## 4 Computational Experiments
According to the negative and positive ideal solutions for \(Z_{1}\), \(Z_{2}\), and \(Z_{3}\), it can be observed that the GA shows better performance than ACO in four of six problems. However, these solutions are used as lower and upper limits for the membership function in \(Z_{4}\). The optimal solution of \(Z_{4}\) cannot be obtained at the lower or upper bounds of membership functions because of conflicting objectives. Therefore, the comparative solutions of ACO and GA for \(Z_{1}\), \(Z_{2}\), and \(Z_{3}\) are not significant indicators in determining the best meta-heuristic approach. The main problem that determines the best performance for proposed meta-heuristic algorithms is \(Z_{4}\). According to the ACO, the positive ideal solution and negative ideal solution values of the objective functions are found as (15,742,124, 4,421,268), (45,856,319, 78,583,274), and (4,964,094, 15,906,761) for Z\({}_{1}\), Z\({}_{2}\), and Z\({}_{3}\), respectively. When the equivalent single-objective 0-1 mixed integer programming model of the auxiliary MOMILP problem is solved, the total profit is obtained as a triangular possibility distribution with (54,920,893, 66,474,301, 78,332,275) and the overall degree of decision maker (DM) satisfaction with multiple goal values is achieved at 0.63. On the other hand, GA obtained the positive ideal solution and negative ideal solution values of the objective functions as (15,757,821, 4,694,713), (45,781,117, 79,004,432), and (4,852,275, 15,781,522) for \(Z_{1}\), \(Z_{2}\), and \(Z_{3}\), respectively. When the equivalent single-objective 0-1 mixed integer programming model is solved, the total profit is obtained as a triangular possibility distribution with (56,243,986, 68,505,864, 80,833,744) and the overall degree of DM satisfaction with multiple goal values is achieved at 0.684.,  
Total profits in triangular fuzzy numbers can be defuzzified by using the expected value (\(EV\)) of fuzzy numbers which is given in Equation (37):  
\[EV(\widetilde{c})=\frac{c^{p}+2c^{m}+c^{o}}{4} \tag{37}\]  
The expected profit values of the ACO and GA have been calculated as 66,550,442 and 68,522,364 Turkish Lira, respectively, by using Equation (37). According to the total profit and DM satisfaction level, it can be concluded that GA found better solutions than ACO. The solutions of the proposed algorithms are summarized in Tables 5-7 because of large sizes of indices. Although ACO produces more product 1 and 2 (j1 and j2), its production quantity for product 3 is significantly smaller than the GA. Therefore, GA produced and sold more products than the ACO in total. The available capacities of the plants are not adequate to meet all demand. This situation caused to backorders. Therefore, there are no inventories in warehouses and retailers. Total backorder level of GA is smaller than ACO which enables reducing the cost in GA. According to the total purchased raw material quantities by plants, it can be absorbed that the numbers of raw materials supplied GA and ACO are close to each other. However, while GA supplied raw materials from 13 different suppliers, ACO used 23 suppliers. Cooperating with more suppliers means extra fixed transportation.