Vehicle Routing Problems are optimization problems centered around determining optimal travel routes for a fleet of vehicles to visit a set of nodes. Optimality is evaluated with regard to some desired quality of the solution, such as time-minimizing or cost-minimizing. There are many established solution methods which makes it meaningful to compare their performance. This thesis aims to investigate how the performances of various solution methods is affected by varying certain problem parameters. Problem characteristics such as the number of customers, vehicle capacity, and customer demand are investigated. The aim was approached by dividing the problem into two subproblems: distributing the nodes into suitable clusters, and finding the shortest route within each cluster. Results were produced by solving simulated sets of customers for different parameter values with different clustering methods, namely sweep, k-means and hierarchical clustering. Although the model required simplifications to facilitate the implementation, theresults provided some significant findings. The thesis concludes that for large vehicle capacity in relation to demand, sweep clustering is the preferred method. Whereas for smaller vehicles, the other two methods perform better.

The vehicle routing problem (VRP) determines preferred vehicle routes to visit multiple customer locations from a depot location based on a defined objective function. The VRP is an NP-hard network optimization problem that is challenging to solve to optimality. Over the past 60 years, multitudes of heuristics and metaheuristics have been developed in order to minimize the computational burden of solving the VRP. In order to compare the performance of VRP heuristics, researchers have developed bench-marking datasets. These datasets, however, lack properties found in industry datasets. In this dissertation, we explore how properties of industry datasets influence VRP heuristics and objective functions. In Chapter 2, we quantify and compare features of bench-marking and industry datasets. In order to determine if these features influence heuristic performance, we conduct extensive computational runs on three heuristics, Tabu Search, Genetic Algorithm, and Clarke-Wright Savings Procedure, on standard and industry datasets. In Chapter 3, we derive worst-case analysis on how VRP objective functions and metrics relate to one another. These bounds depend on properties of customer locations. These bounds illustrate how customer locations can influence how different routes behave for different routing metrics. Finally, in Chapter 4, we improve two VRP heuristics, Clarke-Wright Saving Procedure and Hybrid Genetic Search Algorithm, by developing new enhancements to the algorithms. These enhancements rely on certain properties of the datasets in order to perform well. Thus, these heuristics perform better on specific VRP dataset types. / Doctor of Philosophy / The vehicle routing problem (VRP) creates vehicle routes that have the shortest travel distance. The routes determine how vehicles should visit multipl customer locations, to deliver or pickup goods, and return to a depot location. While explaining what the VRP entails is simple, the VRP is actually very difficult for even the most sophisticated algorithms on the best computers to solve. Over the past 60 years, many algorithms have been developed in order to more easily and quickly solve the VRP. In order to compare the performance of VRP algorithms, researchers have developed bench-marking datasets. However, these datasets lack properties of datasets found in industry. In this dissertation, we look to connect the disconnect between industry and bench-marking datasets by 1) comparing feature differences between these two types of datasets, 2) determining if differences in datasets imply differences in algorithm performance, 3) proving how problem differences influence VRP routes, and 4) enhancing existing VRP algorithms to perform better on specific VRP dataset types.

In this dissertation, the vehicle routing problem and one of its variants, the vehicle routing problem with simultaneous pick up and deliveries (VRPSPD) are studied. The traditional vehicle routing problem (VRP) consists of constructing minimum cost routes for the vehicles to follow so that the set of customers are visited only once. A lot of effort has been devoted to research on developing fast and effective solution methods for many different versions of this problem by different majors of engineering profession. Thus, a structuring effort is needed to organize and document the vast literature so far has accumulated in this field. Over its lifespan the VRP literature has become quite disjointed and disparate. Keeping track of its development has become difficult because its subject matter transcends several academic disciplines and professions that range from algorithm design to traffic management. Consequently, this dissertation begins with defining VRP's domain in its entirety, accomplishes an allencompassing taxonomy for the VRP literature, and delineates all of VRP's facets in a parsimonious and discriminating manner. Sample articles chosen for their disparity are classified to illustrate the descriptive power and parsimony of the taxonomy. Next, a more detailed version of the original problem, the VRPSPD is examined and a more abstract taxonomy is proposed. Additionally, two other existing classification methodologies are used to distinguish all published VRPSPD papers on their respective research strategies and solution methods. By using well-organized methods this study provides a solid multidimensional identification of all VRPSPD studies? attributes thus synthesizing knowledge in the filed. Finally, a hybrid metaheuristic solution algorithm for the VRPSPD problem is presented. To solve this NP-hard vehicle routing problem a GRASP initiated hybrid genetic algorithm is developed. The algorithm is tested on two sets of benchmark problems from the literature with respect to computational efficiency and solution quality. The effect of starting with a better initial population for the genetic algorithm is further investigated by comparing the current results with previously generated ones. The experimental results indicate that the proposed algorithm produces relatively good quality solutions and a better initial population yields a reduction in processing cycles.

