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The purpose of this paper is to realize a location‐routing network optimization in reverse logistics (RL) using grey systems theory for uncertain information.

There is much uncertain information in network optimization and location‐routing problem (LRP) of RL, including fuzzy information, stochastic information and grey information, etc. Fuzzy information and stochastic information have been studied in logistics, however grey information of RL has not been covered. In the LRP of RL, grey recycling demands are taken into account. Then, a mathematics model with grey recycling demands has been constructed, and it can be transformed into grey chance‐constrained programming (GCCP) model, grey simulation and a proposed hybrid particle swarm optimization (PSO) are combined to resolve it. An example is also computed in the last part of the paper.

The results are convincing: not only that grey system theory can be used to deal with grey uncertain information about location‐routing problem of RL, but GCCP, grey simulation and PSO can be combined to resolve the grey model.

The method exposed in the paper can be used to deal with location‐routing problem with grey recycling information in RL, and network optimization result with grey uncertain factor could be helpful for logistics efficiency and practicability.

The paper succeeds in realising both a constructed model about location‐routing of RL with grey recycling demands and a solution algorithm about grey mathematics model by using one of the newest developed theories: grey systems theory.

The purpose of this paper is to realize a multi‐objective location‐routing network optimization in reverse logistics using particle swarm optimization based on grey relational analysis with entropy weight.

Real world network design problems are often characterized by multi‐objective in reverse logistics. This has recently been considered as an additional objective for facility location problem or vehicle routing problem in reverse logistics network design. Both of them are shown to be NP‐hard. Hence, location‐routing problem (LRP) with multi‐objective is more complicated integrated problem, and it is NP‐hard too. Due to the fact that NP‐hard model cannot be solved directly, grey relational analysis and entropy weight were added to particle swarm optimization to decision among the objectives. Then, a mathematics model about multi‐objective LRP of reverse logistics has been constructed, and a proposed hybrid particle swarm optimization with grey relational analysis and entropy weight has been developed to resolve it. An example is also computed in the last part of the paper.

The results are convincing: not only that particle swarm optimization and grey relational analysis can be used to resolve multi‐objective location‐routing model, but also that entropy and grey relational analysis can be combined to decide weights of objectives.

The method exposed in the paper can be used to deal with multi‐objective LRP in reverse logistics, and multi‐objective network optimization result could be helpful for logistics efficiency and practicability.

The paper succeeds in realising both a constructed multi‐objective model about location‐routing of reverse logistics and a multi‐objective solution algorithm about particle swarm optimization and future stage by using one of the newest developed theories: grey relational analysis.

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.

This paper proposed a bi-level mathematical model for location, routing and allocation of medical centers to distribution depots during the COVID-19 pandemic outbreak. The developed model has two players including interdictor (COVID-19) and fortifier (government). Accordingly, the aim of the first player (COVID-19) is to maximize system costs and causing further damage to the system. The goal of the second player (government) is to minimize the costs of location, routing and allocation due to budget limitations.

The approach of evolutionary games with environmental feedbacks was used to develop the proposed model. Moreover, the game continues until the desired demand is satisfied. The Lagrangian relaxation method was applied to solve the proposed model.

Empirical results illustrate that with increasing demand, the values of the objective functions of the interdictor and fortifier models have increased. Also, with the raising fixed cost of the established depot, the values of the objective functions of the interdictor and fortifier models have raised. In this regard, the number of established depots in the second scenario (COVID-19 wave) is more than the first scenario (normal COVID-19 conditions).

The results of the current research can be useful for hospitals, governments, Disaster Relief Organization, Red Crescent, the Ministry of Health, etc. One of the limitations of the research is the lack of access to accurate information about transportation costs. Moreover, in this study, only the information of drivers and experts about transportation costs has been considered. In order to implement the presented solution approach for the real case study, high RAM and CPU hardware facilities and software facilities are required, which are the limitations of the proposed paper.

The main contributions of the current research are considering evolutionary games with environmental feedbacks during the COVID-19 pandemic outbreak and location, routing and allocation of the medical centers to the distribution depots during the COVID-19 outbreak. A real case study is illustrated, where the Lagrangian relaxation method is employed to solve the problem.

The rapid development of smart cities and green logistics has stimulated a lot of research on reverse logistics, and the diversified data also provide the possibility of innovative research on location-routing problem (LRP) under reverse logistics. The purpose of this paper is to use panel data to assist in the study of multi-cycle and multi-echelon LRP in reverse logistics network (MCME-LRP-RLN), and thus reduce the cost of enterprise facility location.

First, a negative utility objective function is generated based on panel data and incorporated into a multi-cycle and multi-echelon location-routing model integrating reverse logistics. After that, an improved algorithm named particle swarm optimization-multi-objective immune genetic algorithm (PSO-MOIGA) is proposed to solve the model.

There is a paradox between the total cost of the enterprise and the negative social utility, which means that it costs a certain amount of money to reduce the negative social utility. Firms can first design an open-loop logistics system to reduce cost, and at the same time, reduce negative social utility by leasing facilities.

This study provides firms with more flexible location-routing options by dividing them into multiple cycles, so they can choose the right option according to their development goals.

This research is a pioneering study of MCME-LRP-RLN problem and incorporates data analysis techniques into operations research modeling. Later, the PSO algorithm was incorporated into the crossover of MOIGA in order to solve the multi-objective large-scale problems, which improved the convergence speed and performance of the algorithm. Finally, the results of the study provide some valuable management recommendations for logistics planning.

