Optimising a modular expansion of a wastewater treatment plant

Abstract

In the design of a wastewater treatment plant, engineers must estimate the future population that the plant will need to serve. When the population growth is uncertain, modular design can reduce up-front capital costs, operating costs and total expected present value costs. Models based on real option theory can provide insights to engineers/decision-makers that will not arise from standard net present value analysis. We consider a municipality faced with a plant expansion decision required to meet the demand of significant, uncertain growth. We present a model that optimises the size of the plant and its maximum modular size. The optimisation requires that multiple solutions be calculated at the decision time for the staged expansion. We utilise a moment matching technique to approximate the solution of the Asian-like option. The results show that as the uncertainty increases, a modular plant can save significant total costs for the municipality.

Keywords:

• real options
• optimisation
• modular expansion
• wastewater
• Asian option

Notes

1. Analysis of the data showed some correlation to the general stock index, but due to the limited amount of total connections, confidence intervals on the correlations were very broad. It is likely that a lag exists between the market index and the rate of connectivity and analysis of the data showed a lag of approximately 9 months. For the analysis presented here, the lag was ignored.

2. We note that this savings was compared with a standard approach where the plant size was determined using an average growth rate, with no safety factor. An increased safety factor would generally reduce this savings.

3. See http://www.gams.com/.

4. The timelines were picked somewhat arbitrarily; however, the municipal engineers felt that a 20-year planning horizon was appropriate in this case.