How can you use modeling languages to optimize stochastic problems?

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Stochastic problems are those that involve uncertainty, randomness, or variability in some aspects of the data, parameters, or outcomes. They are common in many fields of operations research (OR), such as inventory management, supply chain planning, project scheduling, and decision analysis. However, solving stochastic problems can be challenging, as they often require complex mathematical models and algorithms that can account for the different scenarios and probabilities involved. Fortunately, there are some modeling languages that can help you formulate and optimize stochastic problems more easily and efficiently. In this article, we will introduce some of the main features and benefits of using modeling languages for stochastic problems, and provide some examples of how they can be applied in practice.

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Bushra Haque

GPC | GT | Michelin | Micron
Veera Baskar K

End to end supply chain solutions to reduce cost, optimise inventory, improve customer satisfaction, smarter processes…

1 What are modeling languages?

Modeling languages are tools that allow you to express mathematical models in a clear, concise, and structured way, using symbols, variables, expressions, and constraints. Modeling languages can be classified into two main types: algebraic and declarative. Algebraic modeling languages use a notation that resembles the mathematical equations that define the model, such as AMPL, GAMS, or Pyomo. Declarative modeling languages use a syntax that describes the properties and relationships of the model elements, such as OPL, MiniZinc, or Zimpl. Both types of modeling languages have advantages and disadvantages, depending on the problem type, the solver, and the user preference.

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2 Why use modeling languages for stochastic problems?

Modeling languages can offer several benefits for solving stochastic problems, such as simplifying model formulation and modification, facilitating model validation and verification, enhancing model readability and communication, and improving model performance and scalability. By using abstract and logical expressions instead of low-level numerical codes, you can check the consistency and accuracy of the model structure and data. Additionally, a common and standardized language can be understood by different stakeholders, allowing you to leverage the power of various solvers and libraries like CPLEX, Gurobi, SCIP, or PySP.

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3 How to use modeling languages for stochastic problems?

To use modeling languages for stochastic problems, you need to first define the scope and objective of the problem, and identify the sources and types of uncertainty involved. Then, choose a suitable modeling language and solver that can support the stochastic features of the problem. After that, formulate the model using the syntax and commands of the chosen language, and specify the parameters, variables, constraints, and objective function. Additionally, generate and import the data for the model from external sources or using random number generators or simulators. Finally, solve the model using the chosen solver and analyze the results and outputs.

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Veera Baskar K

End to end supply chain solutions to reduce cost, optimise inventory, improve customer satisfaction, smarter processes and capability building | Founder & CEO - 7th Mile Shift | Ex-TVS Motor Company - AVP Logistics.
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Here's a useful strategy from my experience: When handling variables that act similarly to unpredictable and diverse weather conditions, I concentrate on 'what-ifs'. This involves simulating scenarios, which can be seen as mini drills. However, the challenge lies in the complexity. Occasionally, these models evolve into a maze of probabilities. The trick is to maintain your model's realism, yet keep it simple enough to solve. It's not only about finding a solution; it's about comprehending the range of possibilities. As you tackle these stochastic puzzles, let your model guide you, but always remember the practicality of your solutions. In the end, in the real world, it's the practical solutions that prevail.

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4 What are some examples of modeling languages for stochastic problems?

When dealing with stochastic problems, there are many modeling languages to choose from. AMPL is a powerful and expressive algebraic modeling language that can handle stochastic linear, nonlinear, and mixed-integer problems. It can also interface with various solvers and libraries, such as CPLEX, Gurobi, or PySP. Pyomo is another flexible and versatile algebraic modeling language that is embedded in Python and can handle stochastic problems using the PySP package. OPL is a concise and intuitive declarative modeling language that can handle stochastic linear and mixed-integer problems, while MiniZinc is a simple and portable declarative modeling language that can handle stochastic constraint satisfaction and optimization problems. All of these languages are compatible with different solvers and platforms, allowing you to customize your solutions according to your needs.

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Tareq Babaqi

Senior Data Scientist | PhD in Industrial Engineering and Systems Science, Data Science, Optimization
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An example of the prowess of modeling languages in operations research lies in AMPL, GAMS, and Pyomo. Consider AMPL for optimizing a supply chain dealing with variable demand, or GAMS for navigating the complexities of energy production with renewable sources. Pyomo shines as an example when faced with project scheduling and uncertain task durations. These instances showcase the effectiveness of these modeling languages in handling stochastic challenges and improving decision-making processes.

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5 How to learn more about modeling languages for stochastic problems?

If you're looking to learn more about modeling languages for stochastic problems, there are a variety of resources available. Books such as "Model Building in Mathematical Programming" by H. Paul Williams, "Optimization Modeling with Spreadsheets" by Kenneth R. Baker, and "Pyomo - Optimization Modeling in Python" by William E. Hart et al., can provide an in-depth look into the theory and practice of modeling languages for stochastic problems. Courses like "Introduction to Optimization" by Stanford University, "Modeling and Solving Optimization Problems in Python" by Coursera, and "Stochastic Optimization" by edX can teach the basics and applications of modeling languages for stochastic problems. Finally, websites such as the AMPL website, the Pyomo website, the OPL website, or the MiniZinc website offer tutorials and examples of modeling languages for stochastic problems.

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6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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Bushra Haque

GPC | GT | Michelin | Micron
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Mathematical programming is inherently challenging, with solvers often varying in speed across different problems. This variability is sometimes due to certain heuristics performing exceptionally well by chance. Moreover, the complexity of a problem isn’t solely determined by its size; some small instances remain unsolved, while others with millions of constraints are quickly resolved. To optimize performance, it’s crucial to examine the solver’s log file to understand its behavior and tweak parameters as needed. Having access to multiple solvers and testing them on your problem can be advantageous, providing a range of solutions and enhancing the chance of finding the most efficient approach.

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How can you use modeling languages to optimize stochastic problems?

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1 What are modeling languages?

2 Why use modeling languages for stochastic problems?

3 How to use modeling languages for stochastic problems?

4 What are some examples of modeling languages for stochastic problems?

5 How to learn more about modeling languages for stochastic problems?

6 Here’s what else to consider

Operations Research

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How can you use modeling languages to optimize stochastic problems?

1

2

3

4

5

6

1 What are modeling languages?

2 Why use modeling languages for stochastic problems?

3 How to use modeling languages for stochastic problems?

4 What are some examples of modeling languages for stochastic problems?

5 How to learn more about modeling languages for stochastic problems?

6 Here’s what else to consider

Operations Research

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