A simulation-based product diffusion forecasting method using geometric Brownian motion and spline interpolation

Abstract

This study addresses the problem of stochasticity in forecasting diffusion of a new product with scarce historical data. Demand uncertainties are calibrated using a geometric Brownian motion (GBM) process. The spline interpolation (SI) method and curve fitting process have been utilized to obtain parameters of the constructed GBM-based differential equation over the product's life cycle (PLC). The constructed stochastic differential equation is coded as the forecast model and is simulated using MATLAB. The results are several sample demand paths generated from simulation of the forecast model. To evaluate the forecasting performance of the proposed method it is compared with Holt's model, using actual data from the semiconductor industry. The comparison results confirm the applicability of the proposed method in the semiconductor industry. The method can be helpful for policy-makers who require the prediction of uncertain demand over a time horizon, such as decisions associated with aggregate production planning, capacity planning, and supply chain network design. Especially for the semiconductor industry with intensive capital investment the proposed approach can be useful for making decisions associated with capacity allocation and expansion.