The purpose of this paper is to solve the capacitated location routing problem (CLRP), which is an NP-hard problem that involves making strategic decisions as well as tactical and operational decisions, using a hybrid particle swarm optimization (PSO) algorithm.

PSO, which is a population-based metaheuristic, is combined with a variable neighborhood strategy variable neighborhood search to solve the CLRP.

The algorithm is tested on a set of instances available in the literature and gave good quality solutions, results are compared to those obtained by other metaheuristic, evolutionary and PSO algorithms.

Local search is a time consuming phase in hybrid PSO algorithms, a set of neighborhood structures suitable for the solution representation used in the PSO algorithm is proposed in the VNS phase, moves are applied directly to particles, a clear decoding method is adopted to evaluate a particle (solution) and there is no need to re-encode solutions in the form of particles after applying local search.

Finding a rational approach to maintain a freshness of foods and perishable goods and saving their intrinsic attributes during a distribution of these products is one of the main issues for distribution and logistics companies. This paper aims to provide a framework for distribution of perishable goods which can be applied for real life situations.

This paper proposes a novel mathematical model for transportation inventory location routing problem. In addition, the paper addresses the impact of perishable goods age on the demand of final customers. The model is optimally solved for small- and medium-scale problems. Moreover, regarding to NP-hard nature of the proposed model, two simple and one hybrid metaheuristic algorithms are developed to cope with the complexity of problem in large scale problems.

Numerical examples with different scenarios and sensitivity analysis are conducted to investigate the performance of proposed algorithms and impacts of important parameters on optimal solutions. The results show the acceptable performance of proposed algorithms.

The authors formulate a novel mathematical model which can be applicable in perishable goods distribution systems In this regard, the authors consider lost sale which is proportional to age of products. A new hybrid approach is applied to tackle the problem and the results show the rational performance of the algorithm.

A variant of Kohonen's algorithm for the self‐organizing map (SOM) is used to solve a continuous location‐routing problem that can be applied to identify potential sites for subsequent selection by a discrete finite set model. The paper aims to show how the algorithm may be customized to fit the problem structure in a way that allows aspects of location and routing to be integrated into the solution procedure.

A set of test instances is used to compare the solutions of the neural network to those obtained by sequential approaches based on a savings procedure.

Compared to the results of the sequential approaches, the neural network yields good results.

Future work may cover the expansion of the neural approach to multi‐depot and multi‐stage problems. Additionally, application of procedures other than the savings procedure should be evaluated with respect to their potential for further enhancing the solution quality of the sequential approaches.

This paper shows that strategic location decisions in practical applications with long‐term customer relationships can be taken using simultaneously generated routing information on an operational level.

The paper provides a new variety of applications for SOM as well as high quality results for the specific type of problem considered.

The purpose of this paper is to solve large-scale many-to-many hub location-routing problem (MMHLRP) using variable neighborhood search (VNS). The MMHLRP is a combination of a single allocation hub location and traveling salesman problems that are known as one of the new fields in routing problems. MMHLRP is considered NP-hard since the two sub-problems are NP-hard. To date, only the Benders decomposition (BD) algorithm and the variable neighborhood particle swarm optimization (VNPSO) algorithm have been applied to solve the MMHLRP model with ten nodes and more (up to 300 nodes), respectively. In this research, the VNS method is suggested to solve large-scale MMHLRP (up to 1,000 nodes).

Generated MMHLRP sample tests in the previous work were considered and were added to them. In total, 35 sample tests of MMHLRP models between 10 and 1,000 nodes were applied. Three methods (BD, VNPSO and VNS algorithms) were run by a computer to solve the generated sample tests of MMHLRP. The maximum available time for solving the sample tests was 6 h. Accuracy (value of objective function solution) and speed (CPU time consumption) were considered as two major criteria for comparing the mentioned methods.

Based on the results, the VNS algorithm was more efficient than VNPSO for solving the MMHLRP sample tests with 10–440 nodes. It had many similarities with the exact BD algorithm with ten nodes. In large-scale MMHLRP (sample tests with more than 440 nodes (up to 1,000 nodes)), the previously suggested methods were disabled to solve the problem and the VNS was the only method for solving samples after 6 h.

The computational results indicated that the VNS algorithm has a notable efficiency in comparison to the rival algorithm (VNPSO) in order to solve large-scale MMHLRP. According to the computational results, in the situation that the problems were solved for 6 h using both VNS and VNPSO, VNS solved the problems with more accuracy and speed. Additionally, VNS can only solve large-scale MMHLRPs with more than 440 nodes (up to 1,000 nodes) during 6 h.

The purpose of this paper is to present a case study describing a collaboration with Last Mile Health, a non-governmental organization, to develop a framework to inform its community healthcare networks in remote Liberia.

The authors detail the process of using the unique problem setting and available data to inform modeling and solution approaches.

The authors show how the characteristics of the Liberian setting can be used to develop a two-tier modeling framework. Given the operating constraints and remote setting the authors are able to model the problem as a special case of the location-routing problem that is computationally simple to solve. The results of the models applied to three districts of Liberia are discussed, as well as the collaborative process of the multidisciplinary team.

Importantly, the authors describe how the problem setting can enable the development of a properly scoped model that is implementable in practice. Thus the authors provide a case study that bridges the gap between theory and practice.