scholarly journals A Genetic Algorithm on Inventory Routing Problem

2014 ◽  
Vol 3 (3) ◽  
pp. 59-66 ◽  
Author(s):  
Nevin Aydın
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Optimization Problems ◽  
Inventory Routing ◽  
Routing Problems ◽  
Routing Problem ◽  
Inventory Routing Problem ◽  
Combinatorial Optimization Problems ◽  
The Difference ◽  
The Relationship

Inventory routing problem can be defined as forming the routes to serve to the retailers from the manufacturer, deciding on the quantity of the shipment to the retailers and deciding on the timing of the replenishments. The difference of inventory routing problems from vehicle routing problems is the consideration of the inventory positions of retailers and supplier, and making the decision accordingly. Inventory routing problems are complex in nature and they can be solved either theoretically or using a heuristics method. Metaheuristics is an emerging class of heuristics that can be applied to combinatorial optimization problems. In this paper, we provide the relationship between vendor-managed inventory and inventory routing problem. The proposed genetic for solving vehicle routing problem is described in detail.

scholarly journals Models and solution algorithms for inventory routing problems

2017 ◽  
Author(s):  
Παντελής Λάππας
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Time Windows ◽  
Neighborhood Search ◽  
Np Hard ◽  
Inventory Routing ◽  
Routing Problems ◽  
Routing Problem ◽  
Inventory Routing Problem ◽  
Delivery Times

