A note on optimal (s, S) and (R, nQ) policies under a stuttering Poisson demand process

In this note, a new efficient algorithm is proposed to find an optimal (s, S) replenishment policy for inventory systems with continuous reviews and where the demand follows a stuttering Poisson process (the compound element is geometrically distributed). We also derive three upper bounds for the relative increase in cost if one uses the best (R, nQ) policy instead of the optimal (s, S) policy. One of these upper bounds (the most loose of those) can be expressed as the fraction of the variance-to-mean ratio of the geometric distribution and the economic order quantity. We explore numerically when these upper bounds are tight.