Current Concepts in Engineering Research and Technology Vol. 2

The Bass model of product diffusion analysis requires a large quantity of raw data to determine the parameters of the model. To address this limitation, the Grey Bass model proposed the use of a non-linear least squares (NLS) approach for parameter estimation. In the present chapter, a more appropriate method for the Grey Bass equation is offered, which estimates the potential capacity of the market even if the sample size is small. The proposed model is based on the minimisation of the sum of squares of error between actual and predicted data using the Particle Swarm Optimisation (PSO) technique. In PSO, each potential solution (“particle”) is randomly initialised, evaluated via a fitness function, and iteratively updated based on personal and global best positions until convergence, producing an optimal or near-optimal solution. Using a case study dataset, as used by Wang, the accuracy of the improved method was investigated. Data contained consumers from June 2011 to October 2013, and the time interval was two months. The proposed Grey-Bass Model was implemented in MATLAB 14.2 using a program that minimises the sum of squared errors. The results show that the mean absolute percentage error (MAPE) in the present case is 6.52% compared to 7.93% reported by Wang. The model demonstrates strong simulation, prediction, and future forecasting capabilities for new products and is particularly suitable for small sample datasets.