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The purpose of this study is to model a vehicle routing problem with integrated picking and delivery under carbon cap and trade policy. This study also provides sensitivity analyses of carbon cap and price to the total cost.

A mixed integer linear programming (MILP) model is formulated to model the vehicle routing with integrated order picking and delivery constraints. The model is then solved by using the CPLEX solver. Carbon footprint is estimated by a fuel consumption function that is dependent on two factors, distance and vehicle speed. The model is analyzed by considering 10 suppliers and 20 customers. The distance and vehicle speed data are generated using simulation with random numbers.

Significant amount of carbon footprint can be reduced through the adoption of eco-efficient vehicle routing with a marginal increase in total transportation cost. Sensitivity analysis indicates that compared to carbon cap, carbon price has more influence on the total cost.

The model considers mid-sized problem instances. To analyze large size problems, heuristics and meta-heuristics may be used.

This study provides an analysis of carbon cap and price model that would assist practitioners and policymakers in formulating their policy in the context of carbon emissions.

This study provides two significant contributions to low carbon supply chain management. First, it provides a vehicle routing model under carbon cap and trade policy. Second, it provides a sensitivity analysis of carbon cap and price in the model.

Recently, electric vehicles have been widely used in the cold chain logistics sector to reduce the effects of excessive energy consumption and to support environmental friendliness. Considering the limited battery capacity of electric vehicles, it is vital to optimize battery charging during the distribution process.

This study establishes an electric vehicle routing model for cold chain logistics with charging stations, which will integrate multiple distribution centers to achieve sustainable logistics. The suggested optimization model aimed at minimizing the overall cost of cold chain logistics, which incorporates fixed, damage, refrigeration, penalty, queuing, energy and carbon emission costs. In addition, the proposed model takes into accounts factors such as time-varying speed, time-varying electricity price, energy consumption and queuing at the charging station. In the proposed model, a hybrid crow search algorithm (CSA), which combines opposition-based learning (OBL) and taboo search (TS), is developed for optimization purposes. To evaluate the model, algorithms and model experiments are conducted based on a real case in Chongqing, China.

The result of algorithm experiments illustrate that hybrid CSA is effective in terms of both solution quality and speed compared to genetic algorithm (GA) and particle swarm optimization (PSO). In addition, the model experiments highlight the benefits of joint distribution over individual distribution in reducing costs and carbon emissions.

The optimization model of cold chain logistics routes based on electric vehicles provides a reference for managers to develop distribution plans, which contributes to the development of sustainable logistics.

In prior studies, many scholars have conducted related research on the subject of cold chain logistics vehicle routing problems and electric vehicle routing problems separately, but few have merged the above two subjects. In response, this study innovatively designs an electric vehicle routing model for cold chain logistics with consideration of time-varying speeds, time-varying electricity prices, energy consumption and queues at charging stations to make it consistent with the real world.

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 purpose of this paper is to investigate the application of the dynamic vehicle routing problem for last mile distribution during disaster response. The authors explore a model that involves limited heterogeneous vehicles, multiple trips, locations with different accessibilities, uncertain demands, and anticipating new locations that are expected to build responsive last mile distribution systems.

The modified simulated annealing algorithm with variable neighborhood search for local search is used to solve the last mile distribution model based on the criterion of total travel time. A dynamic simulator that accommodates new requests from demand nodes and a sample average estimator was added to the framework to deal with the stochastic and dynamicity of the problem.

This study illustrates some practical complexities in last mile distribution during disaster response and shows the benefits of flexible vehicle routing by considering stochastic and dynamic situations.

This study only focuses day-to-day distribution on road/land transportation for distribution, and additional transportation modes need to be considered further.

The proposed model offers operational insights for government disaster agencies by highlighting the dynamic model concept for supporting relief distribution decisions. The result suggests that different characteristics and complexities of affected areas might require different distribution strategies.

This study modifies the concept of the truck and trailer routing problem to model locations with different accessibilities while anticipating the information gap for demand size and locations. The results show the importance of flexible distribution systems during a disaster for minimizing the disaster risks.

