A Bi-objective Model for Locating and Allocating in a Green Closed-loop Supply Chain by Probabilistic Customers

A closed-loop supply chain model was proposed to optimize the assignment and position of production and distribution centers, product warehouses, retailers, retailer centers, collection, repair, probabilistic customers, and disposal centers. The goal is to minimize environmental pollution and CO2 emissions by considering CO2 to O2 conversion in vehicle gas converters. Two strategies are explored to determine the best retailer locations based on the predicted movement type (Euclidean Square, Euclidean, Chebyshev, and Rectangular) and expected coverage (time and distance). To compare and select the best strategy, a bi-objective nonlinear programming model was introduced. The model simultaneously examines plans 1 and 2 and chooses the superior plan. Given the strategy selected, a heuristic algorithm is employed to determine the best retailer allocation and locations. Given that the problem is NP-hard in nature, it was solved using a meta-heuristic, the non-dominated sorting genetic algorithm. Finally, to validate the effectiveness, a numerical example is presented and solved using optimization software. The algorithm's findings demonstrate a strong correlation with meta-heuristic algorithms, indicating it as a promising starting point that can be further enhanced by incorporating such methods. For instance, the optimized suggestion algorithm resulted in a reduction of 739 units in carbon dioxide emissions, while the genetic algorithm achieved a reduction of 703 units. Furthermore, the cost computed by the algorithm stands at 7,484,935 units, a figure close to the output of 7,030,846 units generated by the genetic algorithms.