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Tempelmeier (2007) considers the problem of computing replenishment cyclepolicy parameters under non-stationary stochastic demand and service levelconstraints. He analyses two possible service level measures: the minimum nostock-out probability per period ({\alpha}-service level) and the so called"fill rate", that is the fraction of demand satisfied immediately from stock onhand ({\beta}-service level). For each of these possible measures, he presentsa mixed integer programming (MIP) model to determine the optimal replenishmentcycles and corresponding order-up-to levels minimizing the expected total setupand holding costs. His approach is essentially based on imposing service leveldependent lower bounds on cycle order-up-to levels. In this note, we argue thatTempelmeier's strategy, in the {\beta}-service level case, while being aninteresting option for practitioners, does not comply with the standarddefinition of "fill rate". By means of a simple numerical example wedemonstrate that, as a consequence, his formulation might yield sub-optimalpolicies.

A note on Tempelmeier's {\beta}-service measure under non-stationary stochastic demand