Social cost-vehicle routing problem and its application to the delivery of water in post-disaster humanitarian logistics

Abstract

In the aftermath of a disaster, delivering critical supplies, especially water, is of critical importance. Water, as well as other commodities such as rice and fuel, can be transported in different formats. Bottled water has the advantage of self-storage and easy distribution compared with bulk water, but it needs to be brought in from outside the impacted area and has high logistics costs. Bulk water can be accessed from local streams and water purification stations but requires survivors to have containers. The logistics costs and form of transportation necessary for these two different forms of water resources create tradeoffs normally overlooked in the literature. This paper introduces the Social Cost Vehicle Routing Problem: a mathematical optimization model to determine the right mix of formats for this critical commodity in terms of transportation, routing, and delivery considering social costs in the objective function. Due to the NP-hard nature of the problem, a hybrid metaheuristic algorithm with a novel local search is developed to solve large instances of the problem. The algorithm uses tabu search, simulated annealing, and variable neighborhood search in a combined manner. The model is applied to a case study of post-disaster water distribution in Puerto Rico after Hurricanes Irma and Maria in 2017. Numerical experiments indicate that having a combination of bottled and bulk water maximizes aid to survivors while minimizing response costs.