Inventory routing for the last mile delivery of humanitarian relief supplies

Fast and equitable distribution of the humanitarian relief supplies is key to the success of relief operations. Delayed and inequitable deliveries can result in suffering of affected people and loss of lives. In this study, we analyze the routing operations for the delivery of relief supplies from a distribution center to the dispensing sites. We assume that the relief supplies to be distributed arrive at the distribution center in batches and are consumed at the dispensing sites with a certain daily rate. When forming delivery schedules, we use the ratio of the inventory to the daily consumption rate at the dispensing sites as our decision criterion. This ratio is called the slack and can be considered as the safety stock (when positive) in case of a delay in the deliveries. Negative value for the slack means the dispensing site has stock-outs. Our objective is to maximize the minimum value of this slack among all dispensing sites. This is equivalent to maximizing the minimum safety stock or minimizing the maximum duration of the stock-outs. Due to multi-period structure of the problem, it is modeled as a variant of the Inventory Routing Problem. To address the problem, we propose a general framework which includes clustering, routing and improvement steps. The proposed framework considers the interdependence between all three types of decisions (clustering, routing and resource allocation) and makes the decisions in an integrated manner. We test the proposed framework on randomly generated instances and compare its performance against the benchmark algorithms in the literature. The proposed framework not only outperforms the benchmark algorithms by at least 1% less optimality gap but also provides high-quality solutions with around 2–3% optimality gaps.