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

Abstract: 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 harm metric of estimated exposure-years is described at the parcel level, which can then be aggregated to the project level and minimized globally by posing project selection as a 0/1 knapsack problem. Simplifying further for use by non-experts, the implied linear programming relaxation is solved intuitively with the greedy algorithm; ordering projects by benefit cost ratio produces a priority list which planners can then consider holistically alongside harder to quantify factors. A case study demonstrates the successful application of this framework to a small U.S. city's existing data 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.