The complexity of cost constrained vehicle scheduling problem

The complexity of cost constrained vehicle scheduling problem

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This paper Beauty Mirrors 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 Body 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.