Optimasi Capacitated Vehicle Routing Problem with Time Windows dengan Menggunakan Ant Colony Optimization

In recent years, minimization of logistics and transportation costs has become essential for manufacturing companies to increase profits. One thing is done to reduce logistics and transportation costs by optimizing the route of taking or transporting components from each supplier. Route optimization to minimize total transportation costs is a problem that often finds in Vehicle Routing Problems (VRP). Problem Capacitated Vehicle Routing with Time Windows (CVRPTW) is one variant of VRP that considers the vehicle capacity and the service period of each vehicle. CVRPTW is a Non-Polynomial Hard (NP-Hard) problem that requires an efficient and effective algorithm in solving problems that occur in this automotive company. This study uses the Ant Colony Optimization (ACO) algorithm by testing using several parameters to solve the CVRPTW problem. The test results using the ACO algorithm obtained a faster route compared to the method applied by the company

Optimasi Biaya Distribusi pada HFVRP Menggunakan Algoritma Particle Swarm Optimization

Distribution systems play a significant role in logistics operations. For the companies with consumer goods products this even more important as consumer goods production has fairly cheap price compared to the distribution cost that must be spent by the company. In addition, increased fuel costs have urged the company to be more efficient in planning and schedule the transportation routes. This paper presents the application of the Particle Swarm Optimization (PSO) algorithm to minimize the travel distance and total cost of a Heterogeneous Fleet Vehicle Routing Problem (HFVRP). Experimental results from its application to a real-world case study are presented. The model in this research is the HFVRP where vehicles have different capacities, variable costs, and fixed costs. PSO algorithm was applied because of the high number of customers served, and therefore the exact methods may not be sufficient. PSO parameter setting which produced the optimum result was with the number of swarms 50, C1 1,5, and C2 2 determined through the design of the experiment. The results of computation show that using PSO can minimize the total traveled distance with an average savings of 51.55% and minimize total cost with an average savings of 44.92% from the existing vehicle routes operated by the company.Distribution systems play a significant role in logistics operations. For the companies with consumer goods products this even more important as consumer goods production has fairly cheap price compared to the distribution cost that must be spent by the company. In addition, increased fuel costs have urged the company to be more efficient in planning and schedule the transportation routes. This paper presents the application of the Particle Swarm Optimization (PSO) algorithm to minimize the travel distance and total cost of a Heterogeneous Fleet Vehicle Routing Problem (HFVRP). Experimental results from its application to a real-world case study are presented. The model in this research is the HFVRP where vehicles have different capacities, variable costs, and fixed costs. PSO algorithm was applied because of the high number of customers served, and therefore the exact methods may not be sufficient. PSO parameter setting which produced the optimum result was with the number of swarms 50, C1 1,5, and C2 2 determined through the design of the experiment. The results of computation show that using PSO can minimize the total traveled distance with an average savings of 51.55% and minimize total cost with an average savings of 44.92% from the existing vehicle routes operated by the company

Enhancement on the modified artificial bee colony algorithm to optimize the vehicle routing problem with time windows

The vehicle routing problem with time windows (VRPTW) is a non-deterministictime hard (NP-hard) with combinatorial optimization problem (COP). The Artificial Bee Colony (ABC) is a popular swarm intelligence algorithm for COP. In this study, existing Modified ABC (MABC) algorithm is revised to solve the VRPTW. While MABC has been reported to be successful, it does have some drawbacks, including a lack of neighbourhood structure selection during the intensification process, a lack of knowledge in population initialization, and occasional stops proceeding the global optimum. This study proposes an enhanced Modified ABC (E-MABC) algorithm which includes (i) N-MABC that overcomes the shortage of neighborhood selection by exchanging the neighborhood structure between two different routes in the solution; (ii) MABC-ACS that solves the issues of knowledge absence in MABC population initialization by incorporating ant colony system heuristics, and (iii) PMABC which addresses the occasional stops proceeding to the global optimum by introducing perturbation that accepts an abandoned solution and jumps out of a local optimum. The proposed algorithm was evaluated using benchmark datasets comprising 56 VRPTW instances and 56 Pickup and Delivery Problems with Time Windows (PDPTW). The performance has been measured using the travelled distance (TD) and the number of deployed vehicles (NV). The results showed that the proposed E-MABC has lower TD and NV than the benchmarked MABC and other algorithms. The E-MABC algorithm is better than the MABC by 96.62%, MOLNS by 87.5%, GAPSO by 53.57%, MODLEM by 76.78%, and RRGA by 42.85% in terms of TD. Additionally, the E-MABC algorithm is better than the MABC by 42.85%, MOLNS by 17.85%, GA-PSO and RRGA by 28.57%, and MODLEN by 46.42% in terms of NV. This indicates that the proposed E-MABC algorithm is promising and effective for the VRPTW and PDPTW, and thus can compete in other routing problems and COPs

