Optimization location routing problem (LRP) of humanitarian aid distribution in Sigi district using NSGA II methods

Disasters are events that disturb and threaten people’s lives caused by nature or/and non-natural factors as well as human factors that cause casualties and economic losses. Since the 1950s, the number and scale of major natural disasters such as earthquakes, tsunamis, cyclones, floods, volcanoes, etc. have grown exponentially (Hu & Dong, 2019). The polemic of uneven assistance and delays in the event of a natural disaster is the most common thing that occurs during a natural disaster. Location Routing Problem is a continuation of the classical routing problem that combines strategic and operational decisions with the facility location problem and the vehicle routing problem. This study aims to determine the location of the distribution center construction and the optimal route using the NSGA II methods with the objective function of minimizing total costs and minimization of maximum travelling time for the distribution of humanitarian aid in the 2018 natural disaster in Sigi Regency. Optimization is designed into two scenarios, namely the construction of two distribution centers and three distribution centers. The result show that construction of two distribution centers can be designed at locations D3 and D4 with a total cost of IDR406 280 000 and a maximum service time of 12.002 hours, while the construction of three distribution centers can be done at locations DC1, DC4 and DC 7 or with a total cost of IDR605 363 000 and a maximum service time of 7.4253 hours.This research develops a new mathematical model that optimizes humanitarian aid distribution by balancing the setup cost of distribution centers and minimizing travel time. It utilizes the NSGA-II algorithm for multi-objective optimization and the Displaced Ideal Solution (DIS) method to select the best solution from the Pareto front.