Optimal Scheduling of Rainwater Collection Vehicles: Mixed Integer Programming and Genetic Algorithms

Abstract

Due to climate change, some areas in the world witnessed higher levels of heavy rain than the capacity of the wastewater system of the streets. Therefore, water tankers are used for the dewatering process to take the extra rainwater from the streets to keep a smooth flow of vehicles and to use the water in agriculture and industry. Water is taken to a water treatment plant. Performing the dewatering process as fast as possible, especially in crowded streets, was ignored by researchers. In this study, at first, the problem was solved using two mixed integer programming (MIP) models. A new variant of identical parallel machine scheduling with job splitting is proposed for the first time, where one or at most two tankers can work at the same flood location at the same time. This is performed in the second model. However, the first model considers dividing the dewatering processes into two phases, where the first one, which is more urgent, is to reduce the amount of floodwater. The second one is for dewatering the rest of the water. Then two genetic algorithms (GAs) were used to solve faster the two MIP models, which are NP-hard problems. At first, the MIP and GA models were applied to small-sized problems. Then GA was used for large practical data sets. Results showed that for small problems, MIP and GA gave optimal solutions in a reasonable number of iterations, while for larger problems, good solutions were obtained in a reasonable number of iterations.