A global satisfaction degree method for fuzzy capacitated vehicle routing problems

Abstract

There are several uncertain capacitated vehicle routing problems whose delivery costs and demands cannot be estimated using deterministic/statistical methods due to a lack of available and/or reliable data. To overcome this lack of data, third–party information coming from experts can be used to represent those uncertain costs/demands as fuzzy numbers which combined to an iterative–integer programming method and a global satisfaction degree is able to find a global optimal solution. The proposed method uses two auxiliary variables α,λ and the cumulative membership function of a fuzzy set to obtain real–valued costs and demands prior to find a deterministic solution and then iteratively find an equilibrium between fuzzy costs/demands via α and λ. The performed experiments allow us to verify the convergence of the proposed algorithm no matter the initial selection of parameters and the size of the problem/instance.