Στόχος της παρούσας διατριβής είναι η παρουσίαση αλγοριθμικών προσεγγίσεων για την επίλυση του Προβλήματος Δρομολόγησης Αποθεμάτων (Inventory Routing Problem, IRP) και του Προβλήματος Δρομολόγησης Αποθεμάτων με Χρονικά Παράθυρα (Inventory Routing Problem with Time Windows, IRPTW). Τα ανωτέρω προβλήματα πηγάζουν από την προσέγγιση της Διαχείρισης Αποθεμάτων από τον Προμηθευτή/Πωλητή (Vendor Managed Inventory, VMI) που διαδόθηκε ιδιαίτερα κατά τα τέλη της δεκαετίας του ’80 από τις Wal-Mart και Procter & Gamble και στη συνέχεια υιοθετήθηκε από πολλές εταιρίες όπως οι Johnson & Johnson, Black & Decker κ.ά. Σύμφωνα με το VMI, ο προμηθευτής διανέμει προϊόντα σε έναν αριθμό από γεωγραφικά διάσπαρτους πελάτες αποφασίζοντας ταυτόχρονα για τα ακόλουθα: (1) τους χρόνους εξυπηρέτησης πελατών, (2) τις ποσότητες διανομής και (3) τις διαδρομές που πρέπει να ακολουθηθούν. Οι πρώτες δύο αποφάσεις, σχετίζονται με το Πρόβλημα Ελέγχου Αποθεμάτων (Inventory Control Problem, ICP), ενώ η τρίτη με το Πρόβλημα της Δρομολόγησης Οχημάτων (Vehicle Routing Problem, VRP). Αξίζει να σημειωθεί πως το IRPTW αποτελεί βασική επέκταση του IRP, καθώς ισχύουν οι ίδιοι περιορισμοί, αλλά για κάθε πελάτη η εξυπηρέτηση πρέπει να ξεκινήσει και να ολοκληρωθεί μέσα σε ένα χρονικό παράθυρο (time window), ενώ το όχημα θα παραμένει στο χώρο του πελάτη για συγκεκριμένο χρόνο εξυπηρέτησης. Κατά συνέπεια, το IRPTW αποτελεί σύνθεση του ICP και του Προβλήματος Δρομολόγησης Οχημάτων με Χρονικά Παράθυρα (Vehicle Routing Problem with Time Windows, VRPTW). Η διαφοροποίηση των προβλημάτων δρομολόγησης αποθεμάτων έναντι των υπολοίπων προβλημάτων δρομολόγησης (routing problems) οφείλεται στον παράγοντα απόθεμα, ο οποίος προσθέτει στο πρόβλημα τη διάσταση του χρόνου. Ως εκ τούτου, τα IRP και IRPTW αντιμετωπίζονται ως προβλήματα πολλαπλών περιόδων (multi-period problems). Ο παράγοντας απόθεμα περιπλέκει το πρόβλημα σε δύο διαστάσεις. Πρώτον, η περιορισμένη δυνατότητα διατήρησης αποθέματος στον προμηθευτή και/ ή στους πελάτες θα πρέπει να λαμβάνεται υπόψη όταν αποφασίζονται οι ποσότητες που θα διανεμηθούν, ενώ τυχόν κόστη που συνδέονται με τη διατήρηση αποθέματος στον προμηθευτή ή τους πελάτες πρέπει να συμπεριλαμβάνονται στην αντικειμενική συνάρτηση. Τα προβλήματα δρομολόγησης αποθεμάτων ανήκουν στην κλάση πολυπλοκότητας NP και χαρακτηρίζονται ως NP-δυσχερή (NP-Hard), καθώς περικλείουν το κλασικό πρόβλημα της δρομολόγησης οχημάτων. Με τη μαθηματική μοντελοποίηση των προβλημάτων παρουσιάζεται, επιπλέον, για κάθε πρόβλημα μία αντίστοιχη αλγοριθμική επίλυση. Στην περίπτωση του IRP, η αντικειμενική συνάρτηση του προβλήματος αναπαριστά το συνολικό κόστος που αποτελείται από το κόστος μεταφοράς (transportation cost) και το κόστος αποθήκευσης/διατήρησης αποθέματος (inventory holding cost) στους πελάτες. Για το IRPTW, η αντικειμενική συνάρτηση του προβλήματος αναπαριστά μόνο το συνολικό κόστος μεταφοράς. Λόγω της NP-hard φύσης του IRP προτείνεται ένας υβριδικός εξελικτικός αλγόριθμος βελτιστοποίησης (hybrid evolutionary optimization algorithm) που αξιοποιεί δύο ευρέως γνωστούς μεθευρετικούς αλγόριθμους (meta-heuristics): τον Γενετικό Αλγόριθμο (Genetic Algorithm, GA) και τoν Αλγόριθμο της Προσομοιωμένης Ανόπτησης (Simulated Annealing Algorithm, SA). Ο GA αξιοποιείται στη φάση του σχεδιασμού (planning) όπου καθορίζονται οι προγραμματισμένες προς αποστολή ποσότητες προϊόντος (delivery quantities), καθώς επίσης και οι χρονικές στιγμές του ορίζοντα όπου οι πελάτες θα λάβουν τις σχετικές ποσότητες (delivery times). Ο SA χρησιμοποιείται στη φάση της δρομολόγησης (routing) για την επίλυση των προβλημάτων δρομολόγησης που προκύπτουν σε κάθε περίοδο του χρονικού ορίζοντα. Τα αποτελέσματα των δύο αλγορίθμων συνδυάζονται επαναληπτικά έως την εύρεση της βέλτιστης λύσης του προβλήματος.Όσον αφορά το IRPTW, παρουσιάζεται ένας αλγόριθμος επίλυσης δύο φάσεων (two-phase solution algorithm) που βασίζεται σε μία απλή Προσομοίωση (simple simulation) για τη φάση του σχεδιασμού και στον Αλγόριθμο Μεταβλητής Γειτονιάς Αναζήτησης (Variable Neighborhood Search, VNS) για τη φάση της δρομολόγησης. Τέλος, για τη μέτρηση της αποτελεσματικότητας των δύο προτεινόμενων αλγοριθμικών προσεγγίσεων, νέα δεδομένα προβλημάτων (benchmark instances) έχουν σχεδιαστεί για τα IRP και IRPTW, ενώ παρουσιάζονται αναλυτικά υπολογιστικά αποτελέσματα επί των προβλημάτων.

