The maxisum and maximin-maxisum HAZMAT routing problems

•We formulate and solve models for two new HAZMAT transportation route design problems for multiple origin destination pairs.•The models minimize the danger to which vulnerable centers (schools, hospitals) are exposed by the routes.•We propose a polynomial efficient heuristic for the problems.•We apply the methods to actual data. We design routes for transportation of hazardous materials (HAZMAT) in urban areas, with multiple origin-destination pairs. First, we introduce the maxisum HAZMAT routing problem, which maximizes the sum of the population-weighted distances from vulnerable centers to their closest point on the routes. Secondly, the maximin-maxisum HAZMAT routing problem trades-off maxisum versus the population-weighted distance from the route to its closest center. We propose efficient IP formulations for both NP-Hard problems, as well as a polynomial heuristic that reaches gaps below 0.54% in a few seconds on the real case in the city of Santiago, Chile.