Newsvendor model with Brownian motion demand

The newsvendor model is beneficial in managing inventories and determining the optimal ordering quantity. It assumes that the newsvendor knows the demand distribution and costs associated with it beforehand. However, due to demand uncertainty, predicting the demand before the selling period is a challenging task for the newsvendor. In this report, the uncertain demand is modeled to follow a geometric Brownian motion for its suitability for handling demand uncertainty. A numerical example is provided along with sensitivity analysis. This report illustrates that the parameters such as mean, customer loss-of-goodwill, and selling price per unit are inversely proportional to the expected total cost. On the contrary, the parameters such as holding cost, variance, and variable cost per unit are directly proportional to the expected total cost. This report shows that lower values of variance and higher values of mean contribute to the minimum values of the expected total cost.