Equity and social acceptability in multiple hazardous materials routing through urban areas

In this article we study the problem of routing hazardous materials (hazmat) form an origin to a destination on an urban transportation network in which the arcs lay on irregular zones with different population densities. Hazmat are transported on a regular basis instead of a single shipment. In addition, different types of hazmat, posing different levels of risk, must be transported at the same time. We developed a methodology to incorporate the concept of equity in the spatial distribution of risk when multiple types of hazmat must be distributed along various simultaneous routes including not only the risk added by the transportation process but also other baseline risks from exogenous sources. The article describes the development of a multi-product multi-shipment hazmat routing model with equity constraints, departing from a theoretically rich single product single shipment hazmat routing model found in the literature, aimed to minimize the conditional expectation of the consequence of a catastrophic accident. The resultant modeling approach is a linear fractional programming model that incorporates a flexible set of linear constraints that allow a fair distribution of risk among populated zones, restricting the total level of risk below a socially acceptable threshold. We applied this modeling framework to two hypothetical examples and to an actual case in Santiago, Chile (a large capital city with over 6 million inhabitants) showing to be both mathematically tractable and useful for decision makers in practice.