Dear all,

I am a newbie to optimization and I am currently working on some stochastic (integer) programming problems. I found a huge number of books/resources on the theory of multi-stage stochastic programming with recourse but I did not manage to find any similar resources on solving these problems (how to fit distributions based on previous data, generate the scenarios and solve the resulting deterministic equivalent on some programming language). I would be grateful if you could provide me pointers to such resources.

asked 02 Sep '15, 10:49

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lstavr
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edited 02 Sep '15, 14:18


Here is a nice tutorial that touches on the last part; solving the deterministic equivalent in some programming language.

For answers to the rest of your question, I will assume that you are looking for academic information. I'll try to help you organize what you need to search for.

If you are trying to solve a business problem instead, you can contact me offline.

Fitting

There are two main categories of models for scenarios. General models that rely only on statistics; and application-specific models that assume some underlying physics. There are, of course, hybrid models.

The most common practical references for fitting data to general models are in Time Series Analysis. In particular, I have found Periodic Autoregressive models to relatively simple models that are very useful. By historical accident, the OR and Time Series literatures are rather disjoint, which is part of why finding the best references will take extra work on your part.

There is no pattern that I can detect in physical models. Those used in energy are not the same used in finance, or in epidemiology, etc. Many of these models are based on differential equations.

A key question you need to address is how precisely you need to handle correlation in your application.

Generation of Scenario Trees

Within static scenario generation, there is a body of work on how to compress scenario trees, i.e., how to reduce the number of scenarios you generate while bounding information loss. This is often called Scenario Reduction.

You can also generate scenarios dynamically, i.e., sample, solve an approximation, look at your progress, then sample and solve some more, until convergence criteria are met. There is a large body of recent literature on this topic. Much of that literature assumes far less structure than you describe in your question. These are called sampling-based methods.

Implementation Issues

This is a very exciting area, especially for Stochastic Integer Programming, with the changes we see now (2015) in the underlying computing architectures. People working on this in practice rarely have the incentive or the time (or, for the most part, the venue) to publish. However, you may have some luck with research from national labs, especially Sandia.

link

answered 05 Sep '15, 01:02

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Leo
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accept rate: 8%

@Leo Thank you a lot for the answer. It seems that the current focus is on the theoretical advancement of the field and there are very few resources on examples with solutions in contrast to other areas such as statistics where some code is published along with the paper.

(05 Sep '15, 10:36) lstavr
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Asked: 02 Sep '15, 10:49

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Last updated: 05 Sep '15, 10:36

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