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In order to reduce logistics transportation costs and respond to low-carbon economy, the purpose of this paper is to study the more practical and common simultaneous pickup and delivery vehicle routing problem, which considers the carbon tax policy. A low-carbon simultaneous pickup and delivery vehicle routing problem model is constructed with the minimum total costs as the objective function.

This study develops a mathematical optimization model with the minimum total costs, including the carbon emissions costs as the objective function. An adaptive genetic hill-climbing algorithm is designed to solve the model.

First, the effectiveness of the algorithm is verified by numerical experiments. Second, the research results prove that carbon tax mechanism can effectively reduce carbon emissions within effective carbon tax interval. Finally, the research results also show that, under the carbon tax mechanism, the effect of vehicle speed on total costs will become more obvious with the increase of carbon tax.

This paper only considers the weight of the cargo, but it does not consider the volume of the cargo.

Few studies focus on environmental issues in the simultaneous pickup and delivery problem. Thus, this paper constructs a green path optimization model, combining the carbon tax mechanism for the problem. This paper further analyzes the impact of carbon tax value on total costs and carbon emission; at the same time, the effect of vehicle speed on total cost is also analyzed.

This paper proposes an approach to solve the vehicle routing problem with simultaneous pickup and delivery (VRPSPD) in the context of the Physical Internet (PI) supply chain. The main objective is to minimize the total distribution costs (transportation cost and holding cost) to supply retailers from PI hubs.

Mixed integer programming (MIP) is proposed to solve the problem in smaller instances. A random local search (RLS) algorithm and a simulated annealing (SA) metaheuristic are proposed to solve larger instances of the problem.

The results show that SA provides the best solution in terms of total distribution cost and provides a good result regarding holding cost and transportation cost compared to other heuristic methods. Moreover, in terms of total carbon emissions, the PI concept proposed a better solution than the classical supply chain.

The sustainability of the route construction applied to the PI is validated through carbon emissions.

This approach also relates to the main objectives of transportation in the PI context: reduce empty trips and share transportation resources between PI-hubs and retailers. The proposed approaches are then validated through a case study of agricultural products in Thailand.

This approach is also relevant with the reduction of driving hours on the road because of share transportation results and shorter distance than the classical route planning.

This paper addresses the VRPSPD problem in the PI context, which is based on sharing transportation and storage resources while considering sustainability.

This paper aims to focus on a medical goods distribution problem and pharmacological waste collection by plug-in hybrid vehicles with some real-world restrictions. In this research, considering alternative energy sources and simultaneous pickup and delivery led to a decrease in greenhouse gas emissions and distribution costs, respectively.

Here, this problem has been modeled as mixed-integer linear programming with the traveling and energy consumption costs objective function. The GAMS was used for model-solving in small-size instances. Because the problem in this research is an NP-hard problem and solving real-size problems in a reasonable time is impossible, in this study, the artificial bee colony algorithm is used.

Then, the algorithm results are compared with a simulated annealing algorithm that recently was proposed in the literature. Finally, the results obtained from the exact solution and metaheuristic algorithms are compared, analyzed and reported. The results showed that the artificial bee colony algorithm has a good performance.

In this paper, medical goods distribution with pharmacological waste collection is studied. The paper was focused on plug-in hybrid vehicles with simultaneous pickup and delivery. The problem was modeled with environmental criteria. The traveling and energy consumption costs are considered as an objective function.

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 specific variant of vehicle routing problem with simultaneous full pickup and delivery problem (VRPSFPD) known as one-to-many-to-one (1-M-1) problem with several vehicles, where every customer can receive and send goods simultaneously, which has added the notion of the totality for the pickup goods. Currently, hybrid metaheuristics have become more popular because they offer the best solutions to several combinatorial optimization problems. Therefore, due to the complexity of 1-M-1 a hybrid genetic algorithm with variable neighborhood descent (HGAVND) local search is proposed. To improve the solution provided by the HGAVND the authors suggest applying a structure OR-Opt. To test the performance of the algorithm the authors have used a set of benchmarks from the literature and apply the HGAVND algorithm to solve the real case of distribution of soft drink in Tunisia. The experimental results indicate that the algorithm can outperform all other algorithms proposed in literature with regard to solution quality and processing time. Moreover, the authors improve the best known solution of the majority of benchmark instances taken from the literature.

