A Mathematical Model of Inventory Cash Flow for Deteriorating Items in a Pharmaceutical Industry

A pharmaceutical economic order quantity (EOQ) inventory model is proposed in which the dynamics of the inventory is mainly affected by demand and the rate of deterioration. The deterioration rate is taken to be time dependent, and the time due to deterioration is assumed to follow three-parameter Weibull distribution, the demand rate is price dependent and shortages are allowed and partially backlogged. A simple analytical procedure for deriving the model is provided and also the necessary and sufficient condition for the optimal replenishment policy for the inventory model is established. Finally, a numerical example is provided to illustrate the solution procedure of the model and a comprehensive sensitivity analysis was conducted to analyze the effect of changes in the basic model parameters on the optimal solution.