Multimodal container terminals are an important part of the logistics systems in international trade. Any improvement in the terminal efficiency is likely to reduce the costs of transporting goods, and to strengthen the trading position of the nation. During the import process, containers flow from ships to the storage yard for temporary storage and then are later moved to the hinterland by rail, or by road. The export process is the reverse of the import process. From the marshalling area, it is possible for a yard machine to carry an inbound container to the storage area and back with an inbound container in one round trip. This thesis investigates the inbound and outbound container process of multimodal container terminals in a multi-ship and multi-berth environment. The aim is to develop mathematical models and analytical tools for yard operation and planning. This study concerns the yardlayout, storage locations, operation strategies as well as the sequencing and scheduling of container process. Several models are developed for the scheduling of container process, taking account of planned and unplanned disruptions, and the intermediate buffer at the marshalling area. The problem is NP-hard and real-life problems often involve large number of containers. In addition, many schedules may not be feasible due to deadlock or violation of precedence-constraints. Good results were achieved on benchmark problems using the proposed innovative. In dealing with unplanned disruptions, reactive scheduling approach was found to give the results similar to as if the disruptions were planned in advance. Numerical investigations are also presented on various factors affecting the efficiency of seaport container terminals including the number of yard machines, and the number of quay crane. As with the various yard-layouts studied, it was found that containers are best stored in rows perpendicular to the quay-line with about 10 to 14 bays in each row. For a shorter ship service time, ideally the containers should be stored as close as possible to the ship. The best storage locations, however, are scarce resources and are not always available. Another model is developed for the best storage location as well as the best schedule for the container process. From an initial best schedule with predefined storage locations, the problem is solved by iterating through the refinement of storage scheme and re-scheduling. At a seaport terminal, ships are planned to arrive and leave within a scheduled time window. Nevertheless, a ship may arrive late due to poor weather conditions or disruptions at the previous port. Such delay may also affect its departure to the subsequent port. To minimise the impact of ship delays, port operators must consider alternate arrangements including re-assignment of berths, re-sequencing of ships and rescheduling of the container process. A ship delay model is developed and the problem is solved by combining branching and Tabu Search. The models developed in this thesis establish the relationship between significant factors and the options for increasing throughput by discovering the bottlenecks. The models are applicable as decision tools for operation planning, yard layout, and cost and benefit analysis for investment in infrastructures.

Dans le cadre de cette thèse, nous nous intéressons au problème du transport à la demande. Nous proposons des heuristiques pour résoudre ce problème de manière rapide et efficace. Dans cette thèse, nous traitons trois problèmes : le premier est le Dial-a-ride (DARP standard). Pour ce problème, nous proposons des heuristiques basées sur la technique d’insertion et une technique de propagation de contrainte. Nous proposons aussi la procédure SPLIT et des opérateurs classiques de recherche locale pour résoudre ce problème. Le second est le DARP multicritères pour laquelle nous proposons un schéma de type ELS. Le troisième est un problème de transport à la demande avec contraintes financières (DARPF), qui est une extension de DARP. Nous résolvons ce problème grâce à une heuristique d’insertion et une technique de propagation de contraintes. La fonction objectif détermine les caractéristiques des tournées. Des résultats expérimentaux montrent que nos (méta-) heuristiques donnent des résultats plus favorables aux clients (meilleure qualité de service) / As part of this thesis, we investigate the vehicle routing problem. We propose heuristics to solve this problem quickly and efficiently. In this thesis, we deal with three problems: the first is the Dial-a-ride problem. For this problem, we propose heuristics based on the technique of insertion and a constraint propagation technique. We propose also the procedure SPLIT and some operators of local research to solve this problem. The second is the multi-criteria DARP for which we propose an ELS framework. The third is a DARP problem with financial constraints (DARPF), which is an extension of DARP. We solve this problem thanks to insertion heuristics using a constraint propagation technique. The objective function determines the characteristics of the tour. Experimental results show that our (meta-) heuristics give results more favorable to customers (better quality of service)

