## 5 Conclusions  
In this paper, a fuzzy stochastic PDP has been considered for an SCS which includes four echelons. The PDP handled in this study was considered by [PERSON] [1] and modeled as a 0-1 mixed integer model. He developed a solution procedure and successfully implemented it for small SCS. However, it is not possible to solve the mathematical model global optimally by using optimization packages for large SCS because of the binary variables which are designed for selecting routes between echelons in SCS. Therefore, it is required to develop meta-heuristic algorithms to solve NP-hard PDP. In this study, we have developed two meta-heuristic algorithms, GA and ACO, in order to solve [PERSON]'s model for large size SCS. In the solution process of PDP, meta-heuristic algorithms (GA/ACO) are performed for route optimization. By determining routes, 0-1 mixed integer model is converted into a deterministic linear programming model and can be solved optimally by the COIN-OR solver of GAMS. The proposed solution approaches have been performed for randomly generated test problems. The results of the test problems have showed that both proposed meta-heuristic algorithms are capable of solving the problem where the GA obtain better solutions than the ACO. In real-life applications, some parameters of the PDP can be affected by the conditions of dynamic market structure and it is not possible to define them precisely in the decision making process at the tactical or strategic level. This challenge can be overcome by including the manager's expertise and judgments into the modeling process by using fuzzy, random fuzzy, and fuzzy random parameters. Therefore, decision or policy makers can manage the large production and distribution systems more effectively by using the proposed approach. The proposed approach can be used in several industries, such as automotive, electronic devices, and textiles, by implementing the proposed extended procedure in ten steps. The proposed approach is implemented iteratively for real-life problems. In each solution, the proposed approach produces several performance values that show capacity usage proportions in the production-distribution system. In this way, decision makers can detect the bottlenecks in the system and take preventive measures for balancing the capacities of supply, transport, manufacture, and storage. On the other hand, the proposed approach can be used to manage customer demand. The proposed approach enables the analysis of the results of changes in demand quantity on profitability by using random fuzzy parameters. Therefore, managers can specify their marketing and pricing strategies. Consequently, decision makers can evaluate the effects of different predictions and judgments by performing the proposed approach several times. There are two main limitations of the proposed approach. The first one is determining the minimum acceptable possibility degree (\(\alpha\)) which represents the decision maker satisfaction level and takes values between 0 and 1. A very low possibility degree may cause obtaining an optimistic and unrealistic solution. On the contrary, a very high possibility degree may cause obtaining a conservative solution which can be feasible, but not robust. Therefore, the proposed approach has to be performed with different \(\alpha\) values in real-life applications, which means longer processing time. The second one is starting with the GA/ACO with a better feasible solution. According to the nature of proposed approaches, the starting solutions have just been selected randomly. This situation directly affects the processing time which is required to approximate the optimal solution. If GA/ACO start from a better feasible solution, they reach the best solution which is close to the optimal value in a shorter processing time.