A new spanning tree-based genetic algorithm for the design of multi-stage supply chain networks with nonlinear transportation costs

Abstract

The design of configuration and the transportation planning are crucial issues to the effectiveness of multi-stage supply chain networks. The decision makers are interested in the determination the optimal locations of the hubs and the optimal transportation routes to minimize the total costs incurred in the whole system. One may formulate this problem as a 0-1 mixed integer non-linear program though commercial packages are not able to efficiently solve this problem due to its complexity. This study proposes a new spanning tree-based Genetic Algorithm (GA) using determinant encoding for solving this problem. Also, we employ an efficient heuristic that fixes illegal spanning trees existing in the chromosomes obtained from the evolutionary process of the proposed GA. Our numerical experiments demonstrate that the proposed GA outperforms the other previously published GA in the solution quality and convergence rate.

A possibilistic approach to the modeling and resolution of uncertain closed-loop logistics

“…Abuali et al (1995) proposed the determinant encoding and proved that this code is better than that of Prüfer. Both the works of Chou et al (2001) and Yao and Hsu (2009) on logistic networks further confirmed this conclusion. Wang and Hsu (2010a) proposed a revised spanning tree-based genetic algorithm with determinant encoding that was applied successfully to the closed-loop logistics model.…”

“…However, empirical investigations have shown that Prüfer encoding is an unsatisfactory method for evolutionary algorithms and should therefore be avoided (Yeh 2005). However, the spanning tree-based GAs have the advantage of being capable of using the least number of arcs between two stages to solve logistics problems, thereby saving memory and time (Yao and Hsu 2009). Abuali et al (1995) proposed the determinant encoding and proved that this code is better than that of Prüfer.…”

“…Yao and Hsu (2009) showed that no more than (n − 1) links exist when optimality is reached in two consecutive stages in a logistics problem. Wang and Hsu (2010a) emphasized that the rules of spanning tree properties can be relaxed and a possibility of simultaneously improving the solution exists.…”

“…Based on the reports by Chou et al (2001), Yao and Hsu (2009), and Wang and Hsu (2010a), the proper methods for the crossover and mutation of spanning-tree problems are the two-point crossover and exchange mutation. For these methods, the heuristic is applied to restrict the connection of the same stage and to improve the solution.…”

Model-based design of integrated production systems: a review

“…Many optimization methods have been developed and applied to the models mentioned above. These techniques range from linear programming algorithms to more complex ones such as spanning tree algorithms, evolutionary algorithms, taboo search, simulated annealing, and specific heuristics (Current et al 1987;Lotarev 1989;Klempous et al 1994;Babel and Kellerer 2003;Nepal and Park 2005;Creput and Koukam 2007;Song et al 2007;Sanchez-Silva et al 2009;Unnikrishnan et al 2009;Yao and Hsu 2009).…”