A just-in-time supply pickup and delivery system (JSS) manages the logistic operations between a manufacturing plant and its suppliers by controlling the sequence, timing, and frequency of container pickups and parts deliveries, thereby coordinating internal conveyance, external conveyance, and the operation of cross-docking facilities. The system is important to just-in-time production lines that maintain small inventories. This research studies the logistics, supply chain, and production control of JSS. First, a new meta-heuristics approach (taboo search) is developed to solve a general frequency routing (GFR) problem that has been formulated in this dissertation with five types of constraints: flow, space, load, time, and heijunka. Also, a formulation for cross-dock routing (CDR) has been created and solved. Second, seven issues concerning the structure of JSS systems that employ the previously studied common frequency routing (CFR) problem (Chuah and Yingling, in press) are explored to understand their impacts on operational costs of the system. Finally, a discreteevent simulation model is developed to study JSS by looking at different types of variations in demand and studying their impacts on the stability of inventory levels in the system. The results show that GFR routes at high frequencies do not have common frequencies in the solution. There are some common frequencies at medium frequencies and none at low frequency, where effectively the problem is simply a vehicle routing problem (VRP) with time windows. CDR is an extension of VRP-type problems that can be solved quickly with meta-heuristic approaches. GFR, CDR, and CFR are practical routing strategies for JSS with taboo search or other types of meta-heuristics as solvers. By comparing GFR and CFR solutions to the same problems, it is shown that the impacts of CFR restrictions on cost are minimal and in many cases so small as to make simplier CFR routes desirable. The studies of JSS structural features on the operating costs of JSS systems under the assumption of CFR routes yielded interesting results. First, when suppliers are clustered, the routes become more efficient at mid-level, but not high or low, frequencies. Second, the cost increases with the number of suppliers. Third, negotiating broad time windows with suppliers is important for cost control in JSS systems. Fourth, an increase or decrease in production volumes uniformly shifts the solutions cost versus frequency curve. Fifth, increased vehicle capacity is important in reducing costs at low and medium frequencies but far less important at high frequencies. Lastly, load distributions among the suppliers are not important determinants of transportation costs as long as the average loads remain the same. Finally, a one-supplier, one-part-source simulation model shows that the systems inventory level tends to be sticky to the reordering level. JSS is very stable, but it requires reliable transportation to perform well. The impact to changes in kanban levels (e.g., as might occur between route planning intervals when production rates are adjusted) is relatively long term with dynamic after-effects on inventory levels that take a long time to dissapate. A gradual change in kanban levels may be introduced, prior to the changeover, to counter this effect.

There are many real world assignment, scheduling and planning tasks which can be classified as combinatorial optimisation problems (COPs). These are usually formulated as a mathematical problem of minimising or maximising some cost function subject to a number of constraints. Usually, such problems are NP hard, and thus, whilst it is possible to find exact solutions to specific problems, in general only approximate solutions can be found. There are many algorithms that have been proposed for finding approximate solutions to COPs, ranging from special purpose heuristics to general search meta-heuristics such as simulated annealing and tabu search. General meta-heuristic algorithms like simulated annealing have been applied to a wide range of problems. In most cases, the designer must choose an appropriate data structure and a set of local operators that define a search neighbourhood. The variability in representation techniques, and suitable neighbourhood transition operators, has meant that it is usually necessary to develop new code for each problem. Toolkits like the one developed by Ingber's Adaptive Simulated Annealing (Ingber 1993, 1996) have been applied to assist rapid prototyping of simulated annealing codes, however, these still require the development of new programs for each type of problem. There have been very few attempts to develop a general meta-heuristic solver, with the notable exception being Connolly's General Purpose Simulated Annealing (Connolly 1992). In this research, a general meta-heuristic based system is presented that is suitable for a wide range of COPs. The main goal of this work is to build an environment in which it is possible to specify a range of COPs using an algebraic formulation, and to produce a tailored solver automatically. This removes the need for the development of specific software, allowing very rapid prototyping. Similar techniques have been available for linear programming based solvers for some years in the form of the GAMS (General Algebraic Modelling System) (Brooke, Kendrick, Meeraus and Raman 1997) and AMPL (Fourer, Gay and Kernighan 1993) interfaces. The new system is based on a novel linked list data structure rather than the more conventional vector notation due to the natural mapping between COPS and lists. In addition, the modelling system is found to be very suitable for processing by meta-heuristic search algorithms as it allows the direct application of common local search operators. A general solver is built that is based on the linked list modelling system. This system is capable of using meta-heuristic search engines such as greedy search, tabu search and simulated annealing. A number of implementation issues such as generating initial solutions, choosing and invoking appropriate local search transition operators and producing suitable incremental cost expressions, are considered. As such, the system can been seen as a good test-bench for model prototypers and those who wish to test various meta-heuristic implementations in a standard way. However, it is not meant as a replacement or substitute for efficient special purpose search algorithms. The solver shows good performance on a wide range of problems, frequently reaching the optimal and best-known solutions. Where this is not the case, solutions within a few percent deviation are produced. Performance is dependent on the chosen transition operators and the frequency with which each is applied. To a lesser extent, the performance of this implementation is influenced by runtime parameters of the meta-heuristic search engine.