In this dissertation, two main topics are explored, the vehicle routing problem (VRP) and model reference adaptive control (MRAC) for unknown nonlinear systems. The VRP and its extension, the split delivery VRP (SVRP), are analyzed to determine the effects of using two different objective functions, the total cost objective, and the last delivery objective. A worst-case analysis suggests that using the SVRP can improve total costs by as much as a factor of 2 and the last delivery by a factor that scales with the number of vehicles over the classical VRP. To test the theoretical worst-cases against the solutions of benchmark datasets, a heuristic is developed based on embedding a random variable neighborhood search within an iterative local search heuristic. Results suggest that the split deliveries do in fact improve total cost and last delivery times over the classical formulation. The SVRP has been developed classically for use with vehicles such as trucks which have large payload capacities and typically long ranges for deliveries, but are limited to traversing on roads. Unmanned aerial vehicles (UAVs) are useful for their high maneuverability, but suffer from limited capacity for payloads and short ranges. The classical SVRP formulation is extended to one more suitable for UAVs by accounting for limited range, limited payloads, and the ability to swap batteries at known locations. Instead of Euclidean distances, path plans which are adjusted for a known, constant wind underlie the cost matrix of the optimization problem. The effects of payload on the vehicle's range are developed using propeller momentum theory, and simulations verify that the proposed approach could be used in a realistic scenario. Two novel MRAC laws are then developed. The first, MRAC laws for prescribed performance, exploits barrier Lyapunov functions and a 2-Layer approach to guarantee user-defined performance. This control law allows unknown nonlinear systems to verify a user-defined rate of convergence of the tracking error while verifying apriori control and tracking error constraints. Numerical simulations are performed on the roll dynamics of a delta-wing aircraft. The second novel MRAC law is MRAC for switched dynamical systems which is proven in two different mathematical frameworks. Applying the Caratheodory framework, it is proven that if the switching signal has an arbitrarily small, but non-zero, dwell-time, then solutions of both the trajectory tracking error's and the adaptive gains' dynamics exist, are unique, and are defined almost everywhere, and the trajectory tracking error converges asymptotically to zero. Employing the Filippov framework, it is proven that if the switching signal is Lebesgue integrable and has countably many points of discontinuity, then maximal solutions of both the trajectory tracking error and the adaptive gains dynamics exist and are defined almost everywhere, and the trajectory tracking error converges to zero asymptotically. The proposed MRAC law is experimentally verified in the case where a UAV with tilting propellers is tasked with mounting an unknown camera onto a wall. The previous results are then combined into a novel application in construction. A method for using a UAV to measure autonomously the moisture of an exterior precast concrete envelope is developed which can provide data feedback through contact-based measurements to improve safety and real-time data acquisition through the integration with the Building Information Model (BIM). To plan the path of the vehicle, the path planning and SVRP for UAV approaches developed in previous chapters are utilized. To enable the UAS to contact surfaces, a switched MRAC law is employed to control the vehicle throughout and guarantee successful measurements. A full physics-based simulation environment is developed, and the proposed framework is used to simulate taking multiple measurements. / Doctor of Philosophy / The main goal of this dissertation is to provide an implementable approach to the routing and control problem for unmanned aerial vehicles (UAVs) tasked with delivering payloads or taking images or videos of known locations. To plan routes for the fleet of vehicles, a split vehicle routing (SVRP) approach is utilized. UAVs are useful for their high maneuverability, but suffer from limited capacity for payloads and short ranges. Before extending the SVRP to a formulation more suitable for UAVs, we study the effects of using two different objective functions on the solutions to the optimization problem through a worst-case analysis. Namely, we study the minimum total cost function and the minimum last delivery function and their effects on both the classical vehicle routing problem (VRP), where only one vehicle can visit each customer, and the SVRP, where multiple vehicles can visit each customer. A custom heuristic is developed to solve several benchmark instances, and the results suggest that using the SVRP can save in total cost and last delivery over the VRP when using the same objective functions. The classical SVRP formulation is then extended to one more suitable for UAVs by accounting for limited range, limited payloads, and the ability to swap batteries at known locations. Instead of using straight line approaches to traversing between locations, a path planning approach is utilized and wind is accounted for. The effects of payload on the vehicle's range are also considered, and simulations verify that the proposed approach could be used in a realistic scenario. After developing a routing approach for UAVs, the control problem is considered. The first control approach developed is for unknown nonlinear systems which necessitate control and tracking error constraints that can be set before the start