Amirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24492120210201The complexity of cost constrained vehicle scheduling problem109115427410.22060/ajmc.2021.19454.1046ENMaliheNiksiratDepartment of Computer Science, Faculty of Computer and Industrial Engineering, Birjand University of Technology, Birjand, IranSeyed NaserHashemiDepartment of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, IranJournal Article20210104This paper considered the cost constrained vehicle scheduling problem under the constraint that the total number of vehicles is known in advance. Each depot has a different time processing cost. The goal of this problem is to find a feasible minimum cost schedule for vehicles. A mathematical formulation of the problem is developed and the complexity of the problem when there are more than two depots is investigated. It is proved that in this case, the problem is NP-complete. Also, it is showed that there is not any constant ratio approximation algorithm for the problem, i.e., it is in the complexity class APX.https://ajmc.aut.ac.ir/article_4274_68f3cbb47d8809e62a4acbba2ee0cc75.pdf