A hybrid GA-BFO algorithm for the profit-maximizing capacitated vehicle routing problem under uncertain paradigm

Abstract

This study designs a new variant of the capacitated vehicle routing problem (CVRP) under a fuzzy environment. In CVRP, several vehicles start their journey from a central depot to provide services to different cities and finally return to the depot. This paper introduces an additional time beyond the service time at each city to fulfill the pre-ordered demands. The need for this excess service time is to provide the services to new customers who are not enlisted at the start of the process. It is a market enhancement step. The proposed model’s main objective is to find the maximum time-dependent profit by using the optimum number of vehicles in an appropriate route and spending optimum excess service time in each city. The model considers travel time and travel cost as fuzzy numbers. An expected value model (EVM) is formulated using the credibility approach on fuzzy variables. A hybrid meta-heuristic method combining a genetic algorithm (GA) and bacteria foraging optimization algorithm (BFOA) is designed to solve the proposed model. The proposed model is explained with the help of some numerical examples. Sensitivity analyses based on different independent parameters of the algorithms are also conducted.