Methodology to Solve a Special Case of the Vehicle Routing Problem: A Case Study in the Raw Milk Transportation System

Abstract

This research aims to solve the problem of the raw milk collection and transportation system which can be interpreted as a special case of the vehicle routing problem. In the proposed problem, the factory will send the trucks, multiple fleets composed of several compartments, to collect the raw milk from the raw milk farms. The objective of this research is to minimize the total transportation cost and the trucks’ and tanks’ cleaning costs. The transportation cost directly depends on the fuel usage. The fuel usage occurs during the transportation of the milk and during the waiting times when it arrives at the factory and cannot transfer the raw milk into the production tank. We develop the modified differential evolution algorithm (MDE) to solve the proposed problem. The original process of the Differential Evolution algorithm (DE) has been modified in two folds which are as follows: (1) In the recombination process, the 2nd order of trial vectors has been generated using 3 different strategies and compared with the 1st order trial vector; the better from the 1st and the 2nd order of trial vectors will move to the selection process. (2) The probability function has been used to select the new target vector from one of two sources which are the trial vector and the current target vector so that the worse solution can be accepted in order to increase the diversity of the original DE. The computational result shows that the modified DE (MDE) outperforms the original DE in finding a better solution.