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The traveling purchaser problem (TPP) has gained attention in academics to deal with different variants in real business world. This study aims to study a green TPP with quantity discounts and soft time windows (TPPQS), in which a firm needs to purchase products from a set of available markets and deliver the products to a set of customers.

Vehicles are available to visit the markets, which offer products at different prices and with different quantity discount schemes. Soft time windows are present for the markets and the customers, and earliness cost and tardiness may incur if a vehicle cannot arrive a market or a customer within the designated time interval. The environmental impact of transportation activities is considered. The objective of this research is to minimize the total cost, including vehicle-assigning cost, vehicle-traveling cost, purchasing cost, emission cost, earliness cost and tardiness cost, while meeting the total demand of the customers and satisfying all the constraints. A mixed integer programming (MIP) model and a genetic algorithm (GA) approach are proposed to solve the TPPQS.

The results show that both the MIP and the GA can obtain optimal solutions for small-scale cases, and the GA can generate near-optimal solutions for large-scale cases within a short computational time.

The proposed models can help firms increase the performance of customer satisfaction and provide valuable supply chain management references in the service industry.

The proposed models for TPPQS are novel and can facilitate firms to design their green traveling purchasing plans more effectively in today’s environmental conscious and competitive market.

This study aims to investigate a locating-routing-allocating problems and the supply chain, including factories distributor candidate locations and retailers. The purpose of this paper is to minimize system costs and delivery time to retailers so that routing is done and the location of the distributors is located.

The problem gets closer to reality by adding some special conditions and constraints. Retail service start times have hard and soft time windows, and each customer has a demand for simultaneous delivery and pickups. System costs include the cost of transportation, non-compliance with the soft time window, construction of a distributor, purchase or rental of a vehicle and production costs. The conceptual model of the problem is first defined and modeled and then solved in small dimensions by general algebraic modeling system (GAMS) software and non-dominated sorting genetic algorithm II (NSGAII) and multiple objective particle swarm optimization (MOPSO) algorithms.

According to the solution of the mathematical model, the average error of the two proposed algorithms in comparison with the exact solution is less than 0.7%. Also, the algorithms’ performance in terms of deviation from the GAMS exact solution, is quite acceptable and for the largest problem (N = 100) is 0.4%. Accordingly, it is concluded that NSGAII is superior to MOSPSO.

In this study, since the model is bi-objective, the priorities of decision makers in choosing the optimal solution have not been considered and each of the objective functions has been given equal importance according to the weighting methods. Also, the model has not been compared and analyzed in deterministic and robust modes. This is because all variables, except the one that represents the uncertainty of traffic modes, are deterministic and the random nature of the demand in each graph is not considered.

The results of the proposed model are valuable for any group of decision makers who care optimizing the production pattern at any level. The use of a heterogeneous fleet of delivery vehicles and application of stochastic optimization methods in defining the time windows, show how effective the distribution networks are in reducing operating costs.

This study fills the gaps in the relationship between location and routing decisions in a practical way, considering the real constraints of a distribution network, based on a multi-objective model in a three-echelon supply chain. The model is able to optimize the uncertainty in the performance of vehicles to select the refueling strategy or different traffic situations and bring it closer to the state of certainty. Moreover, two modified algorithms of NSGA-II and multiple objective particle swarm optimization (MOPSO) are provided to solve the model while the results are compared with the exact general algebraic modeling system (GAMS) method for the small- and medium-sized problems.

In the present research, location and routing problems, as well as the supply chain, which includes manufacturers, distributor candidate sites and retailers, are explored. The goal of addressing the issue is to reduce delivery times and system costs for retailers so that routing and distributor location may be determined.

By adding certain unique criteria and limits, the issue becomes more realistic. Customers expect simultaneous deliveries and pickups, and retail service start times have soft and hard time windows. Transportation expenses, noncompliance with the soft time window, distributor construction, vehicle purchase or leasing, and manufacturing costs are all part of the system costs. The problem's conceptual model is developed and modeled first, and then General Algebraic Modeling System software (GAMS) and Multiple Objective Particle Swarm Optimization (MOPSO) and non-dominated sorting genetic algorithm II (NSGAII) algorithms are used to solve it in small dimensions.

According to the mathematical model's solution, the average error of the two suggested methods, in contrast to the exact answer, is less than 0.7%. In addition, the performance of algorithms in terms of deviation from the GAMS exact solution is pretty satisfactory, with a divergence of 0.4% for the biggest problem (N = 100). As a result, NSGAII is shown to be superior to MOSPSO.

Since this paper deals with two bi-objective models, the priorities of decision-makers in selecting the best solution were not taken into account, and each of the objective functions was given an equal weight based on the weighting procedures. The model has not been compared or studied in both robust and deterministic modes. This is because, with the exception of the variable that indicates traffic mode uncertainty, all variables are deterministic, and the uncertainty character of demand in each level of the supply chain is ignored.

