An effective two-stage stochastic multi-trip location-transportation model with social concerns in relief supply chains

The distribution of emergency aid from warehouses to relief centers to satisfy the needs of the victims in the aftermath of a disaster is a complex problem because it requires a rapid response to human suffering when resources are scarce amidst great uncertainty. In order to provide an effective response and use resources efficiently, this paper presents a novel model to optimize location, transportation, and fleet sizing decisions. In contrast with existing models, vehicles can be reused for multiple trips within micro-periods (blocks of hours) and/or over periods (days). Uncertainty regarding demand, incoming supply, and availability of routes is modeled via a finite set of scenarios, using two-stage stochastic programs. ‘Deprivation costs’ are used to represent social concerns and minimized via two objective functions. Mathematical programming based heuristics are devised to enable good-quality solutions within reasonable computing time. Experimental results based on data from the disastrous 2011 floods and landslides in the Serrana Region of Rio de Janeiro, Brazil, show that the model’s novel characteristics help get aid faster to victims and naturally enforce fairness in its distribution to disaster areas in a humanitarian spirit.