## 4 Computational Experiments  
The computational experiments described in this section have been conducted in order to analyze the performance of the proposed solution procedures. According to our best knowledge, this is the first study that handles PDP for a large SCS which includes multiple-supplier, multiple-product, multiple-plant, multiple-warehouse, multiple-retailers, multiple-transport paths, and multiple time periods. Thus, any data for comparison does not exist. Therefore, five test problems have been considered to evaluate the proposed algorithms which are randomly generated. On the other side, proposed ACO and GA have been compared with a Simulated Annealing (SA), which is a well-known and widely used algorithm in order to analyze and observe the superiorities (or weakness) of them. SA is a general form of optimization which refers to tempering materials such as alloys of metal, glass etc. by heating and cooling to reach perfect atomic structure [64]. SA is based on finding global optima using hill climbing method. Firstly, movement (position) is selected randomly from a pool of all possible movements and applied to the objective function. Then, if the current movement improves the solution it is accepted and the search area is moved to this position. Otherwise, the next movement is chosen from other ones, which are probably less than current [65]. The pseudo-code of SA is given in Table 10 in Appendix A. In each test problem, there are six parameters: the number of suppliers (s), the number of plants (p), the number of warehouses (w), the number of retailers (r), the number of time periods (t), and the number of transportation paths (_k_) between echelons of the SCS. The characteristics of test problems are given in Table 3. There are five raw materials and one product in each test problem. The proposed algorithms were implemented in MATLAB (The MathWorks Inc., New York, NY, USA), using the COIN-OR (Computational Infrastructure for Operations Research) solver of GAMS (GAMS Software GmbH, Frechen, Germany) optimization package. The computational experiments and validation were performed on a PC with Intel (Core i7-7700K CPU at 4.20 GHz having 64 GB RAM. In each test problem, \(\alpha\) and \(\beta\) values were set as 0.4 and 0.95 respectively. Test problems were solved by COIN-OR and the optimal solutions for NIS and PIS of \(Z_{1}\), \(Z_{2}\), \(Z_{3}\), and \(Z_{4}\) are given in rows which are entitled \"Optimal\" in Table 4. On the other hand, the proposed ACO and GA were repeated five times with 250 iterations for each test problem. The best solutions for NIS and PIS of \(Z_{1}\), \(Z_{2}\), \(Z_{3}\), and \(Z_{4}\) obtained by the proposed approaches are reported in Table 4. The performances of the proposed algorithms are measured in terms of the solution gap (in %). The proposed algorithms achieved to obtain optimal solutions for Problem 1 and 2 which are small in size. When the size of the problem increases, such as in Problems 3, 4, and 5, the proposed approaches are capable of obtaining near-optimal solutions in an acceptable gap. It can be stated that the results of the ACO and GA approaches are close to each other while the GA finds relatively better solutions. According to the gaps (%) given in Table 4, ACO and GA obtained lower values than SA in test Problems 3, 4, and 5. It is observed that the proposed ACO and GA approaches are more promising methods for fuzzy stochastic PDP than SA. After the validation and verification of proposed approaches, a new test problem (Problem 6), which has a larger size than the other problems, was generated. Only ACO and GA have been performed to Problem 6 because of their robustness. Problem 6 includes 40 suppliers (s = 40) 12 raw materials (_i_ = 12), three plants (_p_ = 3), three products (_j_ = 3), 12 warehouses (_w_ = 12), 40 retailers