Planning the delivery of home-based long-term care: A mathematical programming-based tool to support routes' planning

The adequate planning of home-based long-term care (HBLTC) is essential in the current European setting where long-term care (LTC) demand is increasing rapidly, and where home-based care represents a potential cost-saving alternative from traditional inpatient care. Particularly, this planning should involve proper route planning to ensure visits of health professionals to patients’ homes. Nevertheless, literature in the specific area of HBLTC planning is still scarce. Accordingly, this paper proposes a tool based on a mathematical programming model – the LTCroutes – for supporting the daily planning of routes to visit LTC patients’ homes in National Health Service-based countries. The model allows exploring the impact of considering different objectives relevant in this sector, including the minimization of costs and the maximization of service level. Patients’ preferences, traffic conditions and budget constraints are also considered in the proposed model. To illustrate the applicability of the model, a case study based on the National Network of LTC in Portugal (RNCCI) is analysed.O planeamento adequado de cuidados continuados ao domicílio é essencial na conjuntura atual Europeia em que a procura de cuidados continuados está a aumentar rapidamente, e em que os cuidados ao domicílio representam uma alternativa com potencial de poupança de custos relativamente ao tradicional internamento hospitalar. Particularmente, é necessário haver um planeamento adequado das rotas dos profissionais de saúde às casas dos pacientes. No entanto, a literatura na área específica de planeamento de cuidados continuados ao domicílio ainda é escassa. Nesse sentido, este artigo propõe uma ferramenta baseada num modelo de programação matemática - o LTCroutes - para apoiar o planeamento diário das rotas para visitar as casas dos pacientes com necessidade de cuidados continuados em países com Serviço Nacional de Saúde. O modelo desenvolvido permite explorar o impacto de considerar diferentes objetivos relevantes neste setor, incluindo a minimização de custos e a maximização do nível de serviço. As preferências dos pacientes, condições de trânsito e restrições de orçamento também são consideradas no modelo proposto. Para ilustrar a aplicabilidade do modelo, é analisado um caso de estudo baseado na Rede Nacional de Cuidados Continuados Integrados (RNCCI) em Portugal

A Combination of Genetic Algorithm and Particle Swarm Optimization for Vehicle Routing Problem with Time Windows

A combination of genetic algorithm and particle swarm optimization (PSO) for vehicle routing problems with time windows (VRPTW) is proposed in this paper. The improvements of the proposed algorithm include: using the particle real number encoding method to decode the route to alleviate the computation burden, applying a linear decreasing function based on the number of the iterations to provide balance between global and local exploration abilities, and integrating with the crossover operator of genetic algorithm to avoid the premature convergence and the local minimum. The experimental results show that the proposed algorithm is not only more efficient and competitive with other published results but can also obtain more optimal solutions for solving the VRPTW issue. One new well-known solution for this benchmark problem is also outlined in the following

Planning the delivery of home social services: a mathematical programming-based approach to support routing and scheduling assignments

