When looking at optimization under uncertainty, do you more often use robust optimization (parameters are known within some bounds), or stochastic programming (parameters follow a known distribution)?

asked 20 Jun '12, 05:33

jfpuget's gravatar image

accept rate: 8%

edited 20 Jun '12, 05:36

The main issue to consider for making such decision is that which approach better suits your problem definition and available data. Hence, the answer is problem-dependent. However, some arguments could be made in favor of robust optimization from a (very) practical point of view.

"In general, stochastic programming is a more mature area within the operations research field. However, its application in practice is limited by its heavy dependency on availability of historical data and complex modeling and computational aspects for practitioners with limited operations research knowledge. On the other hand, robust optimization models are usually more easy to understand and implement. Also, they do not significantly increase the complexity of the considered optimization problem in most cases." (See here for a brief discussion in the context of supply chain network design)

Therefore, I believe robust optimization is more applicable in most common situations.


answered 20 Jun '12, 06:02

Ehsan's gravatar image

Ehsan ♦
accept rate: 16%

edited 21 Jun '12, 00:02

Thanks. You're saying that building the distribution requires more data hence makes stochastic programming less likely to be relevant.

Is the quote from you or from someone else?

(20 Jun '12, 22:17) jfpuget

Not necessarily. For example, if your designing a supply chain from the scratch, usually many factors like demand and prices are unknown and there is limited enough data to fit a probability distribution function. However, if you're redesigning a currently-available supply chain, you usually have enough data to fit distributions for the parameters you need. In summary, it depends on your system type and how long it's been working.

Sorry, I forgot to add the link. It's from a paper authored by my colleagues and myself. There, we have briefly compared these methods within a SCM context.

(20 Jun '12, 23:53) Ehsan ♦

Another thought on the question: Robust optimization models are, by nature, usually designed for risk-averse decision-making (one exception is uncertainty budget model by Bertsimas and Sim), while stochastic programming models are more versatile in that area as you have more options on how to define the recourse function. This is an important plus for stochastic programming.

(23 Jun '12, 02:20) Ehsan ♦

I agree that the answer is problem dependent. In my own experience, I have found that both stochastic and robust models have been roughly equally useful in logistics applications.

I also think that it is typically much more difficult to build the right model that incorporates uncertainty, compared to cases where one chooses to build a deterministic model.

Here are some ideas I try to keep in mind when modeling that may help lead to an appropriate model:

  1. Nearly every model is an approximation of a real-world decision problem.
  2. Many parameters used in optimization models are uncertain, but deterministic models where we assume a single value for each can still be the best choice.
  3. If you think it is important to model the uncertainty in a parameter, remember that the user can choose how to model that uncertainty. Remember that fitting a probability distribution is yet another modeling approximation, and that choosing to model a parameter as known is the same as modeling its probability distribution as a unit point mass at its expected value.
  4. Take time to consider when information that you assume to be unknown when planning becomes known, and how you will model the decision stages for your problem. For example, a multiple stage decision problem can still be modeled as a two-stage problem and lead to good decisions.
  5. Strike the right balance between the detail in a model, and our ability to find optimal or nearly-optimal solutions to that model.

answered 21 Jun '12, 10:51

Alan%20Erera's gravatar image

Alan Erera
accept rate: 12%

@Alan: Good points. Thanks.

(21 Jun '12, 11:29) Ehsan ♦

Alan, thanks. I fully agree although you do not answer my question!

(04 Jul '12, 20:12) jfpuget

Jean Francois, I more often formulate 2-stage expected value minimization models that could theoretically be solved as exact stochastic integer programs, but find solutions to those models via heuristics. When I formulate robust optimization models, I tend to solve them exactly with IP codes.

(05 Jul '12, 11:38) Alan Erera

When modeling uncertainty as bounds on a random variable you're implicitly assuming that everything outside those bounds will have probability 0. It's a pretty strong statement to make in some cases, especially because the consequences of unforeseen deviations (the infamous "black swans") can be catastrophic.

On a more technical note, the results of robust optimization apply for some very well defined cases, e.g. log-concave distributions over convex sets and specific (e.g. LP) structure of the optimization problem.


answered 08 Mar '16, 10:02

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Asked: 20 Jun '12, 05:33

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Last updated: 08 Mar '16, 10:02

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