Probabilistic approaches to scheduling reserve selection

Most existing reserve selection algorithms are static in that they assume that a reserve network is designed and patches are selected by decision-makers at a single point in time. In reality, however, selection processes are often dynamic and patches are selected one by one or in several groups because for example there are insufficient funds at the beginning of the process to put all the patches under protection. Finding an optimal dynamic selection strategy is tricky since due to the complementarity principle the value of a particular patch depends on the presence of other patches in the network - including those that have not yet been selected. As unprotected patches may be lost, e.g., through development, the long-term value of selecting a particular patch is uncertain. Existing dynamic selection algorithms are either 'myopic' and consider only those patches that have already been protected, totally ignoring future uncertainty, or they are based on stochastic dynamic programming, which delivers the optimal strategy taking uncertainty into account but is numerically too complex to be employed in actual selection problems. In this paper, a 'foresighted' selection strategy as well as a number of variants are developed using probability theory. The different strategies are compared for a large number of selection problems. All variants outperform the myopic strategy and perform close to the optimal strategy. However, the performances of all strategies, including the optimal and the myopic one, are not dramatic.