Selective routing problems in humanitarian operations

Abstract

In this thesis, we investigate the critical role of demand frequency in disaster response. We categorize demand into three types: one-time, continuous, and periodic. We define three distinct problems for each demand type. For one-time demand, we define a location-allocation problem with service duration decisions. For continuous demand, we define a maximal covering location problem. For periodic demand, we define a scheduling problem with duration decisions. For each problem, we develop tailored mathematical formulations that integrate realistic demand functions. Firstly, we consider one-time demand, which is characterized by immediate and non-recurring needs in the aftermath of a disaster. We develop three integer programming models for location-allocation problem with service duration decisions which incorporate a stepwise demand function that captures the gradual decline in demand over time. We compare the mathematical models on real-world datasets in terms of solution time and optimality gap for large instances. Through extensive computational experiments, we observe that the best-performing model achieves optimal or near-optimal solutions significantly faster with smaller optimality gaps, especially when solving large-scale instances. The results show that adopting temporal coverage of demand at different locations satisfies more demand over time. We observe that dynamically changing disaster environment requires adopting more agile deployment strategies for mobile service units. Secondly, we consider continuous demand to represent critical and ongoing service requirements. We take into account different types of mobile service units (highcapacity, medium-capacity, and low-capacity). We provide a mathematical formulation maximal covering location problem that determines the optimal locations of mobile service units and allocation of demand points to mobile service units. We also integrate a demand function that accounts for diminishing demand due to coverage. We consider two concepts for how demand is satisfied from covered areas: binary and gradual coverage. In binary coverage, demand is fully satisfied if the demand location is within the coverage radius of a mobile service unit. On the other hand, in gradual coverage, the total demand satisfied drops significantly because it follows a decay function to reflect a decrease with respect to distance. According to our results, we observe that the model prioritizes locating mobile service units closer to demand areas to decrease the decay effect. Finally, we consider periodic demand to represent recurring service needs over specific time intervals. We introduce four mathematical formulations for a scheduling problem with duration decisions: compact 5-index, 4-index models and two 3-index non-compact models. The latter two are derived through a Benders-type projection method and solved using a branch-and-cut algorithm strengthened with valid inequalities. Although decomposition-friendly formulations are attractive, they face significant computational overhead. We also conduct a sensitivity analysis on the parameters and identify the most influential setting. Additionally, we analyze demand functions, including linear, exponential, sigmoid, quadratic, logarithmic, and step functions. We evaluate those functions by post-processing their solutions with a neutral demand function for fair comparison. We finally provide a case study using data from the 2023 Kahramanmaraş earthquakes to validate the model’s practical applicability. According to the solutions, the high-density districts receive extended service durations, while the low-density districts receive the minimum visit requirements. It is noted that to enhance fairness, the parameters regarding the minimum requirement can be updated for low-density areas. Based on these comprehensive computational studies across all three demand types, we provide strategic insights for deploying mobile service units in complex disaster settings.