Abstract
During the last decade, the stringent pressures from environmental and social requirements have spurred an interest in designing a reverse logistics (RL) network. The success of a logistics system may depend on the decisions of the facilities locations and vehicle routings. The location-routing problem (LRP) simultaneously locates the facilities and designs the travel routes for vehicles among established facilities and existing demand points. In this paper, the location-routing problem with time window (LRPTW) and homogeneous fleet type and designing a multi-echelon, and capacitated reverse logistics network, are considered which may arise in many real-life situations in logistics management. Our proposed RL network consists of hybrid collection/inspection centers, recovery centers and disposal centers. Here, we present a new bi-objective mathematical programming (BOMP) for LRPTW in reverse logistic. Since this type of problem is NP-hard, the non-dominated sorting genetic algorithm II (NSGA-II) is proposed to obtain the Pareto frontier for the given problem. Several numerical examples are presented to illustrate the effectiveness of the proposed model and algorithm. Also, the present work is an effort to effectively implement the e-constraint method in GAMS software for producing the Pareto-optimal solutions in a BOMP. The results of the proposed algorithm have been compared with the e-constraint method. The computational results show that the e-constraint method is able to solve small-size instances to optimality within reasonable computing times, and for medium-to-large-sized problems, the proposed NSGA-II works better than the e-constraint.
Highlights
During the last decade, growing attention has been paid to reverse logistics network design (RLND), which focuses on the backward network
The main contributions of this paper that differentiate our efforts from those already published on this issue can be summarized as follows: (1) We introduce a new formulation of the CLRPTW, in which vehicle routing is considered in first echelon and facilities location is considered for collection and inspection centers, recycling centers
This paper has presented a new bi-objective locationrouting problem (LRP) with attributes such as multi–level in a reverse logistics network, multiple depots, capacitated and heterogeneous fleets of vehicles, soft time windows, and penalty cost
Summary
During the last decade, growing attention has been paid to reverse logistics network design (RLND), which focuses on the backward network. We have utilized a bi-objective capacitated location-routing problem with soft time window (LRPTW) and with four layers (e.g., collection and inspection centers, recycling centers, disposal centers and customers) in reverse logistics and heterogeneous vehicle fleet with capacity. LRP deals with determining the location of facilities and the routes of the vehicles for serving the customers under some constraints, such as facility and vehicle capacities, route time, to minimize total cost including transportation costs, vehicle fixed costs, facility location fixed costs, recycling centers operating costs and penalty cost and to satisfy demands of all customers by minimizing total time as second objective function. Computational experiments are presented and analyzed in ‘‘Comparative methods’’, and the summary of conclusions is explained in ‘‘Computational experiments’’
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