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The deterministic problem is to minimize operational cost subject to constraints in demand, supply and capacity. The ordering policy is periodic review, order-up-to.

The stochastic version of the model is to optimize the parameters for the order-up-to policy.

I've looked at the literature on using multi-stage stochastic programming with news-vendor type of models for this application, but my model has additional complexities:

  1. Multi-period, multi-item, multi-sourcing
  2. Supply and capacity constraints are important and cannot be ignored

It is not clear to me how to extend existing news-vendor models with all of these complexities.

The simplest approach would be to generate a number of scenarios (scenario-tree) with different realizations of demand - and solve the corresponding MILPs. Each of the scenarios would be independent of others. The final answer would be an appropriately weighted "expectation" of the variables of interest.

Depending on how many scenarios, along with some cleverness in choosing realizations - I can expect to come up with a reasonable set.

Will this simple approach work? For example - will the average order quantity across all the MILP runs be a good estimate of the actual optimal?

Are there other approaches I am missing out on?

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