The increased average lifespan, together with low birth rates, are transforming the European Union's age pyramid. Currently, we are experiencing a transition towards a much older population structure. Given that the institutions that provide care to these population groups are limited by budgetary constraints, it is imperative to optimize several processes, among which route planning and staff scheduling stand out. This dissertation aims to develop a mathematical programming model to support the planning of routes and human resources for providers of Home Social Services. Beyond general Vehicle Routing Problems assumptions, the proposed model also considers the following features: i) working time regulations, ii) mandatory breaks, iii) users' autonomy, and iii) meals' distribution. The present model, implemented using GAMS software, focuses simultaneously on two objective functions: minimization of operating costs, and maximization of equity through the minimization of differences in teams' working times. Chebyshev's method was chosen to solve the developed multiobjective model. The model was built based on a Portuguese Private Institution of Social Solidarity. Through the application of the model, significant improvements are obtained when compared to the current planning of the partner institution, such as it is the case of an improved workload distribution between caregivers and routes that will result in lower costs for the institution. This model is fully enforceable to other institutions that provide services similar or equal to the institution used as a reference.O aumento da esperança média de vida, juntamente com baixas taxas de natalidade, estão a transformar a pirâmide etária da União Europeia. Atualmente, estamos a vivenciar uma transição direcionada para uma estrutura populacional muito mais envelhecida. Dado que as instituições que prestam cuidados a esta fração se encontram limitadas por restrições orçamentais, torna-se imperativo otimizar vários processos, dos quais se destacam planeamento de rotas e escalonamento de funcionárias. Esta dissertação visa introduzir um modelo de programação matemática com a finalidade de apoiar o planeamento de rotas e recursos humanos para prestadores de Serviços de Apoio Domiciliário. O modelo assenta, além dos pressupostos de um "Vehicle Routing Problem", nos seguintes: i) regulações de tempo de trabalho, ii) pausas obrigatórias, iii) autonomia dos utentes, e iv) distribuição de refeições. O modelo, desenvolvido através de software GAMS, foca-se em duas funções objetivo, simultaneamente: minimização dos custos operacionais, e maximização da equidade, através da minimização das diferenças nos tempos de trabalho das equipas. O método de Chebyshev foi o escolhido para desenvolver o modelo multiobjetivo. O modelo foi construído tendo por base uma Instituição Particular de Solidariedade Social em Portugal. Através da aplicação do modelo, obtêm-se melhorias significativas, quando comparado com o atual planeamento da instituição parceira, como é o caso de uma melhor distribuição da carga de trabalho entre as funcionárias e das rotas que resultam da redução dos custos operacionais da instituição. Este modelo é totalmente extensível a outras instituições que prestem serviços semelhantes ou iguais à instituição utilizada como referência

Desenho e planeamento de rotas de um serviço de apoio domiciliário

JEL Classification System: L91 - Transportation: General R41 - Transportation: Demand, Supply, and Congestion; Travel Time; Safety and Accidents; Transportation Noise.O número de instituições que prestam Serviços de Apoio Domiciliário em Portugal tem crescido significativamente nos últimos anos. Este crescimento tem-se registado para fazer face à também crescente procura por esta tipologia de serviços que é, na maioria dos casos, usufruído por população idosa. Esta, por sua vez, não só em Portugal, mas um pouco por toda a Europa, tem crescido significativamente em comparação com as restantes classes etárias num contexto em que se prevê que esta tendência se acentue. Neste contexto, o planeamento deste tipo de serviços torna-se fundamental para que seja possível prestar serviços com mais qualidade e em maior quantidade, dado o aumento da procura. A Apoio - Associação de Solidariedade Social, perante este cenário e prestando este serviço diariamente a 36 utentes pretende que, através de uma melhoria do processo de definição tanto de rotas como da sequência de visitas a efetuar, seja possível incluir mais utentes da sua lista de espera no seu planeamento atual mantendo os recursos atuais. Assim, pretende-se definir um planeamento semanal que minimize o tempo total de deslocação dos técnicos que prestam os serviços de apoio domiciliário aos utentes. O problema em análise é modelado como um problema de rotas de veículos com janelas temporais (VRPTW). Foi aplicado um modelo da literatura ao caso real em estudo e permitiu obter, como solução final, o planeamento de rotas a realizar diariamente que, em comparação com a solução atual da Associação, permite reduzir 12% do tempo de deslocações da mesma.The number of institutions providing home care services in Portugal have been growing significantly during last years. This growth has occurred to face the evolution in demand for this kind of services that is, in most of cases, enjoyed by elderly. This age group, in turn, not just in Portugal as well as throughout Europe, has been growing considerably comparing to the remaining age groups in a context where it is forecasted that this trend to accentuate. In this context, the planning of such services take a huge importance in order to be possible to provide services with higher quality and greater quantity given the increase in demand. APOIO - Social Solidarity Association, faced with this scenario and providing this service on a daily basis to 36 users intends, by improving the definition process both routes and the sequence of visits to make, to include more users of its waiting list in their current planning keeping its existing resources. Therefore, it is intended to define a weekly scheduling that minimizes the total travel time spent by caregivers. The problem studied in this document is modelled as a Vehicle Routing Problem with Time Windows (VRPTW). To the real case study was applied one model from literature and allowed to obtain, as a final solution, the routing planning to perform daily. This one, comparing to the current solution carried out by the Association, allow a decrease of about 12% in total travel time spent by caregivers

