Joint Vehicle and Crew Routing and Scheduling

2020 ◽  
Vol 54 (2) ◽  
pp. 488-511
Author(s):  
Edward Lam ◽  
Pascal Van Hentenryck ◽  
Phil Kilby
Keyword(s):  
Vehicle Routing ◽  
Mixed Integer ◽  
Neighborhood Search ◽  
Routing Problems ◽  
Routing Problem ◽  
Military Logistics ◽  
Routing And Scheduling ◽  
Constraint Program ◽  
Mip Model ◽  
Optimization Constraint

Traditional vehicle routing problems implicitly assume that only one crew operates a vehicle for the entirety of its journey. However, this assumption is violated in many applications arising in humanitarian and military logistics. This paper considers a joint vehicle and crew routing and scheduling problem in which crews are able to interchange vehicles, resulting in space and time interdependencies between vehicle routes and crew routes. The problem is formulated as a mixed integer programming (MIP) model and a constraint programming (CP) model that overlay crew routing constraints over a standard vehicle routing problem. The constraint program uses a novel optimization constraint to detect infeasibility and to bound crew objectives. This paper also explores methods using large neighborhood search over the MIP and CP models. Experimental results indicate that modeling the vehicle and crew routing problems jointly and supporting vehicle interchanges for crews may bring significant benefits in cost reduction compared with a method that sequentializes these decisions.

Variable Fixing for Two-Arc Sequences in Branch-Price-and-Cut Algorithms on Path-Based Models

2020 ◽  
Vol 54 (5) ◽  
pp. 1170-1188 ◽  
Author(s):  
Guy Desaulniers ◽  
Timo Gschwind ◽  
Stefan Irnich
Keyword(s):  
Vehicle Routing ◽  
Time Windows ◽  
Solution Process ◽  
Mixed Integer ◽  
Linear Programs ◽  
Vehicle Routing Problems ◽  
Routing Problems ◽  
Routing Problem ◽  
Benchmark Instances ◽  
Variable Fixing

Variable fixing by reduced costs is a popular technique for accelerating the solution process of mixed-integer linear programs. For vehicle-routing problems solved by branch-price-and-cut algorithms, it is possible to fix to zero the variables associated with all routes containing at least one arc from a subset of arcs determined according to the dual solution of a linear relaxation. This is equivalent to removing these arcs from the network used to generate the routes. In this paper, we extend this technique to routes containing sequences of two arcs. Such sequences or their arcs cannot be removed directly from the network because routes traversing only one arc of a sequence might still be allowed. For some of the most common vehicle-routing problems, we show how this issue can be overcome by modifying the route-generation labeling algorithm in order to remove indirectly these sequences from the network. The proposed acceleration strategy is tested on benchmark instances of the vehicle-routing problem with time windows (VRPTW) and four variants of the electric VRPTW. The computational results show that it yields a significant speedup, especially for the most difficult instances.

scholarly journals Collaborative Vehicle Routing Problem in the Urban Ring Logistics Network under the COVID-19 Epidemic

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Wenjia Zheng ◽  
Zhongyu Wang ◽  
Liucheng Sun
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Mixed Integer ◽  
Neighborhood Search ◽  
Multicommodity Flow ◽  
Integer Programming Problem ◽  
Distribution Centers ◽  
Routing Problem ◽  
Logistics Network ◽  
The City

This paper explored the problem of collaborative vehicle routing in the urban ring logistics network (Co-VRP-URLN) during the COVID-19 epidemic. According to the characteristics of urban distribution and the restriction of traffic all over China during this period, this study mainly considers a common distribution mode of order exchange through the outer ring of the city and then solves the vehicle routing problem of distribution, which belongs to a special multidepot vehicle routing problem with time windows. According to the definition of the problem, the corresponding mixed-integer programming problem of multicommodity flow is established, and the variable neighborhood search algorithm is designed in detail to solve it. The effectiveness of the algorithm is verified by a standard example, and the benefits of joint distribution are revealed through the improved standard example. At last, the influence of different distribution centers is compared. The results show that this model can significantly improve the distribution efficiency within the city under the restriction of traffic.

