the first chapter, the philosophy, concepts, and typology of uncertainty in mathematical programming have been discussed.
The second part of the book is dedicated to stochastic programming methodology and its various methods.
In the third chapter, robust optimization methods based on closed uncertainty sets are discussed.
The fourth chapter of the book is dedicated to fuzzy mathematical programming methods and
various robust fuzzy programming methods are investigated.
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<h2 class="fw-bolder mb-4">Extra Resources and Codes</h2>
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<h2 class="accordion-header" id="headingOne">
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Chapter a. Introduction
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<div class="accordion-body">
<ul>
<li>Chapter Overview 1</li>
<li>Importance and Influence of Uncertainty</li>
<li>Philosophy of Uncertainty and Risk</li>
<li>Law of Noncontradiction and Uncertainty</li>
<li>Uncertainty Taxonomy</li>
<li>Uncertainty Methodologies in Mathematical Modelling</li>
<li>Robustness and Resiliency</li>
<li>Uncertainty Methodologies Taxonomy</li>
<li>Systematic Framework for Uncertainty Methodologies Taxonomy</li>
<li>Exercises</li>
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Chapter b. Stochastic Programming
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data-bs-parent="#accordionExample">
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<ul>
<li>Chapter Overview</li>
<li>Probabilistic Prgramming with Costraints</li>
<li>Scenario-based Stochastic Programming</li>
<ul>
<li>
<a href="https://github.com/Uncertain-Programming/Uncertain-Programming.github.io/blob/main/content/ch2/LeungSupplyChain.zip?raw=true"
download>Leung Method in Supply Chain (CPLEX)</a>
</li>
</ul>
<li>Realistic Robust Two-stage Scenario-based Programming</li>
<li>Worst-case Robust Two-stage Scenario-based Programming</li>
<li>Regret-based Robust Two-stage Scenario-based Programming</li>
<li>Mixed Chanced Scenario-based Approach</li>
<li>Multi-stage Scenario-based Approach</li>
<li>Scenario Generation Methods</li>
<li>Sample Average Approximation</li>
<ul>
<li>
<a href="https://github.com/Uncertain-Programming/Uncertain-Programming.github.io/blob/main/content/ch2/SAA_shabbir.ipynb.zip?raw=true"
download>Shabbir Ahmed Method (Python)</a>
</li>
</ul>
<li>Stochastic Value at Risk</li>
<ul>
<li>
<a href="https://github.com/namakshenas/Python-Coherent-Risk-Measures"
download>Value at Risk Models (Python)</a>
</li>
</ul>
<li>Exercises</li>
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Chapter c. Robust Optimization based on Closed Uncertainty Sets
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<ul>
<li>Chapter Overview</li>
<li>Uncertainty Sets</li>
<li>Box Uncertainty Set</li>
<li>Ellipsoidal Uncertainty Set</li>
<ul>
<li>
<a href="https://github.com/Uncertain-Programming/Uncertain-Programming.github.io/blob/main/content/ch3/l2norm_files_robust.rar?raw=true"
download>Supply Chain Problem with Ellipsoidal Uncertainty (CPLEX)</a>
</li>
</ul>
<li>Polyhedral Uncertainty Sets</li>
<li>Mixed Uncertainty Sets</li>
<li>Budgeted Uncertainty Sets</li>
<ul>
<li>
<a href="https://github.com/Uncertain-Programming/Uncertain-Programming.github.io/blob/main/content/ch3/knapsackRobustBertsimas.ipynb.zip?raw=true"
download>Price of Robustness Sensitivity Analysis (Python)</a>
</li>
</ul>
<li>Probabilistic Guarantees of Robust Counterparts</li>
<li>Uncertainty in Right Hand Side</li>
<ul>
<li>
<a href="https://github.com/Uncertain-Programming/Uncertain-Programming.github.io/blob/main/content/ch3/RHS_Robustness-main.zip?raw=true"
download>Supply Chain with Uncertain Demand (Python)</a>
</li>
</ul>
<li>Periodic Uncertainty Budget</li>
<li>Adjustable Robust Optimization</li>
<li>Data-driven Robust Optimization</li>
<ul>
<li>
<a href="https://github.com/Uncertain-Programming/Uncertain-Programming.github.io/blob/main/content/ch3/DDRO-Knapsack-Model-main.zip?raw=true"
download>Data-driven Knapsack Model (Python)</a>
</li>
</ul>
<li>Exercises</li>
</ul>
</div>
</div>
</div>
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<h2 class="accordion-header" id="headingFour">
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Chapter d. Robust Fuzzy Programming
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</h2>
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data-bs-parent="#accordionExample">
<div class="accordion-body">
<ul>
<li>Chapter Overview</li>
<li>Robust Possibilistic Programming</li>
<li>Flexible Programming</li>
<li>Robust Flexible Programming</li>
<li>Uncertainty in Equality Constraints</li>
<li>Exercises</li>
</ul>
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Appendix
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<ul>
<li>Convex Optimization and Conic Programming</li>
<ul>
<li>
<a href="https://github.com/Uncertain-Programming/Uncertain-Programming.github.io/blob/main/content/ch3/socp_faci_eucle.mod.zip?raw=true"
download>Location Model with Euclidean Distance (CPLEX)</a>
</li>
</ul>
<li>Semi-definite Programming</li>
<li>Fuzzy Programming</li>
</ul>
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</div>
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