Multi-stage Stochastic Integer Programming Model for Sustainable Carbon Nanotube Production Scale-up Planning

Abstract

As nanotechnology moves from development to commercialization, the number of nanomaterial embedded products in the market is increasing exponentially [1]. With various nanotechnologies growing rapidly, nanotechnology becomes attractive to investors. It is estimated that the market share for nanotechnology goods will be $1 trillion in 2020 [2]. Therefore, small to medium enterprise companies in nanotechnology markets are likely to expand their capacities to full scale production. However, capacity expansion in nanotechnology has high investment risk due to the large amount of uncertainties about future market conditions, appropriate workplace safeguards and regulations. Therefore, investors could struggle to make the capacity expansion decisions in order to maximize their profit. Multi-stage stochastic integer programming (MISP) approach [3] is suitable for the problems dealing with the uncertainties. This work illustrates MISP model for the capacity expansion problem in nanotechnology. ææA start-up company that produces carbon nanotubes (CNTs) is considered in the model. It is assumed that the company aims to achieve sustainable manufacturing while meeting the growing demand. Therefore, sustainability indicators/metrics [4] are considered as a constraint in the model. The decision variables are capacity expansion size (number of additional process), time when capacity expansion decision is made, time when the old technology will be replaced, and also the allocation of capacity to product types. The model is run for various demand and possible future regulation scenarios. The results of the model show that regulations and sustainable manufacturing goals affect the companiesÍ investment size and timing decisions.