We study a class of assortment optimization problems where customers choose products according to the cross-nested logit (CNL) model and the number of products offered in the assortment cannot exceed a fixed number. Currently, no exact method exists for this NP-hard problem that can efficiently solve even small instances (e.g., 50 products with a cardinality limit of 10). In this paper, we propose an exact solution method that addresses this problem by finding the fixed point of a function through binary search. The parameterized problem at each iteration corresponds to a nonlinear binary integer programming problem, which we solve using a tailored Branch-and-Bound algorithm incorporating a novel variable-fixing mechanism, branching rule and upper bound generation strategy. Given that the computation time of the exact method can grow exponentially, we also introduce two polynomial-time heuristic algorithms with different solution strategies to handle larger instances. Numerical results demonstrate that our exact algorithm can optimally solve all test instances with up to 150 products and more than 90% of instances with up to 300 products within a one-hour time limit. Using the exact method as a benchmark, we find that the best-performing heuristic achieves optimal solutions for the majority of test instances, with an average optimality gap of 0.2%.

Aquifer thermal energy storage (ATES) has great potential to mitigate CO₂ emissions associated with the heating and cooling of buildings and offers wide applicability. Thick productive aquifer layers have been targeted first, as these are the most promising hydrogeological context for ATES. Regardless, there is currently an increasing trend to target more complex aquifers such as low-transmissivity and alluvial aquifers or fractured rock formations. There, the uncertainty of subsurface characteristics and, with that, the risk of poorly performing systems is considerably higher. Commonly applied strategies to decide upon the ATES feasibility and well design standards for optimization need to be adapted. To further promote the use of ATES in such less favorable aquifers an efficient and systematic methodology evaluating the optimal conditions, while not neglecting uncertainty, is crucial. In this context, the distance-based global sensitivity analysis (DGSA) method is proposed. The analysis focuses on one promising thick productive aquifer, first used to validate the methodology, as well as a complex shallow alluvial aquifer. Through this method, multiple random model realizations are generated by sampling each parameter from a predetermined range of uncertainty. The DGSA methodology validates that the hydraulic conductivity, the natural hydraulic gradient and the annual storage volume dominate the functioning of an ATES system in both hydrogeological settings. The method also advances the state of the art in both settings. It efficiently identifies most informative field data ahead of carrying out the field work itself. In the studied settings, Darcy flux measurements can provide a first estimate of the relative ATES efficiency. It further offers a substantiated basis to streamline models in the future. Insensitive parameters can be fixed to average values without compromising on prediction accuracy. It also demonstrates the insignificance of seasonal soil temperature fluctuations on storage in unconfined shallow aquifers and it clarifies the thermal energy exchange dynamics directly above the storage volume. Finally, it creates the opportunity to explore different storage conditions in a particular setting, allowing to propose cutoff criteria for the investment in ATES. The nuanced understanding gained with this study offers practical guidance for enhanced efficiency of feasibility studies. It proves that the DGSA methodology can significantly speed up the development of ATES in more complex hydrogeological settings.