Efficient Golden-Ball Algorithm Based Clustering to solve the Multi-Depot VRP With Time Windows

2018 ◽  
Vol 9 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Lahcene Guezouli ◽  
Mohamed Bensakhria ◽  
Samir Abdelhamid
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Clustering Algorithm ◽  
Optimization Problems ◽  
Time Window ◽  
Time Windows ◽  
Routing Problem ◽  
Combinatorial Optimization Problems ◽  
Acceptable Quality ◽  
Golden Ball

In this article, the authors propose a decision support system which aims to optimize the classical Capacitated Vehicle Routing Problem by considering the existence of multiple available depots and a time window which must not be violated, that they call the Multi-Depot Vehicle Routing Problem with Time Window (MDVRPTW), and with respecting a set of criteria including: schedules requests from clients, the capacity of vehicles. The authors solve this problem by proposing a recently published technique based on soccer concepts, called Golden Ball (GB), with different solution representation from the original one, this technique was designed to solve combinatorial optimization problems, and by embedding a clustering algorithm. Computational results have shown that the approach produces acceptable quality solutions compared to the best previous results in similar problem in terms of generated solutions and processing time. Experimental results prove that the proposed Golden Ball algorithm is efficient and effective to solve the MDVRPTW problem.

The Traveling Salesman Problem, the Vehicle Routing Problem, and Their Impact on Combinatorial Optimization

2010 ◽  
Vol 1 (2) ◽  
pp. 82-92 ◽  
Author(s):  
Gilbert Laporte
Keyword(s):  
Combinatorial Optimization ◽  
Vehicle Routing ◽  
Traveling Salesman Problem ◽  
Vehicle Routing Problem ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Traveling Salesman ◽  
Routing Problem ◽  
Combinatorial Optimization Problems ◽  
The Traveling Salesman Problem

The Traveling Salesman Problem (TSP) and the Vehicle Routing Problem (VRP) are two of the most popular problems in the field of combinatorial optimization. Due to the study of these two problems, there has been a significant growth in families of exact and heuristic algorithms being used today. The purpose of this paper is to show how their study has fostered developments of the most popular algorithms now applied to the solution of combinatorial optimization problems. These include exact algorithms, classical heuristics and metaheuristics.

scholarly journals Focusing on the Golden Ball Metaheuristic: An Extended Study on a Wider Set of Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-17 ◽  
Author(s):  
E. Osaba ◽  
F. Diaz ◽  
R. Carballedo ◽  
E. Onieva ◽  
A. Perallos
Keyword(s):  
Genetic Algorithms ◽  
Combinatorial Optimization ◽  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Optimization Problems ◽  
Traveling Salesman ◽  
Routing Problem ◽  
Combinatorial Optimization Problems ◽  
Golden Ball ◽  
The One

Nowadays, the development of new metaheuristics for solving optimization problems is a topic of interest in the scientific community. In the literature, a large number of techniques of this kind can be found. Anyway, there are many recently proposed techniques, such as the artificial bee colony and imperialist competitive algorithm. This paper is focused on one recently published technique, the one called Golden Ball (GB). The GB is a multiple-population metaheuristic based on soccer concepts. Although it was designed to solve combinatorial optimization problems, until now, it has only been tested with two simple routing problems: the traveling salesman problem and the capacitated vehicle routing problem. In this paper, the GB is applied to four different combinatorial optimization problems. Two of them are routing problems, which are more complex than the previously used ones: the asymmetric traveling salesman problem and the vehicle routing problem with backhauls. Additionally, one constraint satisfaction problem (the n-queen problem) and one combinatorial design problem (the one-dimensional bin packing problem) have also been used. The outcomes obtained by GB are compared with the ones got by two different genetic algorithms and two distributed genetic algorithms. Additionally, two statistical tests are conducted to compare these results.