scholarly journals Spatiotemporal-Dependent Vehicle Routing Problem Considering Carbon Emissions

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Ziqi Liu ◽  
Yeping Chen ◽  
Jian Li ◽  
Dongqing Zhang
Keyword(s):  
Vehicle Routing ◽  
Carbon Emissions ◽  
Vehicle Routing Problem ◽  
Programming Model ◽  
Travel Speed ◽  
Mixed Integer ◽  
Neighborhood Search ◽  
Adaptive Genetic Algorithm ◽  
Local Optimum ◽  
Routing Problem

Aiming to improve the timeliness of logistics distribution and render the optimized route scheme effective under the real traffic network, we study the green vehicle routing problem with dynamic travel speed from both dimensions of time and space. A discrete formulation is proposed to calculate the travel time based on periods and arcs, which allows a vehicle to travel across an arc in multiple periods. Then, we establish a mixed-integer nonlinear programming model with minimum distribution costs including transportation costs, carbon emissions costs, and penalty costs on earliness and tardiness. A hybrid adaptive genetic algorithm with elite neighborhood search is developed to solve the problem. In the algorithm, a neighborhood search operator is employed to optimize elite individuals so that the algorithm can stimulate the intensification and avoid falling into a local optimum. Experimental instances are constructed based on benchmark instances of vehicle routing problem. The numerical results indicate that the proposed algorithm is rather effective in global convergence. Compared with the routing schemes in which travel speed merely varies with time periods or locations, the vehicle route optimized on spatiotemporal-varying speed outperforms them in terms of carbon emissions and timeliness. The research can provide a scientific and reasonable method for logistics enterprises to plan the vehicle schedule focusing on spatiotemporal-dependent speed of the road network.

scholarly journals Vehicle Routing Problem with Transshipment: Mathematical Model and Algorithm

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Thanapat Leelertkij ◽  
Parthana Parthanadee ◽  
Jirachai Buddhakulsomsiri
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Programming Model ◽  
Mixed Integer ◽  
Neighborhood Search ◽  
Retail Stores ◽  
Routing Problem ◽  
Hybrid Heuristics ◽  
New Variant ◽  
Problem Instances

This paper presents a new variant of vehicle routing problem with paired transshipment demands (VRPT) between retail stores (customers) in addition to the regular demand from depot to retail stores. The problem originates in a real distribution network of high-end retail department stores in Thailand. Transshipment demands arise for one-order-per-season expensive items, whose inventories at the depot may become shortage after the middle of a season, while they remain available at some retail stores. A transshipment demand is a request for items that need to be picked up from a specific store that has the items and delivered to the store that requests the items. The objective of solving the VRPT is to find delivery routes that can satisfy both regular demands and transshipment demands in the same routes without incurring too much additional transportation distance. A mixed integer linear programming model is formulated to represent the VRPT. Six small problem instances are used to test the model. A hybrid threshold accepting and neighborhood search heuristic is also developed to solve large problem instances of VRPT. The heuristic is further extended to include a forbidden list of transshipment demands that should not be included in the same routes. The purpose is to prevent incurring too much additional distance from satisfying transshipment demands. With the forbidden list, the problem becomes vehicle routing problem with optional transshipment demands (VRPOT). Computational testing shows promising results that indicate effectiveness of the proposed hybrid heuristics as well as the forbidden list.

scholarly journals An Enhanced Approach for the Multiple Vehicle Routing Problem with Heterogeneous Vehicles and a Soft Time Window

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 650 ◽  
Author(s):  
He-Yau Kang ◽  
Amy Lee
Keyword(s):  
Computer Science ◽  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Time Window ◽  
Optimal Solution ◽  
Mixed Integer ◽  
Computational Time ◽  
Routing Problem ◽  
Mip Model ◽  
Science Theory

