Switching surfaces for optimal natural resource extraction under uncertainty

Abstract

The flexibility to revise managerial and/or operational decisions over time in response to uncertain market conditions can significantly increase the value of a project. In order to maximise the project value, the operational decisions need to be made sequentially, in an optimal manner, in response to the evolution of uncertainties. Although dynamic strategies brings substantial improvements of the project, its complexity from stochastic control algorithm makes modern real option theory rarely adopted by industry. Thus it calls for a methodology to display graphically the results obtained by real options analysis. An intuitive display of the information about the boundaries between the regions of different optimal decisions (called switching boundaries) would greatly assist industry with optimal sequential decision-making under uncertainty. This paper presents a methodology to construct switching boundaries/surfaces for optimal natural resource extraction under uncertainty, based on the regression Monte Carlo approach. We extend previous research by (1) incorporating recently proposed advanced techniques (such as adaptive local basis and memory reduction methods) that allow considerable improvement of the accuracy of the switching boundaries; and (2) constructing and analysing the higher-dimensional switching boundaries. We illustrate how to construct and use switching boundaries using a classical model of a copper mine with flexibility to delay, temporarily close, reopen or completely abandon the mineral extraction in response to the stochastic behaviour of the copper price. For such a model, the switching boundaries are the critical copper prices that trigger a change of operating regime. For this example, the switching boundaries are two-dimensional copper price surfaces that depend on the remaining reserve and the remaining time horizon. We display and analyse these surfaces using both 3D graphs and dynamic 2D graphs. The paper demonstrates several benefits of the switching boundaries. They can be used by mining companies: 1. as a simple and intuitive decision support tool for identification of optimal operational strategies and for optimal management of resources projects; 2. to gain insight into optimal strategies under different market conditions and project settings; 3. to benefit financially from dynamic strategies.