of the mission. This result is achieved using a novel model reference adaptive control (MRAC) approach. In addition to verifying the constraints, a drawback of classical MRAC approaches, the poor performance in the transient stages, is addressed by providing the ability to guarantee a user-defined rate of convergence of the system. Numerical simulations are performed on the roll dynamics of a delta-wing aircraft. A second MRAC approach is then developed for the cases in which the UAVs may be tasked with installing a payload at the customer location. An approach is used where the vehicles are considered to have different flight states, one where the vehicle is in free flight, and one where the vehicle contacts the wall. These types of systems are denoted as switched dynamical systems, and an adaptive control law is developed for unknown nonlinear switched plants that must follow the trajectory of user-defined linear switched reference models. The proposed MRAC law is experimentally verified in the case where a UAV with tilting propellers is tasked with mounting an unknown camera onto a wall. Finally, we seek to combine the new routing and control approach into an application to improve safety within a construction site. A method for using a UAV to measure autonomously the moisture of an exterior precast concrete envelope is developed which can provide data feedback through contact-based measurements to improve safety and real-time data acquisition through the integration with the Building Information Model (BIM). To plan the path of the vehicle, the path planning and SVRP for UAV approaches developed in previous chapters are utilized. To enable the UAS to contact surfaces, a switched MRAC law is employed to control the vehicle throughout and guarantee successful measurements. A full physics-based simulation environment is developed, and the proposed framework is used to simulate taking multiple measurements.

[pt] O problema de roteamento de veículos escolares, do inglês School Bus Routing Problem (SBRP), trata de planejar as rotas de uma frota de veículos para locomover os alunos dos pontos de embarque até suas respectivas escolas. O SBRP é um caso especial do problema de roteamento de veículos, do inglês Vehicle Routing Problem (VRP) e é conhecido por ser um problema NP-difícil. A maior parte da literatura referente ao SBRP se concentra, principalmente, em modelos matemáticos para resolver o problema de roteamento aplicando restrições da vida real. Já em relação à geocodificação dos endereços das escolas e alunos, bem como a busca de distâncias e tempos de deslocamentos reais, estas também são pontos de vital importância, visto que as distâncias reais se diferem da euclidiana e geodésica principalmente em áreas rurais, região de estudo deste trabalho. Neste contexto, uma metodologia é proposta para o problema, junto com um protótipo para automatizar os procedimentos necessários para à obtenção de informações, cuja a aplicação, a partir de um cenário real no contexto brasileiro, é apresentada e dividida em oito fases: definir abrangência, geocodificar o endereço de escolas, alunos e pontos de embarque, definir as características, calcular a distância e o tempo de percurso, montar o banco de dados georreferenciado e de veículos, aplicar uma ferramenta para a obtenção das rotas, geoespacilizar as rotas e elaborar diagnóstico. A proposta é testada aplicando uma ferramenta para a obtenção das rotas que utiliza a meta-heurística Adaptative Large Neighborhood Search (ALNS) para resolver instâncias do VRP. Desta forma, uma das contribuições do estudo consiste no georreferenciamento das unidades escolares estaduais, estando as informações presentes na plataforma do Google Maps para visualização do público. No estudo são localizados e roteados 150 alunos de 7 unidades escolares da cidade de Nova Friburgo. O resultado apresenta valores consistentes e satisfatórios, demonstrando economia média de 41,62 por cento nos custos praticados nas rotas. / [en] The School Bus Routing Problem (SBRP) deals with planning the routes of a fleet of vehicles to move the students from boarding points to their respective schools. The SBRP is a special case of Vehicle Routing Problem (VRP) and is known to be an NP-hard problem. Most of the SBRP literature focuses, mainly, on mathematical models to solve the routing problem by applying real-life restrictions. Regarding the geocoding of the addresses of schools and students, as well as the search for distances and times of real displacements, are also points of vital importance, since the actual distances differ from the euclidean and geodesic ones mainly in rural areas, study region this work. In this context, a methodology is proposed for the problem, along with a prototype to automate the procedures required to obtain information, whose application, based on a real scenario in the Brazilian context is presented, divided into eight phases: to define scope, to geocode the address of schools, student and boarding points, to define the characteristics, to calculate the distance and travel time, to set the georeferenced database and vehicles, to apply a tool to obtain the routes, to geospatialize the routes and elaborate diagnosis. The proposal is tested by applying a tool to obtain routes using the Adaptive Large Neighborhood Search (ALNS) meta-heuristic to solve VRP instances. Thus, one of the contributions of the study consists in the georeferencing of the state school units, with the information present in the Google Maps platform for public viewing. In the study, 150 students from 7 school units in the city of Nova Friburgo were located. The result presents consistent and satisfactory values, demonstrating savings of 41.62 percent in the costs practiced on th routes.