An Improved Ant Colony Optimization for VRP with Time Windows

2012 ◽  
Vol 263-266 ◽  
pp. 1609-1613 ◽  
Author(s):  
Su Ping Yu ◽  
Ya Ping Li
Keyword(s):  
Ant Colony Optimization ◽  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Distribution Systems ◽  
Optimization Problems ◽  
Time Windows ◽  
Optimal Solution ◽  
Ant Colony ◽  
Routing Problem ◽  
Combinatorial Optimization Problems

The Vehicle Routing Problem (VRP) is an important problem occurring in many distribution systems, which is also defined as a family of different versions such as the Capacitated Vehicle Routing Problem (CVRP) and the Vehicle Routing Problem with Time Windows (VRPTW). The Ant Colony Optimization (ACO) is a metaheuristic for combinatorial optimization problems. Given the ACO inadequacy, the vehicle routing optimization model is improved and the transfer of the algorithm in corresponding rules and the trajectory updated regulations is reset in this paper, which is called the Improved Ant Colony Optimization (I-ACO). Compared to the calculated results with genetic algorithm (GA) and particle swarm optimization (PSO), the correctness of the model and algorithm is verified. Experimental results show that the I-ACO can quickly and effectively obtain the optimal solution of VRFTW.

scholarly journals Heuristic Algorithms for Solving the Generalized Vehicle Routing Problem

2011 ◽  
Vol 6 (1) ◽  
pp. 158 ◽  
Author(s):  
Petrică Claudiu Pop ◽  
Ioana Zelina ◽  
Vasile Lupşe ◽  
Corina Pop Sitar ◽  
Camelia Chira
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Routing Problem ◽  
Practical Applications ◽  
Combinatorial Optimization Problems ◽  
The Many ◽  
The Given ◽  
Generalized Vehicle Routing Problem

The vehicle routing problem (VRP) is one of the most famous combinatorial optimization problems and has been intensively studied due to the many practical applications in the field of distribution, collection, logistics, etc. We study a generalization of the VRP called the generalized vehicle routing problem (GVRP) where given a partition of the nodes of the graph into node sets we want to find the optimal routes from the given depot to the number of predefined clusters which include exactly one node from each cluster. The purpose of this paper is to present heuristic algorithms to solve this problem approximately. We present constructive algorithms and local search algorithms for solving the generalized vehicle routing problem.

VRoptBees

2018 ◽  
Vol 7 (1) ◽  
pp. 32-56
Author(s):  
Thiago A.S. Masutti ◽  
Leandro Nunes de Castro
Keyword(s):  
Combinatorial Optimization ◽  
Vehicle Routing ◽  
Optimization Problems ◽  
The Other ◽  
Vehicle Routing Problems ◽  
Routing Problems ◽  
Routing Problem ◽  
Combinatorial Optimization Problems ◽  
Biological Phenomena ◽  
The Traveling Salesman Problem

Combinatorial optimization problems are broadly studied in the literature. On the one hand, their challenging characteristics, such as the constraints and number of potential solutions, inspires their use to test new solution techniques. On the other hand, the practical application of these problems provides support of daily tasks of people and companies. Vehicle routing problems constitute a well-known class of combinatorial optimization problems, from which the Traveling Salesman Problem (TSP) is one of the most elementary ones. TSP corresponds to finding the shortest route that visits all cities within a path returning to the start city. Despite its simplicity, the difficulty in finding its exact solution and its direct application in practical problems in multiple areas make it one of the most studied problems in the literature. Algorithms inspired by biological phenomena are being successfully applied to solve optimization tasks, mainly combinatorial optimization problems. Those inspired by the collective behavior of insects produce good results for solving such problems. This article proposes the VRoptBees, a framework inspired by honeybee behavior to tackle vehicle routing problems. The framework provides a flexible and modular tool to easily build solutions to vehicle routing problems. Together with the framework, two examples of implementation are described, one to solve the TSP and the other to solve the Capacitated Vehicle Routing Problem (CVRP). Tests were conducted with benchmark instances from the literature, showing competitive results.