Due to the complexity of 1-M-1 a HGAVND local search is proposed.

First, in the presence of full pickup constraints, the problem becomes more complex, this implies that the choice of a good metaheuristic can provide good results. Second, the best contribution consists in a specific variant of VRPSFPD problem as 1-M-1 which the paper present the first application of metaheuristics to solve the specific 1-M-1 and to apply it in real case of distribution of soft drink.

In this paper, the author introduces a new variant of the pickup and delivery transportation problem, where one commodity is collected from many pickup locations to be delivered to many delivery locations within pre-specified time windows (one–to many–to many). The author denotes to this new variant as the 1-commodity pickup-and-delivery vehicle routing problem with soft time windows (1-PDVRPTW).

The author proposes a hybrid genetic algorithm and a scatter search to solve the 1-PDVRPTW. It proposes a new constructive heuristic to generate the initial population solution and a scatter search (SS) after the crossover and mutation operators as a local search. The hybrid genetic scatter search replaces two steps in SS with crossover and mutation, respectively.

So, the author proposes a greedy local search algorithm as a metaheuristic to solve the 1-PDVRPTW. Then, the author proposes to hybridize the metaheuristic to solve this variant and to make a good comparison with solutions presented in the literature.

The author considers that this is the first application in one commodity. The solution methodology based on scatter search method combines a set of diverse and high-quality candidate solutions by considering the weights and constraints of each solution.

This paper aims to provide an integrated production-routing model in a three-echelon supply chain containing a two-layer transportation system to minimize the total costs of production, transportation, inventory holding and expired drugs treatment. In the proposed problem, some specifications such as multisite manufacturing, simultaneous pickup and delivery and uncertainty in parameters are considered.

At first, a mathematical model has been proposed for the problem. Then, one possibilistic model and one robust possibilistic model equivalent to the initial model are provided regarding the uncertain nature of the model parameters and the inaccessibility of their probability function. Finally, the performance of the proposed model is evaluated using the real data collected from a pharmaceutical production center in Iran. The results reveal the proper performance of the proposed models.

The results obtained from applying the proposed model to a real-life production center indicated that the number of expired drugs has decreased because of using this model, also the costs of the system were reduced owing to integrating simultaneous drug pickup and delivery operations. Moreover, regarding the results of simulations, the robust possibilistic model had the best performance among the proposed models.

This research considers a two-layer vehicle routing in a production-routing problem with inventory planning. Moreover, multisite manufacturing, simultaneous pickup of the expired drugs and delivery of the drugs to the distribution centers are considered. Providing a robust possibilistic model for tackling the uncertainty in demand, costs, production capacity and drug expiration costs is considered as another remarkable feature of the proposed model.

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.

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.

This paper aims to explore the commodity transshipment planning among customers, which is commonly observed in production/sales enterprises to save the operational costs.

A mixed integer programming (MIP) model is built and five types of valid inequalities for tightening the solution space are derived. An improved variable neighborhood search (IVNS) algorithm is presented combining the developed multistart initial solution strategy and modified neighborhood local search procedure.

Experimental results demonstrate that: with less decision variables considered, the proposed model can solve more instances compared to the existing model in previous literature. The valid inequalities utilized to tighten the searching space can efficiently help the model to obtain optimal solutions or high-quality lower bounds. The improved algorithm is efficient to obtain optimal or near-optimal solutions and superior to the compared algorithm in terms of solution quality, computational time and robustness.

This research not only can help reduce operational costs and improve logistics efficiency for relevant enterprises, but also can provide guidance for constructing the decision support system of logistics intelligent scheduling platform to cater for centralized management and control.

This paper develops a more compact model and some stronger valid inequalities. Moreover, the proposed algorithm is easy to implement and performs well.