Over the past fifty years, inventory management has generated a wealth of literature and a proliferation of models. For each problem, the first step is to determine the setting that will reflect reality as accurately as possible. We must choose between a short-term and a long-term model, opt for a deterministic or stochastic setting, and define principles of optimal management. Finally, the model's parameters must be set realistically—and that is not the easiest part of the problem.
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Setting the problem's parameters
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The aim is to adjust production (or build up an ideal stock or supply) over a finite horizon T. To do so, we consider a single initial supply of a specified quantity Q of a certain product P, obtained at time 0 to meet demand over the time interval \0, T). Whatever the initial stock, one of two situations may arise:
- demand is lower than the inventory level Q (leaving residual inventory)
- demand exceeds it (a stockout).
