Optimal System Adjustment Under Operational Constraints with Applications to Infectious Disease Screening

We propose an optimization framework to solve problems that involve parameters that are forecast to vary over a given time horizon. We model uncertainty in the forecast through the use of lower and upper bounds that can be seen as time-dependent uncertainty levels. Our framework is applicable in long-term budget planning or resource allocation settings. We propose a model to minimize the maximum deviation from a so-called “ideal function” that we then show can be reformulated as a narrowest path problem on an acyclic directed graph with weights determined by solving minimax regret problems. Given that constructing the graph might be computationally demanding, we devise an optimal path discovery iterative scheme that computes edge weights on an as-needed basis and that results in ε -optimal solutions in a finite number of steps. We conduct an extensive numerical analysis of the proposed procedure to determine average-case performance. We then apply our proposed framework in two real-life settings: (1) large-scale screening of populations for West Nile Virus and (2) the allocation of resources in blood donation centers. The results from both case studies indicate significant reductions in yearly societal costs.