The vehicle routing problem (VRP) is a challenging combinatorial optimization problem. This research focuses on the problem under which a manufacturer needs to outsource materials from other suppliers and to ship the materials back to the company. Heterogeneous vehicles are available to ship the materials, and each vehicle has a limited loading capacity and a limited travelling distance. The purpose of this research is to study a multiple vehicle routing problem (MVRP) with soft time window and heterogeneous vehicles. Two models, using mixed integer programming (MIP) and genetic algorithm (GA), are developed to solve the problem. The MIP model is first constructed to minimize the total transportation cost, which includes the assignment cost, travelling cost, and the tardiness cost, for the manufacturer. The optimal solution can present multiple vehicle routing and the loading size of each vehicle in each period. The GA is next applied to solve the problem so that a near-optimal solution can be obtained when the problem is too difficult to be solved using the MIP. A case of a food manufacturing company is used to examine the practicality of the proposed MIP model and the GA model. The results show that the MIP model can obtain the optimal solution under a short computational time when the scale of the problem is small. When the problem becomes non-deterministic polynomial hard (NP-hard), the MIP model cannot find the optimal solution. On the other hand, the GA model can obtain a near-optimal solution within a reasonable amount of computational time. This paper is related to several important topics of the Symmetry journal in the areas of mathematics and computer science theory and methods. In the area of mathematics, the theories of linear and non-linear algebraic structures and information technology are adopted. In the area of computer science, theory and methods, and metaheuristics are applied.

scholarly journals Vehicle Routing and Scheduling Problem for a multi-period, multi-perishable product system with time window: A Case study

2017 ◽  
Vol 5 (2) ◽  
pp. 45 ◽  
Author(s):  
Alireza Rashidi Komijan ◽  
Danial Delavari
Keyword(s):  
Vehicle Routing ◽  
Time Window ◽  
Programming Model ◽  
Transportation Costs ◽  
Mixed Integer ◽  
Pickup And Delivery ◽  
Routing Problem ◽  
Routing And Scheduling ◽  
Perishable Product ◽  
Proposed Model

<div data-canvas-width="542.172"><p>The well-known Vehicle Routing Problem (VRP) is to find proper sequence of routes in order to minimize transportation costs. In this paper, a mixed-integer programming model is presented for a food distributer company and the model outputs are to determine the optimal routes and amount of pickup and delivery. In the objective function, the costs of transportation, holding, tardiness and earliness are considered simultaneously. The proposed model with respect to real conditions is multi-period and has two different time periods: one for dispatching vehicles to customers and suppliers and the other for receiving  customers’ orders. Time window and split pickup and delivery are considered for perishable products. The proposed model is  nonlinear and will be linearized using exact techniques. At the end, model is solved using GAMS and the sensitivity analysis  is performed. The results indicate that the trend of changes in holding and transportation costs in compared to tardiness and  earliness costs are closed together and are not so sensitive to demand changes.</p></div>

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.

Intraroute Resource Replenishment with Mobile Depots

2021 ◽  
Author(s):  
Julian Hof ◽  
Michael Schneider
Keyword(s):  
Vehicle Routing ◽  
Distribution Systems ◽  
Time Windows ◽  
Computation Time ◽  
Integer Program ◽  
Mixed Integer ◽  
Neighborhood Search ◽  
Mixed Integer Program ◽  
Routing Problem ◽  
Commercial Solver

