Dynamic capacitated lot sizing with random demandand dynamic safety stocks

We present a stochastic version of the single-level, multi-product dynamic lotsizingproblem subject to a capacity constraint. A production schedule has tobe determined for random demand so that expected costs are minimized and aconstraint based on a new backlog-oriented Sigma-service-level measure is met. Thisleads to a non-linear model that is approximated by two dierent linear models.In the rst approximation, a scenario approach based on random samples is used.In the second approximation model, the expected values of physical inventory andbacklog as functions of the cumulated production are approximated by piecewiselinear functions. Both models can be solved to determine efficient, robust and stableproduction schedules in the presence of uncertain and dynamic demand. They leadto dynamic safety stocks that are endogenously coordinated with the productionquantities...