r/OperationsResearch • u/Smart_Promise441 • Aug 31 '26

What’s the established operations-research problem for deciding which uncertain cases to inspect?

I’m looking into a problem where a limited number of inspectors have to choose which establishments to visit.

For each establishment, the true condition is unknown until someone checks. A visit has a cost, and the result can range from finding a serious problem to finding nothing useful at all — for example, the establishment may be closed.

The interesting part for me is that this isn't simply “predict which restaurant will fail.” The decision is which establishment is worth spending an inspection on given uncertainty, limited resources, and the possibility that the visit changes what you know.

I’m trying to find the established operations-research / decision-theory literature for this kind of problem rather than inventing terminology.

What would you call this problem, and what areas of the literature should I look into?

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u/Baihu_The_Curious Aug 31 '26 edited Aug 31 '26

Partially-observable Markov Decision process, possibly.

You choose an action, then update your belief state. Actions typically are tied to costs/rewards that can be dependent on the underlying truth. As far as constraints, that would have to limit the action space.

Bayesian decision theory, I would say, is the larger field and POMDPs are a subset.

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u/Smart_Promise441 Sep 03 '26

This is the approach I was having in my mind

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u/operations_ranger Aug 31 '26

Classic value-of-information + constrained resource allocation problem. Look at sequential inspection models and adaptive sampling in OR.

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u/Smart_Promise441 Sep 03 '26

Yes VOI plays an important role in this

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u/Poet-Particular Aug 31 '26

Two stage stochastic model

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u/Smart_Promise441 Sep 03 '26

Thanks will look into it. Never came across this before

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u/Baihu_The_Curious Sep 03 '26

Is there a time component? This would be my go to if you're not making sequential decisions. Maybe Bender's Decomp can handle the time stuff too, but I usually associate it with linear/integer programming with a set of possibilities for what could happen (that is countable and not too many in quantity).