---

A fundamental problem is the use of DEA in multistep or multilevel processes such as supply chain, lack of attention to processes’ internal communications in a way that the recent studies on DEA in the context of serial processes have focused on closed systems that the outputs of one level become the inputs of the next level and none of the inputs enter the mediator process. The present study aimed to examine the general dimensions of an open multilevel process. Here, some of the data such as inputs and outputs are supposed to leave the system while other outputs turn into the inputs of the next level. The new inputs can enter the next level as well. We expand this mode for network structures. The overall performance of such a structure is considered as a weighted average of sectors’ performance or distinct steps. Therefore, this suggested model in this study, not only provides the possibility to evaluate the performance of the entire network, but creates the performance analysis for each of the sub-processes. On the other hand, considering the data with undesirable structure leads to more correct performance estimation. In the real world, all productive processes do not comprise desirable factors. Therefore, presenting a structure that is capable of taking into account the undesirable structure is of crucial importance. In this study, a new model in the DEA by network structure is offered that can analyze the performance considering undesirable factors.

---

In this study, a bi-objective model for integrated planning of production-distribution in a multi-level supply chain network with multiple product types and multi time periods is presented. The supply chain network including manufacturers, distribution centers, retailers and final customers is proposed. The proposed model minimizes the total supply chain costs and transforming time of products for customers in the chain. The proposed model is in the class of linear integer programming problems. The complexity of the problem is large and in the literatur, this problem has been shown to be NP-hard. Therefore, for solving this problem, two multi objective meta-heuristic approaches based on Pareto method including non-dominated Sorting Genetic Algorithm-II (NSGA-II) and non-dominated Ranking Genetic Algorithm (NRGA) have been suggested. Since the output of meta- heuristic algorithms are highly dependent on the input parameters of the algorithm, Taguchi method (Taguchi) is used to tune the parameters. Finally, in order to evaluate the performance of the proposed solution methods, different test problems with different dimensions have been produced and the performances of the proposed algorithms on the test problems have been analyzed.