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This paper presents three approaches to support decision-making for production planning, sales and inventory problems. They work in a situation with: non-stationary probabilistic demand; production capacity in regular hours and overtime; shortage leads to lost sales; limited internal storage space; and ordering costs resulting from machine preparation are negligible. In the first approach, we consider the problem as linear and deterministic. In the second, safety inventories are used to fill a probabilistic demand, but the possibility of stockout is not considered. The third approach estimates shortage resulting from demand uncertainty. The last two approaches use iterative processes to re-estimate unit holding cost, which is the basis to calculate safety inventories in each period of the horizon. Using Microsoft Excel Solver, with linear programming and nonlinear search functions, a hypothetical example (but strongly based on real-life companies) and some scenarios permit concluding that developing more realistic and complex models may not provide significant benefits.

Aggregate planning for probabilistic demand with internal and external storage