Die zweiphasige Stichprobe zur Stratifizierung ist ein effizientes Inventurverfahren, das seine Praxistauglichkeit in verschiedenen Waldinventuren unter Beweis stellen konnte. Dennoch sind weitere Effizienzsteigerungen wünschenswert. In der vorliegenden Arbeit werden verschiedene Ansätze die Effektivität dieses Verfahrens zu steigern separat vorgestellt, in Fallstudien mit Daten der Niedersächsischen Betriebsinventur getestet und diskutiert. Der erste Ansatz (Kapitel 2) beschäftigt sich mit der Anwendung der zweiphasigen Stichprobe zur Stratifizierung in Wiederholungsinventuren. In einem Zusammengesetzten Schätzer werden Daten eines aktuellen mit Simulationsergebnissen des vorhergehenden Inventurdurchgangs kombiniert. Dabei kann der Stichprobenumfang der aktuellen Inventur verringert werden, während die Daten aller Inventurpunkte des vorherigen Durchgangs für Simulationen genutzt werden. Zwar kann ein solcher Schätzer konstruiert werden, jedoch lässt die Fallstudie darauf schließen, dass keine, oder zumindest keine ausreichende, Effizienzsteigerung erzielt werden kann. Erklärt werden kann dies durch die großen Unterschiede zwischen den aktuellen Inventurergebnissen aus den reduzierten Inventuren und den prognostizierten Volumina aus den Simulationen. Eine Erhöhung der Effizienz dieses Verfahrens könnte nur durch Weiterentwicklungen der Waldwachstumsmodelle möglich werden. In Wiederholungsinventuren kann jedoch eine höhere Effizienzsteigerung mit einem dreiphasigen Verfahren erreicht werden, das die zweiphasige Stichprobe mit der zwei\-phasigen Regressionsstichprobe kombiniert (Kapitel 3). Mittelwert- und Varianzschätzer, die auf dem sogenannten infinite population approach in der ersten Phase beruhen, werden präsentiert. Genutzt werden dabei die Korrelationen zwischen den aktuellen Inventurergebnissen und den Wachstumssimulationen auf der Basis des vorherigen Inventurdurchgangs. Statt der Simulationsergebnisse können auch einfach die Ergebnisse des vorherigen Inventurdurchgangs zur Berechnung der Korrelationen genutzt werden. Allerdings führt die Nutzung der Simulationsergebnisse als Regressor in den meisten Fällen zu besseren Ergebnissen. Bei verringertem Stichprobenumfang der Folgeinventur und damit einhergehendem Präzisionsverlust, ist die Effizienz des dreiphasigen Verfahrens höher als die des klassischen zweiphasigen Verfahrens. Die Nutzung der Vorinventur in Form eines stratenweisen Regressionsschätzers hat sich damit als erfolgreich und gegenüber dem zusammengesetzten Schätzer als deutlich überlegen gezeigt. Als weiterer Ansatz wird die Erweiterung der zweisphasigen Stichprobe zur Stratifizierung um eine geclusterte Unterstichprobe zu einem dreiphasigen Design vorgestellt (Kapitel 4). Sowohl für den Ratio-to-Size- als auch für den unverzerrten Ansatz werden entsprechende Mittelwert- und Varianzschätzer präsentiert. Verglichen mit dem zweiphasigen Verfahren, führt dieses dreiphasige Design in der Fallstudie zu keiner Effizienzsteigerung. Gründe hierfür können in der vergleichsweise kleinen Größe der Forstämter und der hohen Stichprobendichte der Niedersächsischen Betriebsinventur