Wolfram Alpha based-inventory model for damaged items of pharmaceutics by utilizing exponential demand rate

In this study, an inventory model is developed for pharmaceutical products that deteriorate over time with an exponential demand rate. The discussion of exponential demand is rarely explored but has the advantage that the demand value toward total cost remains positive. This study assumes allowable shortages and complete backlogging, making it necessary to design an optimal policy for deteriorating goods with an exponential demand rate. The model shows that the initial stock decreases over time, potentially leading to shortages before the next order arrives. The optimal solution indicates that the inventory reaches the zero point at 𝑡<sub>1</sub> = 0.0000011 and the cycle length 𝑇<sub>1</sub> = 0.012 resulting in an average minimum total cost of 𝑇𝐶̅̅̅̅ = $17,133.9 per cycle by Wolfram Alpha. Sensitivity analysis measures the changes of the results in the increasing value of 𝑇𝐶̅̅̅̅ for all parameters. Exponential function variables (𝑎 and 𝑏) produces 𝑡<sub>1</sub> and 𝑇<sub>1</sub> stable values. On increasing the cost of each damage (𝐷𝐶) and constant damage rate (𝜃) produces a 𝑡<sub>1</sub> stable value, but the value of 𝑇<sub>1</sub> increases. An increase in storage costs (h) results in a decrease in the value of 𝑡<sub>1</sub> and 𝑇<sub>1</sub>. Increasing in the cost of shortages (s) resulted in an increase in the value of 𝑡<sub>1</sub> and a decrease in the value of 𝑇<sub>1</sub>.