For retail stores which sell tens of thousands of product references, managing inventory is a challenge.

It is all the more difficult as the demand for certain references is subject to important uncertainties and the inertia of restocking can be very long (up to one year).
Keeping an inventory up to date is already difficult given the number of references.

The problem is therefore to manage orders by anticipating demands in order to minimize stocks while avoiding stock-outs.

For a given reference, the model is relatively simple: the stock at a given time T is the stock at time 0, plus the orders that will have arrived at T, minus the sales that will have been made at T. One difficulty comes from the multiple uncertainties weighing on these quantities (for example, the influence of an untimely maritime maneuver in the Suez Canal on the delivery times of some fans or the arrival of an early heat peak on the demand for these same fans).
Another difficulty comes from the number of scenarios to be evaluated since order dates, quantities, delivery times and sales numbers and dates are all variables to be sampled.