gesehen werden. Sinnvolle Anwendungen dieses Verfahrens sind aber möglicherweise unter anderen Erschließungsbedingungen in Großgebieten denkbar. In einer weiteren Fallstudie wird versucht existierende Probepunkte in Clustern von homogener Größe zusammenzufassen (Kapitel 5). Eine solche Zusammenfassung soll der Optimierung der Wegzeiten bei der Aufnahme von Inventurpunkten dienen. Dazu werden sieben verschiedene Methoden getestet und deren Ergebnisse miteinander verglichen. Durch einen Vergleich mit optimierten Richtwert-Lösungen wird zudem die Qualität dieser Lösungen evaluiert. Es zeigt sich, dass drei Algorithmen des Vehicle Routing Problems gut dazu geeignet sind, Cluster von homogener Größe zu erstellen. Nicht empfohlen werden kann dagegen die Verwendung von drei anderen Cluster-Algorithmen, sowie die Nutzung von Bewirtschaftungseinheiten als Cluster, da diese Methoden zu Clustern von sehr heterogener Größe führen.

Optimization of relief networks in humanitarian logistics often exemplifies the need for solutions that are feasible given a hard constraint on time. For instance, the distribution of medical countermeasures immediately following a biological disaster event must be completed within a short time-frame. When these supplies are not distributed within the maximum time allowed, the severity of the disaster is quickly exacerbated. Therefore emergency response plans that fail to facilitate the transportation of these supplies in the time allowed are simply not acceptable. As a result, all optimization solutions that fail to satisfy this criterion would be deemed infeasible. This creates a conflict with the priority optimization objective in most variants of the generic vehicle routing problem (VRP). Instead of efficiently maximizing usage of vehicle resources available to construct a feasible solution, these variants ordinarily prioritize the construction of a minimum cost set of vehicle routes. Research presented in this dissertation focuses on the design and analysis of efficient computational methods for optimizing high-consequence variants of the VRP for relief networks. The conflict between prioritizing the minimization of the number of vehicles required or the minimization of total travel time is demonstrated. The optimization of the time and capacity constraints in the context of minimizing the required vehicles are independently examined. An efficient meta-heuristic algorithm based on a continuous spatial partitioning scheme is presented for constructing a minimized set of vehicle routes in practical instances of the VRP that include critically high-cost penalties. Multiple optimization priority strategies that extend this algorithm are examined and compared in a large-scale bio-emergency case study. The algorithms designed from this research are implemented and integrated into an existing computational framework that is currently used by public health officials. These computational tools enhance an emergency response planner's ability to derive a set of vehicle routes specifically optimized for the delivery of resources to dispensing facilities in the event of a bio-emergency.