Multi-principal element alloys: Design, properties and heuristic explorations

Computational investigations of structural, chemical, and deformation behavior in high entropy alloys (HEAs), which possess notable mechanical strength, have been limited due to the absence of applicable force fields. First by employing Lennard-Jones (LJ) type potential, we explore the atomic origins of the structural phase transformations (PTs) in AlxCrCoFeNi multi-principal element alloys (MPEAs) using classical molecular dynamics (MD) simulations. We report that the amorphous phase exists above the melting temperatures of the participating elements when the concentration of Al 20 %, while for Al \u3e 20 %, a gradual molten-amorphous phase transition is noted. To extend investigations for mechanical properties, we propose a set of intermolecular potential parameters for a quinary Al-Cr-Co-Fe-Ni alloy, using the available ternary Embedded Atom Method and Lennard-Jones potential in classical molecular-dynamics simulations. The simulation results are validated by a comparison to first-principles Korringa-Kohn-Rostoker (KKR) - Coherent Potential Approximation (CPA) [KKR-CPA] calculations for the HEA structural properties (lattice constants and bulk moduli), relative stability, pair probabilities and high-temperature short-range ordering. The simulation (MD)-derived properties are in quantitative agreement with KKR-CPA calculations (first-principles) and experiments. We study AlxCrCoFeNi for Al ranging from 0 $leq$ x $leq$ 2 mole fraction, and and that the HEA shows large chemical clustering over a wide temperature range for x \u3c 0.5. At various temperatures high-strain compression promotes atomistic rearrangements in Al0:1CrCoFeNi, resulting in a clustering-to-ordering transition that is absent for tensile loading. Large fluctuations under stress, at higher temperatures, are attributed to the thermo-plastic instability in Al0:1CrCoFeNi. With the proposed EAM-LJ potential parameters, we then analyze the dislocation dynamics in the FCC Al0:1CrCoFeNi HEA. During plastic deformation, we find that dislocation nucleation and mobility plays a pivotal role in initially triggering twin boundaries followed by the generation of intrinsic and extrinsic stacking faults in the alloy. At room temperature, we find dislocation annihilation contributes to the shear resistance of the alloy eecting a serration laden plastic ow of stress as uniaxial strain is increased. Designing advanced materials for high-temperature applications is a challenging problem. Traditionally superalloys, especially Ni-based, have been the to-go materials whenever strength, and oxidation/corrosion resistance is required in applications ranging across gas turbines to engines. Refractory elements have a high melting point and are ideal candidates to design refractory based MPEAs. We utilized classical Hume-Rothery rules, like Valence Electron Concentration (VEC), size-effect , alongside density functional theory predicted global stability parameter like formation enthalpy and thermodynamic linear response predicted local stability criteria like short-range order (SRO) to explore the 5D design space in a holistic manner for a quinary refractory MPEA. Our investigation revealed the specific design regimes ideal for enhanced electronic stability alongside desired mechanical strength for a novel refractory alloy series based on Mo-W-Ta-Ti-Zr. Findings suggest that the elastic strength of predicted alloy, composition having greater content of Mo and W (at. %), surpasses current commercial high-temperature alloy (Ti-Zr-Mo). Transport properties of refractory MPEAs are also investigated as a potential new class of high-performance thermoelectric material. Investigations in XTa-MoW MPEAs (X=Ti, V, Nb, Zr) revealed dispersion effects and critical doping concentration that helps in tuning the figure-of-merit (ZT) by a factor of 6 at 1250 K. Further investigations in refractory MPEAs revealed twinning-induced pseudoelasticity in (MoW)0:85(TaTi)7:5Zr7:5. Atomistic insights through structural analysis and role of temperature was carried out in this work. Materials for actuators and bio-medical stents are some of the possible application areas for the predicted pseudoelastic MPEA. We design a robust computational framework that couples the metaheuristic cuckoo search technique with classical molecular dynamics simulations to explore the structure-composition phase space of multicomponent alloys. Thereby the predictive scheme explores a vast materials landscape and accelerates the elemental selection for discovery of novel multicomponent alloys. Structural design of MPEAs is generally based on brute-force Monte-Carlo (MC) techniques which are often computationally demanding and less reliable. We proposed a novel exploratory technique to numerically design initial lattice structures for MPEAs for quantum or atomistic calculations that maintains desired cubic symmetry, at required compositions at a fraction of the computational requirements of current algorithms/frameworks. Structural design of BCC alloy systems from binary to quinay were successfully performed and verified with two different density functional approaches