In numerous practical vehicle-routing applications, larger vehicles are employed as mobile depots to support a fleet of smaller vehicles that perform certain tasks. The mobile depots offer the possibility of keeping the task vehicles operational by supplying them en route with certain resources. For example, in two-echelon distribution systems, small task vehicles are used to navigate narrow streets and to deliver/collect goods or to collect waste, and larger vehicles serve as mobile depots to replenish the goods to be delivered or to receive collected goods or waste at the outskirts of the urban area. Accessibility constraints may also be imposed by regulations on emissions, which make some areas only accessible for environmentally friendly vehicles such as, for example, battery-powered electric vehicles. Especially if the respective refueling infrastructure is sparse, mobile refueling stations seem to be an interesting alternative. In this paper, we introduce the vehicle-routing problem with time windows and mobile depots (VRPTWMD) to capture the routing decisions of the described applications in a generalized fashion. The VRPTWMD is characterized by fleets of task vehicles (TVs) and support vehicles (SVs). The SVs may serve as mobile depots to restore either the load or the fuel capacity of the TVs that are used to fulfill the customer requests. We present a mixed-integer program for the VRPTWMD with which small instances can be solved using a commercial solver. Moreover, we develop a high-quality hybrid heuristic composed of an adaptive large neighborhood search and a path relinking approach to provide solutions on larger problem instances. We use a newly generated set of large VRPTWMD instances to analyze the effect of different problem characteristics on the structure of the identified solutions. In addition, our approach shows very convincing performance on benchmark instances for the related two-echelon multiple-trip VRP with satellite synchronization, which can be viewed as a special case of the VRPTWMD. Our heuristic is able to significantly improve a large part of the previous best-known solutions while spending notably less computation time than the comparison algorithm from the literature.

scholarly journals A Two-Echelon Electric Vehicle Routing Problem with Time Windows and Battery Swapping Stations

2021 ◽  
Vol 11 (22) ◽  
pp. 10779
Author(s):  
Dan Wang ◽  
Hong Zhou
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
High Efficiency ◽  
Programming Model ◽  
Time Windows ◽  
Transportation Cost ◽  
Mixed Integer ◽  
Neighborhood Search ◽  
Fixed Cost ◽  
Routing Problem

Driven by the new laws and regulations concerning the emission of greenhouse gases, it is becoming more and more popular for enterprises to adopt cleaner energy. This research proposes a novel two-echelon vehicle routing problem consisting of mixed vehicles considering battery swapping stations, which includes one depot, multiple satellites with unilateral time windows, and customers with given demands. The fossil fuel-based internal combustion vehicles are employed in the first echelon, while the electric vehicles are used in the second echelon. A mixed integer programming model for this proposed problem is established in which the total cost, including transportation cost, handling cost, fixed cost of two kinds of vehicles, and recharging cost, is minimized. Moreover, based on the variable neighborhood search, a metaheuristic procedure is developed to solve the problem. To validate its effectiveness, extensive numerical experiments are conducted over the randomly generated instances of different sizes. The computational results show that the proposed metaheuristic can produce a good logistics scheme with high efficiency.

scholarly journals An adaptive large neighborhood search heuristic for multi-commodity two-echelon vehicle routing problem with satellite synchronization

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Shengyang Jia ◽  
Lei Deng ◽  
Quanwu Zhao ◽  
Yunkai Chen
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Mixed Integer ◽  
Neighborhood Search ◽  
Large Neighborhood Search ◽  
Adaptive Large Neighborhood Search ◽  
Routing Problem ◽  
Large Neighborhood ◽  
Multiple Depots ◽  
Synchronization Constraints

<p style='text-indent:20px;'>In considering route optimization from multiple distribution centers called depots via some intermediate facilities called satellites to final customers with multiple commodities request, we introduce the Multi-Commodity Two-Echelon Vehicle Routing Problem with Satellite Synchronization (MC-2E-VRPSS). The MC-2E-VRPSS involves the transportation from multiple depots to satellites on the first echelon and the deliveries from satellites to final customers on the second echelon. The MC-2E-VRPSS integrates satellite synchronization constraints and time window constraints for satellites on the two-echelon network and aims to determine cost-minimizing routes for the two echelons. The satellite synchronization constraints which trucks from the multiple depots to some satellites need to be coordinated guarantee the efficiency of the second echelon network. In this study, we develop a mixed-integer programming model for the MC-2E-VRPSS. For validating the model formulation, we conduct the computational experiments on a set of small-scale instances using GUROBI and an adaptive large neighborhood search (ALNS) heuristic which we develop for the problem. Furthermore, the computation experiments for evaluating the applicability of the ALNS heuristic compared with large neighborhood search (LNS) on a set of large-scale instances are also conducted, which proved the effectiveness of the ALNS.</p>

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