Prioritizing municipal lead mitigation projects as a relaxed knapsack optimization: a method and case study

Lead pipe remediation budgets are limited and ought to maximize public health impact. This goal implies a non-trivial optimization problem; lead service lines connect water mains to individual houses, but any realistic replacement strategy must batch replacements at a larger scale. Additionally, planners typically lack a principled method for comparing the relative public health value of potential interventions and often plan projects based on non-health factors. This paper describes a simple process for estimating child health impact at a parcel level by cleaning and synthesizing municipal datasets that are commonly available but seldom joined due to data quality issues. Using geocoding as the core record linkage mechanism, parcel-level toxicity data can be combined with school enrollment records to indicate where young children and lead lines coexist. A practical heuristic of estimated exposure-years is described at the parcel level, which can then be aggregated to the project level and minimized globally by selecting projects using a knapsack optimization. The optimization setup can then be relaxed to produce a priority queue which planners can consider alongside numerous harder to quantify factors. A case study demonstrates the successful application of this framework to a small U.S.~city's existing data in order to prioritize federal infrastructure funding. While this paper focuses on lead in drinking water, the approach readily generalizes to other sources of residential toxicity with disproportionate impact on children.