Thesis (MSc (Forest and Wood Science))--University of Stellenbosch, 2011. / ENGLISH ABSTRACT: The percentage yield of sawn timber recovered from logs has a large influence on the profitability of a sawmill. The positioning of the log as it is fed into the primary breakdown saw is one of the factors that impacts on the volume recovery percentage. The log’s position can be adjusted by changes in rotation, offset and skewness and depending on the ranges and increments used for these variables, the number of possible combinations can become substantial. In a sawmill the time available to assess possible log positions is limited and different strategies can be followed to arrive at an optimal or close‐to‐optimal positioning solution without an exhaustive evaluation of solutions. Meta‐heuristics are sometimes used to arrive at solutions for combinatorial optimisation problems in a limited time. The effectiveness of this approach on the optimisation of timber volume recovery based on log form is evaluated in this study using sawmill simulation data of sixty SA pine logs. A new meta‐heuristic, for convenience named the Tentacle algorithm, was developed specifically for the problem of log positioning optimisation. The results obtained with the Tentacle algorithm was compared with results from three existing meta‐heuristics i.e. the Simulated Annealing algorithm, the Population Based Incremental Learning algorithm and the Particle Swarm Optimisation algorithm, in terms of its efficiency and effectiveness in finding good log positioning solutions in a limited time. A fifth method, that of exhaustively searching smaller, high quality areas around the centered and “horns‐up” and “horns‐down” positions in the search space was compared to that of using the meta‐heuristic algorithms. In terms of volume recovery, the Tentacle algorithm performed, on average, the best of the four algorithms evaluated. However, exhaustive searches in the smaller, high quality areas in the search space, outperformed the algorithms. / AFRIKAANSE OPSOMMING: Die herwinningspersentasie van gesaagde planke uit saagblokke het ‘n groot invloed op die winsgewendheid van ‘n saagmeul. Die posisionering van die blok in die primêre saag is een van die faktore wat die herwinningspersentasie beïnvloed. Die blok se posisie kan verstel word deur veranderinge in rotasie, oplyning en skeefheid. Afhangend van die veld ‐en inkrementgrootte kan die hoeveelheid moontlike kombinasies beduidend wees. In ‘n tipiese saagmeul is die beskikbare tyd om moontlike posisies te evalueer beperk en verskeie strategieë kan gevolg word om optimale of nabyoptimale kombinasies te bereik sonder om alle moontlike kombinasies te evalueer. Meta‐heuristieke word soms gebruik om in ‘n beperkte tyd oplossings te vind vir kombinatoriese optimeringsprobleme. Die doeltreffendheid van hierdie metode by die optimering van herwinningspersentasie gebaseer op blokvorm is in hierdie studie ondersoek. Dit is met behulp van saagmeulsimulasiedata soos van sestig SA dennehoutblokke verkry, uitgevoer. ‘n Nuwe meta‐heuristiek, genaamd die Tentakelalgoritme, is tydens hierdie studie spesifiek vir die probleem van blokposisie‐optimering ontwikkel. Die resultate verkry met die Tentakelalgoritme is vergelyk met drie bestaande meta‐heuristieke, nl. die “Simulated Annealing”‐algoritme, die “Population Based Incremental Learning”‐algoritme en die “Particle Swarm Optimisation”‐algoritme in terme van doeltreffendheid om goeie blokposisies in ‘n beperkte tyd te vind. ‘n Vyfde metode, die gebruik van ‘n volledige ondersoek van verkleinde versamelings, rondom hoë‐kwaliteit areas in die soekarea, is vergelyk met die gebruik van die meta‐heuristieke. Hierdie hoë‐kwaliteit areas word gevind rondom die gesentreerde “horns‐up” en “horns‐down” posisies. Die Tentakelalgoritme het gemiddelde die beste herwinningsresultate van die vier meta‐heuristieke wat ondersoek was gelewer. Die volledige ondersoek van verkleinde versamelings in die hoë kwaliteit areas het egter die meta‐heuristieke oortref.