Dedicating less transport resources by grouping goods to be shipped together, or pooling as we name it, has a very crucial role in saving costs in transport networks. Nonetheless, it is not so easy to estimate pooling among different groups of shipments or understand why these groups are poolable. The typical solution would be to consider all shipments of both groups as one and use some Vehicle Routing Problem (VRP) software to estimate costs of the new combined group. However, this brings with it some drawbacks, such as high computational costs and no pooling explainability. On this work we build a tool that estimates the different types of pooling using demand data. This solution includes mapping shipment data to a lower dimension, where each poolability trait corresponds to a latent dimension. We tested different dimensionality reduction techniques and found that the best performing are the autoencoder models based on neural networks. Nevertheless, comparing shipments on the latent space turns out to be more challenging than expected, because distances in these latent dimensions are sometimes uncorrelated to the distances in the real shipment features. Although this limits the use cases of this approach, we still manage to build the full poolability tool that incorporates the autoencoders and uses metrics we designed to measure each poolability trait. This tool is then compared to a VRP software and proves to have close accuracy, while being much faster and explainable. / Att optimera transportresurser genom att gruppera varor som ska skickas tillsammans, även kallat poolning, spelar en avgörande roll för att spara kostnader i transportnätverk. Trots detta är det inte så enkelt att uppskatta poolning mellan olika grupper av försändelser eller förstå varför dessa grupper kan poolas. Den vanliga lösningen skulle vara att betrakta alla försändelser från båda grupperna som en enda enhet och använda mjukvara för att lösa problemet med fordonsschemaläggning (Vehicle Routing Problem, VRP) för att uppskatta kostnaderna för den nya sammanslagna gruppen. Detta medför dock vissa nackdelar, såsom höga beräkningskostnader och bristande förklarbarhet när det kommer till poolning. I detta arbete bygger vi ett verktyg som med hjälp av efterfrågedata uppskattar olika typer av poolning. Lösningen innefattar kartläggning av försändelsedata till en lägre dimension där varje egenskap för poolbarhet motsvarar en dold dimension. Vi testade olika tekniker för att minska dimensionerna och fann att de bäst presterande är autoencoder-modeller baserade på neurala nätverk. Trots detta visade det sig vara mer utmanande än förväntat att jämföra försändelser i det dolda rummet eftersom avstånden i dessa dolda dimensioner ibland inte korrelerar med avstånden i de faktiska försändelseegenskaperna. Trots att detta begränsar användningsområdena för denna metod lyckades vi ändå bygga ett komplett verktyg för poolbarhet som inkluderar autoencoders och använder metriker som vi har utformat för att mäta varje egenskap för poolbarhet. Detta verktyg jämförs sedan med en VRP-mjukvara och visar sig ha liknande noggrannhet samtidigt som det är betydligt snabbare och mer förklarligt. / Dedicare meno risorse di trasporto raggruppando insieme le merci da spedire, o creando un pool come lo chiamiamo noi, svolge un ruolo cruciale nel risparmio dei costi nelle reti di trasporto. Tuttavia, non è facile stimare il grado di aggregazione tra diversi gruppi di spedizioni o comprendere perché tali gruppi siano aggregabili. La soluzione tipica consisterebbe nel considerare tutte le spedizioni di entrambi i gruppi come una sola entità e utilizzare un software di Problema di Routing dei Veicoli (VRP) per stimare i costi del nuovo gruppo combinato. Tuttavia, ciò comporta alcuni svantaggi, come elevati costi computazionali e la mancanza di spiegazioni riguardo all'aggregazione. In questo lavoro abbiamo sviluppato uno strumento che stima i diversi tipi di aggregabilità utilizzando i dati di domanda. Questa soluzione prevede la mappatura dei dati delle spedizioni in una dimensione inferiore, in cui ciascuna caratteristica di aggregabilità corrisponde a una dimensione. Abbiamo testato diverse tecniche di riduzione dimensionale e abbiamo constatato che i modelli autoencoder basati su reti neurali sono i più efficaci. Tuttavia, confrontare le spedizioni nello spazio latente si è rivelato più complesso del previsto, poiché le distanze in queste dimensioni latenti talvolta non sono correlate alle distanze nelle caratteristiche reali delle spedizioni. Sebbene ciò limiti le applicazioni di questo approccio, siamo comunque riusciti a sviluppare uno strumento completo per l'aggregabilità che incorpora gli autoencoder e utilizza metriche da noi progettate per misurare ciascuna caratteristica di aggregabilità. Successivamente, abbiamo confrontato questo strumento con un software VRP e dimostrato che presenta un'accuratezza simile, pur essendo più veloce e fornendo spiegazioni chiare.

This thesis deals with real logistic problem of the Heineken CZ Company. The company sets down an itinerary for each vehicle to distribute its goods to particular customers on daily basis. These itineraries are created manually, only with the skill of experienced driver. The goal of this thesis is to find a solution with an algorithm, which will be able to set optimal itineraries of all vehicles, so the total distance and therefore operating costs are minimized, with only the knowledge of distances between each two nodes.

Split delivery vehicle rating problem is one of the most studied combinatorial optimization problems in operations research. According to the mathematical difficultness, there should be many problems to find the optimal solution. Therefore, there are many exact algorithms and heuristics, which tries to find the best solution in the short period of time. The theoretical part of this thesis describes the basic facts of the split delivery vehicle routing problem and its heuristics. The practical part focuses on the practical usage of the split delivery vehicle routing problem. The main goals of this thesis are the practical usage of this vehicle routing problem and assistance in strategic decision establishing of the secondary store.