A replenishment model with linearly decreasing trend in demand and unit cost

Under a finite planning horizon, this study presents a replenishment inventory model with linearly decreasing trend in demand and unit cost. Unlike the previous contributions which assumed constant holding cost, we assumed the holding cost is a fraction of unit cost per unit time that would be precisely to reflect on the real situation. Actually, many researches and textbooks emphasized that the capital cost is often the most important component of holding cost. Consequently, each replenishment cycle should have not only different unit cost but different unit holding cost. It is necessary to deliberate this issue because this variable holding cost would influence the replenishment schedule and lot size. In this study, a recursive algorithm to obtain the optimal replenishment schedule and complete theoretical demonstrations are presented. In addition, numerical example to illustrate the proposed model is provided as well.