Introduction and objectives: Urban development and the increase in intercity and intracity transportation have led to a significant rise in transportation costs. This rise in cost increases the final product price and consequently the product's market price. Additionally, the economic aspect is not the only concern; increased transportation results in higher CO2 emissions. These issues have driven the design of various transportation and vehicle ROUTING models, including the vehicle LOCATION-ROUTING problem. Facility location is a strategic decision due to the high costs associated with constructing and locating facilities. On the other hand, ROUTING decisions depend on location decisions and are considered mid-term and short-term decisions.In this study, a mathematical model for vehicle LOCATION-ROUTING under uncertainty conditions and considering reliability is developed to simultaneously optimize sustainability objective functions while maintaining minimum reliability levels. The sustainability objectives in this study include minimizing total costs, minimizing CO2 emissions, and maximizing job opportunities based on integrated strategic and tactical decisions. The primary focus of this paper is decision-making for optimal transportation ROUTING, considering time windows and the reliability of facility location based on their failure rates.Methods: Given the uncertainty of the mathematical model parameters, various fuzzy and robust possibilistic programming methods were employed to formulate the model. Four different models were used to manage the uncertainty of demand parameters and transportation costs, and the results were compared. Additionally, two methods—an exact solution approach and a meta-heuristic algorithm—were employed to solve the multi-objective mathematical model. The enhanced epsilon constraint method was used to analyze small-scale mathematical models and conduct sensitivity analyses, while the NSGA-II algorithm was applied to solve larger-scale numerical examples. Furthermore, an initial solution based on prioritization was utilized for the meta-heuristic algorithm.Results and discussion: The results indicate that although an increase in uncertainty rates leads to more job opportunities, it also raises total costs and greenhouse gas emissions. Additionally, the analysis reveals that the RPP-III method achieves the highest model robustness cost with the lowest standard deviation. In the reliability analysis, it was observed that higher facility failure rates result in an increased number of located production and distribution centers. This, in turn, leads to higher total costs, increased CO2 emissions, and more job opportunities. By analyzing 15 numerical examples, it was also found that NSGA-II is highly efficient in solving the mathematical model compared to the enhanced epsilon constraint method.Conclusion: The findings of this research assist managers in making strategic decisions such as facility location and tactical decisions such as vehicle ROUTING in the context of market uncertainty. Given that the model incorporates various realistic decisions and assumptions, the mathematical model can be effectively applied in distribution industries, particularly for pharmaceutical and electronic goods.

In order to manage the expenditures in a road transportation network in which the transport demands between cities are less than a truckload capacity, one needs to determine the location of hubs at first, and then collect the cargo from the cities in some routes which are assigned to the appropriate hubs. In this paper, a special case of hub LOCATION-ROUTING issue was considered that is suitable for the particular conditions of Iran as cities are located in the sparse and distant places. A mixed integer mathematical programming model was proposed. As the model is NP-hard in nature, a two-phase hybrid method including genetic algorithms and simulated annealing was designed to solve the model. The results of the comparison between the model and the outputs demonstrated the accuracy and speed of the proposed solution method.Finally, a real case including all 31 capital cities of Iran provinces was solved to illustrate the appropriate performance of the solution method.

The main objective of sustainable supply chain is to balance the economic, environmental, and social goals that companies have to use closed-loop supply chains for cost reduction and increasing the efficiency of the supply chain. According to the research literature, considering the risk in supply chains, especially the return supply chain, is one of the topics that has been little studied. Therefore, the aim of this study is to locate the components of a three-objective, sustainable closed-loop, MULTI-COMMODITY, and multi-period supply chain, considering uncertainty and market scenarios with a risk approach. Location in the sustainable closed-loop supply chain, considering the risk, and also paying attention to the quality of manufactured products and different scenarios of demand are among the innovations of this research. Due to the NP-Hard nature of the problem, the model is solved by the nondominated sorting genetic algorithm II (NSGA-II). Sensitivity analysis has been performed on the parameters of the problem, and the efficiency of the studied methods has been investigated. The average Pareto points obtained from the first objective function is 56789. 9, the average Pareto points for the second objective function is 1828. 8 and for the third objective function is 77365. 32, and also the average solution time of the model is 15. 9 seconds.

Planning the freight flow from the plants to the customer zones is one of the most challenging problems in the field of supply chain management. Because of many traffic regulations, oversize/overweight vehicles often are not permitted to enter city boundaries. Therefore, intermediate facilities (city distribution centers) play a very important role in distribution networks. Accordingly, in this paper, transportation of goods from the plants to the customers is considered an integrated process containing two phases, namely, transportation from plant to distribution centers and distribution from city distribution centers to customers using small and environmentally-friendly vehicles. The Transportation Location ROUTING Problem (TLRP) studied can be considered as an extension of the two-echelon location ROUTING problem. Minimizing the operational costs, and the workload balancing of the heterogeneous fleet in the distribution phase are considered as the two objective functions. A mixed integer programming (MIP) model, as well as two solution approaches, based on Multi-objective Particle Swarm Optimization Algorithm, and Non-dominated Sorting Genetic Algorithm, is presented for the problem. In order to illustrate the efficacy of the proposed methods, they have been implemented on test problems of different sizes. The results show the methods are able to produce efficient solutions in a reasonable amount of time.

In a hub location problem network, the flow originated from an origin and shipped to a destination via some selected intermediate nodes called hub nodes since using a discount factor of hubs. The hub nodes are fully interconnected in the traditional hub location problem. In any origin-destination path there exists at least one hub element. Rather than directly connecting any pair of locations, all the paths are handled by the hub node. In this paper, a general configuration of hub location problems is considered. The model is presented for hub LOCATION-ROUTING problem which any network topology can be structured. This model application is in the public transportation, telecommunication systems and financial networks. Incomplete hub network is designed in the model. Furthermore, location and ROUTING decisions are considered simultaneously in the model besides multiple allocation strategy. Moreover, non-hub nodes can be connected directly. Objective function of this model minimizes transshipment cost of flows and cost of constructing the network. Family of valid inequalities and some preprocessing are proposed to strengthening the model linear relaxation lower bound and improving solution time. Computational results over test problems driven from the literature show that using all valid inequalities and preprocessing perform better than using each of them separately and solve the model in a reasonable solution time.