Multi-Objective Approach: Multi-Compartment Vehicles For Pick-Up And Delivery Problem With Times Windows

Abstract

In this article, we address the pickup and delivery problem goods. In this problem, goods are collected from suppliers and delivered to different customers. Very often, single compartment vehicles are used to transport these goods. As a result, there are several damages due to some products being harmful to others stored in the same compartment: incompatibility between products. It is therefore necessary to use multi-compartment vehicles to overcome the problems of product incompatibility. It is necessary to produce a service that satisfies a set of customers according to their availability, respects the constraints linked to the capacity of each vehicle compartment and each type of product, and ensures that each supplier is visited before his customer. This work is structured in two main blocks. The first block presents the modelling of the problem taking into account the minimisation of three main criteria, namely: the number of vehicles put into service, the total cost related to the vehicles and the delays on the nodes
min𝑓= (𝑓1= 𝐾 ;𝑓2=ΣΣΣmax (0,𝐷𝑖−𝐺𝑖)𝑥𝑖𝑗𝑘 ; 𝑓3=ΣΣΣ𝐶𝑘𝑑𝑖𝑗𝑘𝑥𝑖𝑗𝑘 𝑗∈𝐹𝑖∈𝐹𝑘∈𝐾𝑗∈𝐹𝑖∈𝐹𝑘∈𝐾). The second part will be devoted to the multi-criteria solution of the pick-up and delivery problem with time windows provided by multi-compartment vehicles by the NSGA-II algorithm.