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I have a demand forecast that gives me a distribution for future demand, for each time period in percentiles (e.g. demand for period 1 will be between 6 and 25 (zero and 100th percentiles, and i know all other percentiles in between, and this is given for each time period). I don't know which distribution each product follows.

The inventory optimization I feed this to currently only uses a point from the forecast, thus I am missing a lot of information I could use to create a better optimization.

I'm currently considering (1) determining a critical factor for each product as the ration of underage and overage cost, or (2) running the optimization across e.g. the 10th, 20th, 30th etc percentile of the forecast of each product, weighing these "scenarios" with their likelihood and choosing the optimal outcome.

I'm missing the vocabulary to be able to research these options. Can you help me with what terms should I search for to find relevant research for this? any other ideas I should look at to solve this?

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Here are three distinct fields of research, any of which might (or might not) be useful to you.

  • Robust optimization deals with uncertainty in the parameters of an optimization model by focusing on worst cases.
  • Stochastic programming with recourse deals with randomness in parameters by incorporating in the optimization model elements related to how the system adapts to the effects of randomness (for instance, expediting orders, outsourcing or suffering stock-out penalties if demand exceeds the inventory levels generated by the model decisions).
  • Chance constrained programming incorporates randomness into the optimization model by constraining solutions to be feasible/optimal with a certain probability (meaning the user accepts a certain risk that the solution will not work when the random variables are observed).
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One addition to the optimization methods/concepts that Prubin proposed is simulation-optimization: https://www.informs-sim.org/wsc97papers/0118.PDF.

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