[pt] Esta tese define os problemas das p-medianas conectadas e o de localização de facilidades não-capacitadas conectadas. Possíveis aplicações incluem problemas de planejamento regional e o projeto de redes de telecomunicações ou de transporte. Para o primeiro problema, duas formulações de programação linear inteira são apresentadas e comparadas. Um destes modelos é adaptado para o segundo problema. Para o problema das p-medianas conectadas, algoritmos aproximados são desenvolvidos. Uma estratégia de busca local híbrida é proposta. Para acelerar as iterações do algoritmo de busca local, idéias como circularidade, melhoria iterativa e o descarte de vizinhos são incorporadas. Heurísticas GRASP e VNS são desenvolvidas incluindo a utilização de um filtro com o objetivo de diminuir os tempos de processamento e do procedimento de reconexão por caminhos com o objetivo de melhorar a qualidade das soluções encontradas. Diversos testes são realizados comparando-se esses algoritmos. Os resultados mostraram a necessidade de se executar um passo adicional de pós-otimização às heurísticas GRASP e VNS propostas. / [en] In this work, the connected p-median and the connected facility location problems are defined. Applications arise in regional planning, design of telecommunications and transportation networks. For the first problem, two integer linear programming formulations are proposed. Adaptations are made in one of these formulations and are used to model the second problem. Approximation algorithms to solve the connected p-median problem are developed. A hybrid local search strategy is proposed. In order to speed up the local search iterations, ideas as circularity, first- improving strategy and discard neighbors are incorporated. A GRASP algorithm and a VNS heuristic are also proposed. A filter is used to reduce the computational time required and a path-relinking is applied to improve the results found. Computational experiments to compare the algorithms are reported. To improve these results, it is applied a post-optimization step to the GRASP and VNS heuristics.

L’optimisation des structures est un processus essentiel dans la conception des systèmes mécaniques et électroniques. Cette thèse s’intéresse à la résolution des problèmes mono-objectifs et multi-objectifs des structures mécaniques et mécatroniques. En effet, les industriels ne sont pas seulement préoccupés à améliorer les performances mécaniques des pièces qu’ils conçoivent, mais ils cherchent aussi à optimiser leurs poids, leurs tailles, ainsi que leurs coûts de production. Pour résoudre ce type de problème, nous avons fait appel à des métaheuristiques robustes qui nous permettent de minimiser le coût de production de la structure mécanique et de maximiser le cycle de vie de la structure. Alors que des méthodes inappropriées de l’évolution sont plus difficiles à appliquer à des modèles mécaniques complexes en raison de temps calcul exponentiel. Il est connu que les algorithmes génétiques sont très efficaces pour les problèmes NP-difficiles, mais ils sont très lourds et trop gourmands quant au temps de calcul, d’où l’idée d’hybridation de notre algorithme génétique par l’algorithme d’optimisation par essaim de particules (PSO) qui est plus rapide par rapport à l’algorithme génétique (GA). Dans notre expérimentation, nous avons obtenu une amélioration de la fonction objectif et aussi une grande amélioration de la minimisation de temps de calcul. Cependant, notre hybridation est une idée originale, car elle est différente des travaux existants. Concernant l’avantage de l’hybridation, il s’agit généralement de trois méthodes : l’hybridation en série, l’hybridation en parallèle et l’hybridation par insertion. Nous avons opté pour l’hybridation par insertion par ce qu’elle est nouvelle et efficace. En effet, les algorithmes génétiques se composent de trois étapes principales : la sélection, le croisement et la mutation. Dans notre cas, nous remplaçons les opérateurs de mutation par l’optimisation par essaim de particules. Le but de cette hybridation est de réduire le temps de calcul ainsi que l’amélioration la solution optimale. / This thesis focuses on solving single objective problems and multiobjective of mechanical and mechatronic structures. The optimization of structures is an essential process in the design of mechanical and electronic systems. Industry are not only concerned to improve the mechanical performance of the parts they design, but they also seek to optimize their weight, size and cost of production. In order to solve this problem we have used Meta heuristic algorithms robust, allowing us to minimize the cost of production of the mechanical structure and maximize the life cycle of the structure. While inappropriate methods of evolution are more difficult to apply to complex mechanical models because of exponential calculation time. It is known that genetic algorithms are very effective for NP-hard problems, but their disadvantage is the time consumption. As they are very heavy and too greedy in the sense of time, hence the idea of hybridization of our genetic algorithm optimization by particle swarm algorithm (PSO), which is faster compared to the genetic algorithm (GA). In our experience, it was noted that we have obtained an improvement of the objective function and also a great improvement for minimizing computation time. However, our hybridization is an original idea, because it is a different and new way of existing work, we explain the advantage of hybridization and are generally three methods : hybridization in series, parallel hybridization or hybridization by insertion. We opted for the insertion hybridization it is new and effective. Indeed, genetic algorithms are three main parts : the selection, crossover and mutation. In our case,we replace the operators of these mutations by particle swarm optimization. The purpose of this hybridization is to reduce the computation time and improve the optimum solution.

