Economic–mathematical Modelling of the Relationship Between Innovation Outcomes and Commercialisation Time in Cotton-Textile Clusters

The article develops an economic-mathematical model linking the economic value of an innovation in cotton-textile clusters to its time to market. Discounting, market-window obsolescence, learningbased production ramp-up, and acceleration costs are integrated into a single net present value function. The optimal commercialisation lag is determined using the Lambert W function, break-even lags are derived, and stochastic stage durations are modelled using an Erlang distribution. The model parameters are calibrated using central bank and cluster lending rates, as well as published estimates of R&D obsolescence, with three illustrative scenarios considered. The optimal commercialisation lags range from 1.2 to 2.0 years, while the break-even lags range from 3.8 to 5.5 years. A one-year delay reduces net present value by 20–34%.