Inventory optimization model for quadratic increasing holding cost and linearly increasing deterministic demand

Abstract

This article proposes an inventory optimization model for quadratic increasing holding cost and with linearly increasing deterministic demand. Demand function changes with time up to the shortage occurrence. During the period of shortages, demand is constant. Partial backlogging type shortage is considered by assuming constant deterioration. As an economic order quantity (EOQ) problem, an equation for the total cost function is formulated as an optimization problem by applying Maclaurin series approximation. For the optimization of this problem, the second order derivative method is applied. The Cost function convexity is demonstrated with the help of graph in three dimensions. Numerical experimentation is carried out with the support of two numerical examples. The experimented optimal results are included in tabular form for more clarity. Some graphical representations are drawn to show the variations in various parameters of the model. An analysis of sensitivity of the model is performed to detect the most as well as the least sensitive parameters in the proposed optimization problem.