Multi-Depot Capacitated Vehicle Routing Problem by Using Stable Marriage and K-Means Clustering to Minimize Number of Unserved Customers and Total Travel Distance

Abstract

Multi-depot capacitated vehicle routing problem is a derivative of vehicle routing problem and a well-known area that has been studied widely with various applications and constraints. Many studies in it focused on minimizing cost and distance with assumption that all nodes are visited. Ironically, number of unserved customers (nodes) in a single trip was rarely explored and often ignored. Based on this problem, this work aims to minimize the total travel distance and the number of unserved customers in single routing cycle. The solution is developed by combining the stable marriage algorithm and k-means clustering in the clustering process. The nearest neighbour algorithm is used in the routing process. This work proposes two contributions. The first is the usage of the stable marriage and k-means clustering. The second is concerning the predetermined distribution of the vehicles in the solution to reduce the number of unserved customers. In the simulation, this proposed model is compared with the hybrid evolutionary algorithm (HEA), partition-based algorithm-nearest neighbour algorithm (PBA-NN), genetic algorithm-nearest neighbour algorithm (GA-NN) and simulated annealing algorithm (SA). Based on the simulation result, it is found that the proposed model performs moderately as a trade-off between the SA and PBA-NN. In the number of unserved customers aspect, when the number of customers is low, the proposed model creates 71 percent lower than the PBA-NN model. Meanwhile, when the number of customers is high, the proposed model creates 73 percent lower than the PBA-NN model. In the total travel distance aspect, when the number of customers is low (50 persons), the proposed model creates 63 percent higher than the GA-NN model and 48 percent lower than the SA model. Meanwhile, when the number of customers is high (100 customers), the proposed model creates 52 percent higher than the PBA-NN model and 54 percent lower than the SA model.