A global satisfaction degree method for fuzzy capacitated vehicle routing problems

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 alpha, lambda 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 alpha and lambda. 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.

Automated summary

This study proposes a method that uses third-party information from experts to represent uncertain costs/demands as fuzzy numbers, solving vehicle routing problems through iterative-integer programming and a global satisfaction degree, with experiments confirming convergence regardless of initial parameter selection.