The suggested model's conclusions are useful for any group of decision-makers concerned with optimizing production patterns at any level. The employment of a diverse fleet of delivery vehicles, as well as the use of stochastic optimization techniques to define the time windows, demonstrates how successful distribution networks are in lowering operational costs.

According to a multi-objective model in a three-echelon supply chain, this research fills in the gaps in the link between routing and location choices in a realistic manner, taking into account the actual restrictions of a distribution network. The model may reduce the uncertainty in vehicle performance while choosing a refueling strategy or dealing with diverse traffic scenarios, bringing it closer to certainty. In addition, two modified MOPSO and NSGA-II algorithms are presented for solving the model, with the results compared to the exact GAMS approach for medium- and small-sized problems.

The vehicle routing problem (VRP) has been widely investigated during last decades to reduce logistics costs and improve service level. In addition, many researchers have realized the importance of green logistic system design in decreasing environmental pollution and achieving sustainable development.

In this paper, a bi-objective mathematical model is developed for the capacitated electric VRP with time windows and partial recharge. The first objective deals with minimizing the route to reduce the costs related to vehicles, while the second objective minimizes the delay of arrival vehicles to depots based on the soft time window. A hybrid metaheuristic algorithm including non-dominated sorting genetic algorithm (NSGA-II) and teaching-learning-based optimization (TLBO), called NSGA-II-TLBO, is proposed for solving this problem. The Taguchi method is used to adjust the parameters of algorithms. Several numerical instances in different sizes are solved and the performance of the proposed algorithm is compared to NSGA-II and multi-objective simulated annealing (MOSA) as two well-known algorithms based on the five indexes including time, mean ideal distance (MID), diversity, spacing and the Rate of Achievement to two objectives Simultaneously (RAS).

The results demonstrate that the hybrid algorithm outperforms terms of spacing and RAS indexes with p-value <0.04. However, MOSA and NSGA-II algorithms have better performance in terms of central processing unit (CPU) time index. In addition, there is no meaningful difference between the algorithms in terms of MID and diversity indexes. Finally, the impacts of changing the parameters of the model on the results are investigated by performing sensitivity analysis.

In this research, an environment-friendly transportation system is addressed by presenting a bi-objective mathematical model for the routing problem of an electric capacitated vehicle considering the time windows with the possibility of recharging.

This paper, considers the multi-depot vehicle routing problem with time window considering two repair and pickup vehicles (CMDVRPTW).

The objective of this problem is minimization of the total traveling cost and the time window violations. Two meta-heuristic algorithms, namely, simple genetic algorithm (GA) and hybrid genetic algorithm (HGA) are used to find the best solution for this problem. A comparison on the results of these two algorithms has been done and based on the outcome, it has been proved that HGA has better performance than GA.

A comparison on the results of these two algorithms has been done and based on the outcome, it has been proved that HGA has better performance than GA.

This paper, considers the multi-depot vehicle routing problem with time window considering two repair and pickup vehicles (CMDVRPTW). The defined problem is a practical problem in the supply management and logistic. The repair vehicle services the customers who have goods, while the pickup vehicle visits the customer with nonrepaired goods. All the vehicles belong to an internal fleet of a company and have different capacities and fixed/variable cost. Moreover, vehicles have different limitations in their time of traveling. The objective of this problem is minimization of the total traveling cost and the time window violations. Two meta-heuristic algorithms (simple genetic algorithm and hybrid one) are used to find the best solution for this problem.

The purpose of this paper is to present a decision support system (DSS) for a Colombian public utility company in order to aid decision-making at the operational level regarding route planning and travel time. The aim is to provide a tool to assist technicians that perform interruption and reconnection of domiciliary services for about 2,000 customers a day.

The real-life problem is modeled as a Single Depot Vehicle Routing Problem with Time Windows (SDVRP-TW), which is a well-known optimization problem in Operations Research/Management Science. A two-stage approach integrated into decision-making software is provided. The first stage considers the clustering of customers generated by a combination of the sweep and the k-means algorithms, while the second phase plans the routing of technicians using the nearest-neighbor and the Or-opt heuristics. The proposed approach is tested using real data sets.

In comparison with the current route planning approach, the proposed method is able to obtain savings in total travel times, improving operational productivity by 22.2 percent.

Since the analysis is carried out based on mathematical modeling, assumptions about the relationships between variables and elements of the actual complex problem might be simplified. Although the proposed approach aids the route planning, decision makers make the final decisions.

The proposed DSS has a critical impact on actual operational practices at the company. Productivity and service level are improved, while reducing operational costs. The decision-making process itself will be improved so technicians and higher decision makers can focus on performing other tasks.

