a sustainable hazmat logistic network design considering scale of economy and route sensitivity and solving with hybrid ga-sa

Researchers have been investigating solutions to the vehicle routing problem (vrp) as a practical means of tackling the rising transportation costs in businesses. the goal is to develop innovative methods that minimize shipping expenses and maximize profits. the transportation of hazardous materials (hazmat) is particularly complex and has attracted significant attention from scholars. when designing logistics networks for hazmat, factors such as time window constraints, uncertainties, vehicle capacity, and mileage capacity in sub-tours need to be considered to minimize overall transportation and pollution costs. this study presents a mathematical model for vehicle routing of  hazmat from economic, route sensitivity, and uncertainty perspectives. an optimization approach using a hybrid genetic and simulated annealing (sa) algorithm is then applied to solve the problem. the study includes numerous numerical examples and sensitivity analyses to demonstrate the model’s efficacy. the results indicate that an increase in the route sensitivity coefficient leads to an increase in the objective function. additionally, the effect of demand on the objective function generally increases, although there are instances where it decreases.