In a modern business environment, employees are a key resource to a company. Hence, the competitiveness of a company depends largely on its ability to treat employees fairly. Fairness can be attained by using the load‐balancing methodology. Develops an integer programming model for vehicle routing problems. There are two objectives, first, to minimize the total distance, and second, to balance the workload among employees as much as possible. We also develop a heuristic algorithm to solve the problems. The findings show that the proposed heuristic algorithm performs well to our 11 test cases.

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.

Distribution systems planning frequently involves two major decisions: facility location and vehicle routing. The facilities to be located may be “primary facilities”, e.g. factories, but more often, these are lighter “secondary facilities” such as depots, warehouses or distribution centres. Routing decisions concern the optimal movement of goods and vehicles in the system, usually from primary to secondary facilities, and from secondary facilities to users or customers. Studies which integrate the two areas are more often than not limited to the case where all deliveries are return trips involving only one destination. There exist, however, several situations where vehicles visit more than one point on the same trip. In such cases, relationships between location and routing decisions become more intricate. Strategies by which the two aspects of the problem are optimised separately and sequentially are often sub‐optimal. Also of importance is the trade‐off between the cost of providing service and customer inconvenience. A framework is proposed for the study of such combined location‐routing problems. A number of real‐life cases described in the literature are summarised and some algorithmic issues related to such problems are discussed.

Drugs are strategic products with essential functions in human health. An optimum design of the pharmaceutical supply chain is critical to avoid economic damage and adverse effects on human health. The vehicle-routing problem, focused on finding the lowest-cost routes with available vehicles and constraints, such as time constraints and road length, is an important aspect of this. In this paper, the vehicle routing problem (VRP) for a pharmaceutical company in Turkey is discussed.

A mixed-integer programming (MIP) model based on the vehicle routing problem with time windows (VRPTW) is presented, aiming to minimize the total route cost with certain constraints. As the model provides an optimum solution for small problem sizes with the GUROBI® solver, for large problem sizes, metaheuristic methods that simulate annealing and adaptive large neighborhood search algorithms are proposed. A real dataset was used to analyze the effectiveness of the metaheuristic algorithms. The proposed simulated annealing (SA) and adaptive large neighborhood search (ALNS) were evaluated and compared against GUROBI® and each other through a set of real problem instances.

The model is solved optimally for a small-sized dataset with exact algorithms; for solving a larger dataset, however, metaheuristic algorithms require significantly lesser time. For the problem addressed in this study, while the metaheuristic algorithms obtained the optimum solution in less than one minute, the solution in the GUROBI® solver was limited to one hour and three hours, and no solution could be obtained in this time interval.

The VRPTW problem presented in this paper is a real-life problem. The vehicle fleet owned by the factory cannot be transported between certain suppliers, which complicates the solution of the problem.

This research is designed to optimize the business process of a green tea dealer, who is a key supply chain partner of the Sri Lankan tea industry. The most appropriate trips for each vehicle in multiple trip routing systems are identified to minimize the total cost by considering the traveling distance.

The study has followed the concepts in vehicle routing problems and mixed-integer programming mathematical techniques. The model was coded with the Python programming language and was solved with the CPLEX Optimization solver version 12.10. In total, 20 data instances were used from the subjected green tea dealer for the validation of the model.

The result of the numerical experiment showed the ability to access supply over the full capacity of the available fleet. The model achieved optimal traveling distance for all the instances, with the capability of saving 17% of daily transpiration cost as an average.

This study contributes to the three index mixed-integer programing model formulation through in-depth analysis and combination of several extensions of vehicle routing problem.

This study contributes to the three index mixed-integer programming model formulation through in-depth analysis and combination of several extensions of the vehicle routing problem.

The proposed model provides a cost-effective optimal routing plan to the green tea dealer, which satisfies all the practical situations by following the multiple trip vehicle routing problems. Licensee green tea dealer is able to have an optimal fleet size, which is always less than the original fleet size. Elimination of a vehicle from the fleet has the capability of reducing the workforce. Hence, this provides managerial implication for the optimal fleet sizing and route designing.

Developing an optimization model for a tea dealer in Sri Lankan context is important, as this a complex real world case which has a significant importance in export economy of the country and which has not been analyzed or optimized through any previous research effort.

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.