Amirkabir University of Technology AUT Journal of Mathematics and Computing 2783-2449 2 1 2021 02 01 The complexity of cost constrained vehicle scheduling problem 109 115 4274 10.22060/ajmc.2021.19454.1046 EN Malihe Niksirat Department of Computer Science, Faculty of Computer and Industrial Engineering, Birjand University of Technology, Birjand, Iran Seyed Naser Hashemi Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran Journal Article 2021 01 04 This 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_ddf88ea64eaed0f3de5531ac964a0a1a.pdf