On recoverable and two-stage robust selection problems with budgeted uncertainty

In this paper the problem of selecting p out of n available items is discussed, such that their total cost is minimized. We assume that the item costs are not known exactly, but stem from a set of possible outcomes modeled through budgeted uncertainty sets, i.e., the interval uncertainty sets with an additional linear (budget) constraint, in their discrete and continuous variants. Robust recoverable and two-stage models of this selection problem are analyzed through an in-depth discussion of variables at their optimal values. Polynomial algorithms for both models under continuous budgeted uncertainty are proposed. In the case of discrete budgeted uncertainty, compact mixed integer formulations are constructed and some approximation algorithms are proposed. Polynomial combinatorial algorithms for the adversarial and incremental problems (the special cases of the considered robust models) under both discrete and continuous budgeted uncertainty are constructed

A review of regional and global estimates of unconventional gas resources

This Research Report assesses the currently available evidence on the size of unconventional gas resources at the regional and global level. Focusing in particular on shale gas, it provides a comprehensive summary and comparison of the estimates that have been produced to date. It also examines the methods by which these resource estimates have been produced the strengths and weaknesses of those methods, the range of uncertainty in the results and the factors that are relevant to their interpretation