Optimal Inventory Rule for a Linear Trend in Demand with a Constant Replenishment Period

The classical deterministic inventory model is considered for the case of constant time between each replenishment and linear trend in demand. The optimum policy is derived and shown to apply to both positive and negative trends. This policy is used in two examples considered in earlier papers on linear trend. It is shown to give only slightly higher costs than the optimal policy with varying replenishment periods, and is compared with a recent heuristic for that case.