In nature animal species often exist in groups. We talk of insect swarms, flocks of birds, packs of lions, herds of wildebeest etc. These are characterised by individuals interacting by following their own rules, privy only to local information. Robotic swarms or simulations can be used explore such interactions. Mathematical formulations can be constructed that encode similar ideas and allow us to explore the emergent group behaviours. Some behaviours show characteristics reminiscent of the phenomena of criticality. A bird flock may show near instantaneous collective shifts in direction: velocity changes that appear to correlated over distances much larger individual separations. Here we examine swarm systems inspired by flocks of birds and the role played by criticality. The first system, Particle Swarm Optimisation (PSO), is shown to behave optimally when operating close to criticality. The presence of a critical point in the algorithm’s operation is shown to derive from the swarm’s properties as a random dynamical system. Empirical results demonstrate that the optimality lies on or near this point. A modified PSO algorithm is presented which uses measures of the swarm’s diversity as a feedback signal to adjust the behaviour of the swarm. This achieves a statistically balanced mixture of exploration and exploitation behaviours in the resultant swarm. The problems of stagnation and parameter tuning often encountered in PSO are automatically avoided. The second system, Swarm Chemistry, consists of heterogeneous particles combined with kinetic update rules. It is known that, depending upon the parametric configuration, numerous structures visually reminiscent of biological forms are found in this system. The parameter set discovered here results in a cell-division-like behaviour (in the sense of prokaryotic fission). Extensions to the swarm system produces a swarm that shows repeated cell division. As such, this model demonstrates a behaviour of interest to theories regarding the origin of life.

Supply chain optimization is one of the key components for the effective management of a company with a complex manufacturing process and distribution network. Companies with a global presence in particular are motivated to optimize their distribution plans in order to keep their operating costs low and competitive. Changing condition in the global market and volatile energy prices increase the need for an automatic decision and optimization tool. In recent years, many techniques and applications have been proposed to address the problem of supply chain optimization. However, such techniques are often too problemspecific or too knowledge-intensive to be implemented as in-expensive, and easy-to-use computer system. The effort required to implement an optimization system for a new instance of the problem appears to be quite significant. The development process necessitates the involvement of expert personnel and the level of automation is low. The aim of this project is to develop a set of strategies capable of increasing the level of automation when developing a new optimization system. An increased level of automation is achieved by focusing on three areas: multi-objective optimization, optimization algorithm usability, and optimization model design. A literature review highlighted the great level of interest for the problem of multiobjective optimization in the research community. However, the review emphasized a lack of standardization in the area and insufficient understanding of the relationship between multi-objective strategies and problems. Experts in the area of optimization and artificial intelligence are interested in improving the usability of the most recent optimization algorithms. They stated the concern that the large number of variants and parameters, which characterizes such algorithms, affect their potential applicability in real-world environments. Such characteristics are seen as the root cause for the low success of the most recent optimization algorithms in industrial applications. Crucial task for the development of an optimization system is the design of the optimization model. Such task is one of the most complex in the development process, however, it is still performed mostly manually. The importance and the complexity of the task strongly suggest the development of tools to aid the design of optimization models. In order to address such challenges, first the problem of multi-objective optimization is considered and the most widely adopted techniques to solve it are identified. Such techniques are analyzed and described in details to increase the level of standardization in the area. Empirical evidences are highlighted to suggest what type of relationship exists between strategies and problem instances. Regarding the optimization algorithm, a classification method is proposed to improve its usability and computational requirement by automatically tuning one of its key parameters, the termination condition. The algorithm understands the problem complexity and automatically assigns the best termination condition to minimize runtime. The runtime of the optimization system has been reduced by more than 60%. Arguably, the usability of the algorithm has been improved as well, as one of the key configuration tasks can now be completed automatically. Finally, a system is presented to aid the definition of the optimization model through regression analysis. The purpose of the method is to gather as much knowledge about the problem as possible so that the task of the optimization model definition requires a lower user involvement. The application of the proposed algorithm is estimated that could have saved almost 1000 man-weeks to complete the project. The developed strategies have been applied to the problem of Caterpillar’s global supply chain optimization. This thesis describes also the process of developing an optimization system for Caterpillar and highlights the challenges and research opportunities identified while undertaking this work. This thesis describes the optimization model designed for Caterpillar’s supply chain and the implementation details of the Ant Colony System, the algorithm selected to optimize the supply chain. The system is now used to design the distribution plans of more than 7,000 products. The system improved Caterpillar’s marginal profit on such products by a factor of 4.6% on average.

