In this article we focus on multi-compartment vehicles that have to pick-up goods from suppliers and deliver them to various customers. Usually these goods cannot be transported by single-compartment vehicles due to the fact that some products are harmful to others: incompatibility between products. It is therefore a question of satisfying a set of customers while respecting the constraints linked to the capacity of each vehicle compartment, each type of product and ensuring that each supplier is visited before his customer. Our work consists firstly of mathematically modelling the problem described and secondly of solving it using methods due to its complexity. In this case we use the genetic algorithm to solve the pick-up and delivery problem of goods with a time window provided by multi-compartment vehicles. Our model allows to find a minimum distance and a minimum cost in the tour carried out by a reasonable number of vehicles.

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