Solving capacitated vehicle routing problem with demands as fuzzy random variable

Capacitated vehicle routing problem (CVRP) is a classical combinatorial optimization problem in which a network of customers with specified demands is given. The objective is to find a set of routes which originates as well as terminates at the depot node. These routes are to be traversed in such a way that the demands of all the customers in the network are satisfied and the cost associated with traversal of these routes come out to be a minimum. In real-world situations, the demand of any commodity depends upon various uncontrollable factors, such as season, delivery time, and market conditions. Due to these factors, the demand can always not be told in advance and a precise information about the demand is nearly impossible to achieve. Hence, the demands of the customers always experience impreciseness and randomness in real life. The decisions made by the customers about the demands may also have some scope of hesitation as well. In order to handle such demands of customers in the network, fuzzy random variables and intuitionistic fuzzy random variables are used in this work. The work bridges the gap between the classical version of CVRP and the real-life situation and hence makes it easier for the logistic management companies to determine the routes that should be followed for minimum operational cost and maximum profit. Mathematical models corresponding to CVRP with fuzzy stochastic demands (CVRPFSD) and CVRP with intuitionistic fuzzy stochastic demands (CVRPIFSD) have been presented. A two-stage model has been proposed to find out the solution for the same. To explain the working of the methodology defined in this work, different examples of networks with fuzzy and intuitionistic fuzzy demands have been worked out. The proposed solution approach is also tested on modified fuzzy stochastic versions of some benchmark instances.