The real-life problem is modeled using mathematical programming and efficiently solved through a two-stage approach based on simple, quite intuitive, solution procedures that have not been implemented for such services. In addition, as actual data from the company is employed for experimental purposes, the solution approach is tested and its efficiency and efficacy are both validated in a realistic setting, hence providing realistic behavior for decision makers at the company.

presentar un sistema de soporte a las decisiones (Decision Support System, DSS) para una empresa colombiana de servicios públicos con el fin de apoyar el proceso de toma de decisiones a nivel operativo en lo relacionado con la planeación de rutas y el tiempo de servicio. El objetivo es suministrar una herramienta que ayude a los técnicos a desempeñar el servicio de corte y reconección de servicios domiciliarios para aproximadamente 2000 clientes por día.

el problema de una empresa real es modelado como un problema de enrutamiento de vehículos un único depósito y ventanas de tiempo (Single Depot Vehicle Routing Problem with Time Windows, SDVRP-TW). Éste es un problema de optimización muy conocido en Investigación de Operaciones / Ciencias de la Administración. Se presenta un enfoque de dos etapas integrado en un software de ayuda a la toma de decisiones. La primera etapa considera el agrupamiento de los clientes generado por una combinación de los algoritmos del barrido y el k-media, mientras que la segunda fase define el plan de rutas para los técnicos utilizando las heurísticas de vecino más cercano y Or-opt. El enfoque propuesto es validado empleando datos reales.

en comparación con el plan de rutas actualmente utilizado por la empresa, el método propuesto es capaz de obtener ahorros en el tiempo total de viaje incrementando la eficiencia operativa en un 22.2%.

puesto que el análisis se lleva a cabo a partir de un modelo matemático, los supuestos sobre las relaciones entre las variables y los elementos del sistema real complejo podrían simplificarse. Además, aunque el sistema propuesto realiza la planeación de rutas, la decisión final es tomada finalmente por las personas.

el DSS propuesto tiene un impacto crítico en la práctica operativa real de la empresa. La productividad y el nivel de servicio se mejoran, mientras se reducen los costos operativos. El proceso de toma de decisiones en sí mismo se verá mejorado pues los técnicos y los tomadores de decisiones pueden enfocarse en realizar otras tareas.

el problema real es modelado utilizando programación matemática y se resuelve de forma efectiva con un procedimiento de dos etapas sencillo y básicamente intuitivo que no ha sido puesto en marcha antes para tales empresas de servicios. Además, puesto que datos reales de la empresa son utilizados en la experimentación, el enfoque de solución es validado y su eficiencia y eficacia son comprobadas en un ambiente real, suministrando así un comportamiento real para los tomadores de decisiones en la empresa.

The purpose of this paper is to explore a real world vehicle routing problem (VRP) that has multi-depot subcontractors with a heterogeneous fleet of vehicles that are available to pickup/deliver jobs with varying time windows and locations. Both the overall job completion time and number of drivers utilized are analyzed for the automated job allocations and manual job assignments from transportation field experts.

A nested genetic algorithm (GA) is used to automate the job allocation process and minimize the overall time to deliver all jobs, while utilizing the fewest number of drivers – as a secondary objective.

Three different real world data sets were used to compare the results of the GA vs transportation field experts’ manual assignments. The job assignments from the GA improved the overall job completion time in 100 percent (30/30) of the cases and maintained the same or fewer drivers as BS Logistics (BSL) in 47 percent (14/30) of the cases.

This paper provides a novel approach to solving a real world VRP that has multiple variants. While there have been numerous models to capture a select number of these variants, the value of this nested GA lies in its ability to incorporate multiple depots, a heterogeneous fleet of vehicles as well as varying pickup times, pickup locations, delivery times and delivery locations for each job into a single model. Existing research does not provide models to collectively address all of these variants.

This paper studies low-carbon vehicle routing problem (VRP) for cold chain logistics with the consideration of the complexity of the road network and the time-varying traffic conditions, and then a low-carbon cold chain logistics routing optimization model was proposed. The purpose of this paper is to minimize the carbon emission and distribution cost, which includes vehicle operation cost, product freshness cost, quality loss cost, penalty cost and transportation cost.

This study proposed a mathematical optimization model, considering the distribution cost and carbon emission. The improved Nondominated Sorting Genetic Algorithm II algorithm was used to solve the model to obtain the Pareto frontal solution set.

The result of this study showed that this model can more accurately assess distribution costs and carbon emissions than those do not take real-time traffic conditions in the actual road network into account and provided guidance for cold chain logistics companies to choose a distribution strategy and for the government to develop a carbon tax.

There are some limitations in the proposed model. This study assumes that there are only one distribution and a single type of vehicle.

Existing research on low-carbon VRP for cold chain logistics ignores the complexity of the road network and the time-varying traffic conditions, resulting in nonmeaningful planned distribution routes and furthermore low carbon cannot be discussed. This study takes the complexity of the road network and the time-varying traffic conditions into account, describing the distribution costs and carbon emissions accurately and providing the necessary prerequisites for achieving low carbon.