Profitable Vehicle Routing Problem with Multiple Trips: Modeling and Variable Neighborhood Descent Algorithm

Abstract In this paper, we tackle a new variant of the Veh icle Routing Problem (VRP) which comb ines two known variants namely the Profitable VRP and the VRP with Mult iple Trips. The resulting problem may be called the Profitable Vehicle Routing Problem with Multiple Trips. The main purpose is to cover and solve a more co mplex realistic situation of the distribution transportation. The profitability concept arises when only a subset of customers can be served due to the lack of means or for insufficiency of the offer. In this case, each customer is associated to an economical profit wh ich will be integrated to the objective function. The latter contains at hand the total collected profit minus the transportation costs. Each vehicle is allowed to perform several routes under a strict workday duration limit. This problem has a very practical interest especially for daily distribution schedules with limited vehicle fleets and short course transportation networks. We point out a new discursive approach for p rofits quantificat ion wh ich is mo re significant than those existing in the literature. We propose four equivalent mathematical formu lations for the problem which are tested and compared using CPLEX solver on small-size instances. Optimal solutions are identified. For large-size instance, two constructive heuristics are proposed and enhanced using Hill Climbing and Variable Neighborhood Descent algorithm based on a specific three-arrays-based coding structure. Finally, extensive co mputational experiments are performed including randomly generated instances and an extended and adapted benchmark fro m literature showing very satisfactory results

An Innovative Genetic Algorithm for a Multi-Objective Optimization of Two-Dimensional Cutting-Stock Problem

This paper addressed an important variant of two-dimensional cutting stock problem. The objective was not only to minimize trim loss, as in traditional cutting stock problems, but rather to minimize the number of machine setups. This additional objective is crucial for the life of the machines and affects both the time and the cost of cutting operations. Since cutting stock problems are well known to be NP-hard, we proposed an approximate method to solve this problem in a reasonable time. This approach differs from the previous works by generating a front with many interesting solutions. By this way, the decision maker or production manager can choose the best one from the set based on other additional constraints. This approach combined a genetic algorithm with a linear programming model to estimate the optimal Pareto front of these two objectives. The effectiveness of this approach was evaluated through a set of instances collected from the literature. The experimental results for different-size problems show that this algorithm provides Pareto fronts very near to the optimal ones

Lower bounds and an enhanced greedy heuristic for the single processor scheduling with release dates

International audienceIn this study, we consider the single machine scheduling problem with release dates to minimize total weighted completion time. This problem is known to be strongly NP-hard. First, we present five different formulations based on mixed integer linear programming different definitions of decision variables. Second, new recursive weights decomposition-based lower bounds are proposed, then we generalize an improved split-based lower bound from literature. A constructive greedy heuristic is proposed based on evaluation function with partially lower bound assessment. A first improvement procedure using Hill Climbing search is presented. Experimental study shows promising results