Public transport network design deals with finding the most efficient network solution among a set of alternatives, that best satisfies the often-conflicting objectives of different network stakeholders like passengers and operators. Simulation-based Optimisation (SBO) is a discipline that solves optimisation problems by combining simulation and optimisation models. The former is used to evaluate the alternative solutions, while the latter searches for the optimal solution among them. A SBO model for designing public transport networks is developed in this dissertation. The context of the research is the MyCiTi Bus Rapid Transit (BRT) network in the City of Cape Town, South Africa. A multi-objective optimisation algorithm known as the Non-dominated Sorting Genetic Algorithm (NSGA-II) is integrated with Activity-based Travel Demand Model (ABTDM) known as the Multi-Agent Transport Simulation (MATSim). The steps taken to achieve the research objectives are first to generate a set of feasible network alternatives. This is achieved by manipulating the existing routes of the MyCiTi BRT with a computer based heuristic algorithm. The process is guided by feasibility conditions which guarantee that each network has routes that are acceptable for public transport operations. MATSim is then used to evaluate the generated alternatives, by simulating the daily plans of travellers on each network. A typical daily plan is a sequential ordering of all the trips made by a commuter within a day. Automated Fare Collection (AFC) data from the MyCiTi BRT was used to create this plan. Lastly, the NSGA-II is used to search for an efficient set of network solutions, also known as a Pareto set or a non-dominated set in the context of Multi-objective Optimisation (MOO). In each generation of the optimisation process, MATSim is used to evaluate the current solution. Hence a suitable encoding scheme is defined to enable a smooth iv translation of the solution between the NSGA-II and MATSim. Since the solution of multi-objective optimisation problems is a set of network solutions, further analysis is done to identify the best compromise solution in the Pareto set. Extensive computational testing of the SBO model has been carried out. The tests involve evaluating the computational performance of the model. The first test measures the repeatability of the model's result. The second computational test considers its performance relative to indicators like the hypervolume and spacing indicators as well as an analysis of the model's Pareto front. Lastly, a benchmarking of the model's performance when compared with other optimisation algorithms is carried out. After testing the so-called Simulation-based Transit Network Design Model (SBTNDM), it is then used to design pubic transport networks for the MyCiTi BRT. Two applications are considered for the model. The first application deals with the public transport performance of the network solutions in the Pareto front obtained from the SBTNDM. In this case study, different transport network indicators are used to measure how each solution performs. In the second scenario, network design is done for the 85th percentile of travel demand on the MyCiTi network over 12 months. The results show that the model can design robust transit networks. The use of simulation as the agency of optimisation of public transport networks represents the main innovation of the work. The approach has not been used for public transport network design to date. The specific contribution of this work is in the improved modelling of public transport user behaviour with Agent-based Simulation (ABS) within a Transit Network Design (TND) framework. This is different from the conventional approaches used in the literature, where static trip-based travel demand models like the four-step model have mostly been used. Another contribution of the work is the development of a robust technique that facilitates the simultaneous optimisation of network routes and their operational frequencies. Future endeavours will focus on extending the network design model to a multi-modal context.