Heuristics for impulse replenishment with continuous periodic demand

We present a model where the demand appears at continuous time, and all demand must be met. The demand function is periodic with active and passive periods – linear increasing and decreasing demand rates, respectively. The inventory is replenished at discrete time. This paper is concerned with the problem of how to determine the replenishment schedule that minimizes the total production and holding cost over a long time horizon. We show that there is no forecast horizon in our model, even if the demand rate is constant. There exists approximate forecast horizon. For such case, we obtain an explicit formula for the minimal sets of rational initial decisions. For the periodic demand rate case, we formulate some necessary conditions for optimal schedules. Two heuristics are also proposed. The first is an improved version of the Silver-Meal heuristic and the second is based on turnpike policies.