A Constraint-Based Local Search for Offline and Online General Vehicle Routing

2017 ◽  
Vol 26 (02) ◽  
pp. 1750004
Author(s):  
Quang Dung Pham ◽  
Kim Thu Le ◽  
Hoang Thanh Nguyen ◽  
Van Dinh Pham ◽  
Quoc Trung Bui
Keyword(s):  
Local Search ◽  
Vehicle Routing ◽  
Optimization Problems ◽  
Vehicle Routing Problems ◽  
School Bus ◽  
Routing Problems ◽  
Routing Problem ◽  
Combinatorial Optimization Problems ◽  
Neighborhood Structures ◽  
Covering Tour Problem

Vehicle routing is a class of combinatorial optimization problems arising in the industry of transportation and logistics. The goal of these problems is to compute an optimal route plan for a set of vehicles for serving transport requests of customers. There are many variants of the vehicle routing problems: routing for delivering goods, routing for demand responsive transport (taxi, school bus, …). Each problem might have different constraints, objectives. In this paper, we introduce a Constraint-Based Local Search (CBLS) framework for general offline and online vehicle routing problems. We extend existing neighborhood structures in the literature by proposing new neighborhoods to facilitate the resolution of different class of vehicle routing problems in a unified platform. A novel feature of the framework is the available APIs for online vehicle routing problems where requests arrive online during the execution of the computed route plan. Experimental results on three vehicle routing problems (the min-max capacitated vehicle routing problem, the multi-vehicle covering tour problem, and the online people-andparcel share-a-ride taxis problem) show the modelling flexibility, genericity, extensibility and efficiency of the proposed framework.

scholarly journals Sensitive Ants in Solving the Generalized Vehicle Routing Problem

2011 ◽  
Vol 6 (4) ◽  
pp. 731 ◽  
Author(s):  
Camelia-M. Pintea ◽  
Camelia Chira ◽  
Dan Dumitrescu
Keyword(s):  
Combinatorial Optimization ◽  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Optimization Problems ◽  
Routing Problem ◽  
Combinatorial Optimization Problems ◽  
Potential Benefits ◽  
Ant Colony Systems ◽  
Pheromone Trail ◽  
Generalized Vehicle Routing Problem

The idea of sensitivity in ant colony systems has been exploited in hybrid ant-based models with promising results for many combinatorial optimization problems. Heterogeneity is induced in the ant population by endowing individual ants with a certain level of sensitivity to the pheromone trail. The variable pheromone sensitivity within the same population of ants can potentially intensify the search while in the same time inducing diversity for the exploration of the environment. The performance of sensitive ant models is investigated for solving the generalized vehicle routing problem. Numerical results and comparisons are discussed and analysed with a focus on emphasizing any particular aspects and potential benefits related to hybrid ant-based models.

scholarly journals A new efficient transformation of the generalized vehicle routing problem into the classical vehicle routing problem

2011 ◽  
Vol 21 (2) ◽  
pp. 187-198 ◽  
Author(s):  
Petrica Pop ◽  
Corina Pop-Sitar
Keyword(s):  
Combinatorial Optimization ◽  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Optimization Problems ◽  
Steiner Tree Problem ◽  
Great Effort ◽  
Routing Problem ◽  
Combinatorial Optimization Problems ◽  
Generalized Traveling Salesman Problem ◽  
Generalized Vehicle Routing Problem

Classical combinatorial optimization problems can be generalized in a natural way by considering a related problem relative to a given partition of the nodes of the graph into node sets. In the literature one can find generalized problems such as: generalized minimum spanning tree, generalized traveling salesman problem, generalized Steiner tree problem, generalized vehicle routing problem, etc. These generalized problems typically belong to the class of NP-complete problems; they are harder than the classical ones, and nowadays are intensively studied due to their interesting properties and applications in the real world. Because of the complexity of finding the optimal or near-optimal solution in case of the generalized combinatorial optimization problems, great effort has been made, by many researchers, to develop efficient ways of their transformation into classical corresponding variants. We present in this paper an efficient way of transforming the generalized vehicle routing problem into the vehicle routing problem, and a new integer programming formulation of the problem.

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