This paper is concerned with gradual land conversion problems, placing the main focus on the interaction between time and uncertainty. This aspect is extremely relevant since most decisions made in the field of natural resources and sustainable development are irreversible decisions. In particular, we discuss and develop a scenario-based multi-stage stochastic programming model in order to determine the optimal land portfolio in time, given uncertainty affecting the market. The approach is then integrated in a decision tree framework in order to account for domain specific (environmental) uncertainty that, diversely from market uncertainty, may depend on the decision taken. Although, the designed methodology has many general applications, in the present work we focus on a particular case study, concerning a semi-degraded natural park located in northern Italy.
Keywords Stochastic programming . Decision analysis . Land management
IntroductionWe examine the effects of uncertainty and irreversibility in valuing and timing conversion and development projects involving land areas or natural resources. This topic has been addressed first by Arrow and Fisher (1974) and Henry (1974), who treat the complete conversion problem as an optimal stopping problem, while the gradual conversion problem was first introduced by Clarke and Reed (1990). Our analysis is focused on a more general problem, that is finding an optimal land/resources portfolio composition through time, in the presence of future market uncertainty. In fact, it is often more realistic to assume that an optimal land management program will involve a gradual sequence of conversion decisions through time, evolving as each land allocation/resource value becomes known more accurately.