A global satisfaction degree method for fuzzy capacitated vehicle routing problems
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Juan Carlos Figueroa-García1, Jhoan Sebastián Tenjo-García2, Carlos Franco3
1Universidad Distrital Francisco José de Caldas, Bogotá - Colombia.
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 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.
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