A multi-objective two-echelon location-routing problem for cash logistics: A metaheuristic approach

A two-echelon location routing problem considering sustainability and hybrid open and closed routes under uncertainty

Location-routing is an extremely important problem in supply chain management. In the location-routing problem, decisions are made about the location of facilities such as distribution centers as well as the set of vehicle routes. Today, organizations seek to reduce the transportation cost by outsourcing leading to a particular kind of transportation problems known as open routing. However, the increasing attention to environment have led to paying more attention to environmental issues and reducing the environmental impacts of logistics activities. To this end, in this paper, both open and closed routes were simultaneously addressed by developing a multi-objective mixed integer linear programming model that included three economic, environmental, and social responsibility aspects. The three objective functions of the proposed model encompass the minimization of total costs and greenhouse gas emissions, and the maximization of employment rate and economic development. Also, in this study, a different type of routing was considered in each echelon. A small-sized problem instance was solved using the Augmented Epsilon Constraint (AEC) method with the CPLEX Optimizer Solver for the validation of the proposed model. Moreover, the sensitivity analysis was performed to investigate the effect of changing main parameters on the values of the objective function. Due to the NP-Hardness of the problem, two efficient metaheuristic algorithms of Non-dominated Sorting Genetic Algorithm (NSGA-II) and Multi-Objective Stochastic Fractal Search (MOSFS) were exploited to solve the medium and large size problems. The performance of the algorithms was compared on the basis of six different well-known indexes of Time, MID, RAS, Diversity, Spacing, and SNS. According to the obtained results, the performance of the MOSFS algorithm was %20, %9, %11.22, %10.03, and %19.06 higher than the performance of the NSGA-II on the basis of SNS, RAS, MID, Diversity, and Time indexes, respectively. On the other hand, the NSGA-II performance was %6.3 higher than the MOSFS performance in terms of Spacing index.

Green two-echelon closed and open location-routing problem: application of NSGA-II and MOGWO metaheuristic approaches

Nowadays organizations outsource transportation of goods or services to reduce cost which leads to a particular type of problem called open location-routing. Also, each logistic organization possesses a limited number of specific vehicles that may not be enough in certain circumstances. This issue indicates the importance of simultaneously considering both open and closed routs. On the other hand, the growing concerns about the detrimental environmental impacts of human activities reveal the necessity of paying attention to environmental issues in logistics. In this study, a bi-objective mathematical programming model is proposed for two-echelon close and open location-routing problem (2E-COLRP) including two echelons of factories, depots and customers to minimize costs and CO2 emissions. The proposed model finds the optimal routs, optimal number of vehicles and facilities as well as the locations of facilities. The augmented epsilon constraint method is used as an exact method to solve the small-sized problems. Due to complexity of model, two metaheuristic algorithms named MOGWO and NSGA-II are utilized to tackle the problems. The efficiency of two aforementioned algorithms is evaluated in terms of several indices considering 22 problem instances with various sizes. The results show that MOGWO performs better than NSGA-II.