The thesis focuses on how to optimize vehicle routes for distributing logistics. This vehicle route optimization is known as a vehicle routing problem (VRP). The VRP has been extended in numerous directions for instance by some variations that can be combined. One of the extension forms of VRP is a capacitated VRP with stochastics demands (CVRPSD), where the vehicle capacity limit has a non-zero probability of being violated on any route. So, a failure to satisfy the amount of demand can appear. A strategy is required for updating the routes in case of such an event. This strategy is called as recourse action in the thesis. The main objective of the research is how to design the model of CVRPSD and find the optimal solution. The EEV (Expected Effective Value) and FCM (Fuzzy C-Means) – TSP (Travelling Salesman Problem) approaches are described and used to solve CVRPSD. Results have confirmed that the EEV approach has given a better performance than FCM-TSP for solving CVRPSD in small instances. But EEV has disadvantage, that the EEV is not capable to solve big instances in an acceptable running time because of complexity of the problem. In the real situation, the FCM –TSP approach is more suitable for implementations than the EEV because the FCM – TSP can find the solution in a shorter time. The disadvantage of this algorithm is that the computational time depends on the number of customers in a cluster.

This diploma work deals with a dynamic multi-level multi-item lot sizing problem in a general production-assembly structure represented by a directed acyclic network, where each node may have several predecessors and successors. We assume stochastic demand, finite planning horizon consisting of discrete time periods, dynamic lot sizes, multiple constrained resources and time-varying cost parameters. The objective is to minimize the total costs over the planning horizon. This thesis includes overview of models with stochastic demand and also general description of genetic algorithm. Using different modifications of genetic algorithm I have proposed and implemented methods for solving a chosen model. Then I have made an experimental comparison of these method on selected problems.

Le problème de tournées de véhicules avec contrainte de capacité est un problème important en optimisation combinatoire. L'objectif du problème est de déterminer l'ensemble des routes, nécessaire pour servir les demandes déterministes des clients ayant un cout minimal, tout en respectant la capacité limite des véhicules. Cependant, dans de nombreuses applications réelles, nous sommes confrontés à des incertitudes sur les demandes des clients. La plupart des travaux qui ont traité ce problème ont supposé que les demandes des clients étaient des variables aléatoires. Nous nous proposons dans cette thèse de représenter l'incertitude sur les demandes des clients dans le cadre de la théorie de l'évidence - un formalisme alternatif pour modéliser les incertitudes. Pour résoudre le problème d'optimisation qui résulte, nous généralisons les approches de modélisation classiques en programmation stochastique. Précisément, nous proposons deux modèles pour ce problème. Le premier modèle, est une extension de l'approche chance-constrained programming, qui impose des bornes minimales pour la croyance et la plausibilité que la somme des demandes sur chaque route respecte la capacité des véhicules. Le deuxième modèle étend l'approche stochastic programming with recourse: l'incertitude sur les recours (actions correctives) possibles sur chaque route est représentée par une fonction de croyance et le coût d'une route est alors son coût classique (sans recours) additionné du pire coût espéré des recours. Certaines propriétés de ces deux modèles sont étudiées. Un algorithme de recuit simulé est adapté pour résoudre les deux modèles et est testé expérimentalement. / The capacitated vehicle routing problem is an important combinatorial optimisation problem. Its objective is to find a set of routes of minimum cost, such that a fleet of vehicles initially located at a depot service the deterministic demands of a set of customers, while respecting capacity limits of the vehicles. Still, in many real-life applications, we are faced with uncertainty on customer demands. Most of the research papers that handled this situation, assumed that customer demands are random variables. In this thesis, we propose to represent uncertainty on customer demands using evidence theory - an alternative uncertainty theory. To tackle the resulting optimisation problem, we extend classical stochastic programming modelling approaches. Specifically, we propose two models for this problem. The first model is an extension of the chance-constrained programming approach, which imposes certain minimum bounds on the belief and plausibility that the sum of the demands on each route respects the vehicle capacity. The second model extends the stochastic programming with recourse approach: it represents by a belief function for each route the uncertainty on its recourses (corrective actions) and defines the cost of a route as its classical cost (without recourse) plus the worst expected cost of its recourses. Some properties of these two models are studied. A simulated annealing algorithm is adapted to solve both models and is experimentally tested.