Ordonnancement sur machines parallèles avec contraintes d'indisponibilité

Les travaux de cette thèse sont articulés autour du problème d ordonnancement sur machines parallèles identiques avec contraintes d indisponibilité pour la minimisation du flow time. Nous avons étudié trois modèles de ce problème. L objectif est de proposer des méthodes théoriques d optimisation qui permettent une résolution efficace. Les approches développées sont variées : des heuristiques qui ont amélioré des méthodes classiques de la littérature, trois types d approches exactes basées sur la programmation linéaire à variables mixtes, branch-and-bound utilisant différents schémas de séparation et programmation dynamique. Nous avons proposé des bornes inférieures constructives et itératives. Celles basées sur la relaxation lagrangienne étaient combinées avec différents outils de la recherche opérationnelle tels que l méthode de sous-gradient, la programmation dynamique et le splitting des travaux. Une méthode de génération de colonnes a été développée. La résolution des problèmes auxiliaires a été réalisée avec une méthode heuristique et une méthode exacte par programmation dynamique. Par ailleurs, nous avons prouvé des propriétés mathématiques et proposé de nouvelles bornes inférieures pour un modèle traité en littérature. Enfin, nous avons élaboré des analyses de performance au pire pour des méthodes heuristiques et une borne inférieureThis thesis is devoted to parallel machine scheduling with availability constraints for minimizing the flow time. We studied three theoretical models of this problem. The objective is to propose theoretical optimization methods that effectively solve these problems. We develop various approaches. Indeed, we proposed heuristic methods that improved classical methods from literature. Three types of exact approaches were considered : methods based on mixes integer linear programming, branch-and-bound methods using different branching schemes and methods based on dynamic programming. We also proposed constructive and iterative lower bounding schemes. In particular, lower bounds based on Lagrangian relaxation are combined with different tools from operational research, such as the subgradient method, dynamic programming and job splitting. Moreover, a method based on column generation has been developed based on a particular formulation of the problem. Auxiliary problems are solves with a heuristic method and an exact method using the dynamic programming. Furthermore, we proved several mathematical properties and proposed new lower bounds for a model already studied in the literature. Finally, we have studied worst-case performance for simple heuristics and a lower boundTROYES-SCD-UTT (103872102) / SudocSudocFranceF

MSPT2 Heuristic and Dynamic Programming Method for the Parallel Machine Scheduling Problem with scheduled Preventive Maintenance

International audienceIn this paper, we consider the parallel-machine scheduling problem with scheduled maintenance periods to minimize the total (non-weighted and weighted) completion time. For the case of single maintenance period on each machine, we provide an adapted definition of the "SPT" algorithm and we propose an MSPT2 heuristic. For the general case, we present a dynamic programming model to solve optimally the problem. In addition, improved dominance properties are proposed. Experimental simulations are done to evaluate the method performances

A Column Generation Method for the Parallel-Machine Scheduling Problem with availability constraint

International audienceIn this paper, we study the problem of scheduling jobs on identical parallel machines with the objective of minimizing the total completion times of jobs where each machine is subject to one unavailability time interval. We provide a column generation based method to obtain a lower bound for the problem. Computational experiments show the interest and the versatility of the proposed metho

Lagrangian relaxation and column generation-based lower bounds for the Pm, hj1 parallel to Sigma wiCi scheduling problem

International audienceWe consider an identical parallel-machine scheduling problem to minimize the sum of weighted completion times of jobs. However, instead of allowing machines to be continuously available as it is generally assumed, we consider that each machine is subject to a deterministic and finite maintenance period. This condition increases the problem complexity. We provide for the problem an adapted heuristic, lower bounds based on Lagrangian relaxation and column generation methods. Computational study shows satisfactory results

Identical parallel-machine scheduling under availability constraints to minimize the sum of completion times

In this paper, we study the identical parallel machine scheduling problem with a planned maintenance period on each machine to minimize the sum of completion times. This paper is a first approach for this problem. We propose three exact methods to solve the problem at hand: mixed integer linear programming methods, a dynamic programming based method and a branch-and-bound method. Several constructive heuristics are proposed. A lower bound, dominance properties and two branching schemes for the branch-and-bound method are presented. Experimental results show that the methods can give satisfactory solutions.Scheduling problem Availability constraints Parallel machines Total completion times

Mixed Integer Linear Programming Models to Solve a Real-Life Vehicle Routing Problem with Pickup and Delivery

This paper presents multiple readings to solve a vehicle routing problem with pickup and delivery (VRPPD) based on a real-life case study. Compared to theoretical problems, real-life ones are more difficult to address due to their richness and complexity. To handle multiple points of view in modeling our problem, we developed three different Mixed Integer Linear Programming (MILP) models, where each model covers particular constraints. The suggested models are designed for a mega poultry company in Tunisia, called CHAHIA. Our mission was to develop a prototype for CHAHIA that helps decision-makers find the best path for simultaneously delivering the company’s products and collecting the empty boxes. Based on data provided by CHAHIA, we conducted computational experiments, which have shown interesting and promising results