An optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand and variable holding cost

Percentage of capital invested for holding the inventory of decaying item is more than that of non‐decaying item. Unfortunately, most of the works done in the era of inventory controlling were and are putting forward without taking into account the aspect of variable holding cost of the deteriorating item. To bring concentrations of inventory practitioners, we present an inventory model for deteriorating item with stock‐dependent demand and variable holding cost. Furthermore, non‐instantaneous deteriorating approach is considered in this work. In the model, shortages are allowed and partially backlogged. The optimal policies are derived and the necessary and sufficient conditions of the existence and uniqueness of the optimal solution are theoretically carried out. As the special cases, the results of the proposed model with instantaneous and non‐instantaneous deterioration rate and with and without shortages are shown. Finally, numerical examples are presented to demonstrate the developed model and the solution procedure. Sensitivity analysis of the optimal solution with respect to major parameters for giving managerial insights in conclusion is carried out.