A Probabilistic Framework for Optimizing Real-time Decisions in Humanitarian Aid Delivery Systems

TL;DR

This paper introduces a probabilistic, hierarchical optimization model for real-time humanitarian aid delivery, improving reliability and efficiency by considering transfer time uncertainties and late delivery penalties.

Contribution

It develops a novel mixed-integer, probabilistic, non-linear optimization framework with an innovative algorithm combining DAG-based discrete optimization and homotopy methods.

Findings

Model maximizes system reliability within budget constraints

Algorithm effectively handles discrete and continuous variables

Preliminary numerical examples show promising results

Abstract

This paper presents a computationally efficient model for optimizing real-time decisions in humanitarian aid delivery systems. Our formulation models a hierarchical system and is a mixed integer, probabilistic, non-linear and non-concave optimization problem. The proposed model considers the costs and probabilistic nature of transfer times and maximizes the reliability of the system using the available budget. We account for late deliveries using a nonlinear penalty function. We also propose an algorithm that uses a directed acyclic graph to deal with the discrete variables in tandem with a homotopy method for optimizing the continuous variables. We then offer a pruning method to eliminate the cost inefficiencies in the system. The effectiveness of formulation is examined in some numerical examples under progress.