Solving a tri-objective supply chain problem with modified NSGA-II algorithm

In this paper, we propose the modification of an existing Multi-Objective Evolutionary Algorithm (MOEA) known as Non-dominated Sorting Genetic Algorithm-II (NSGA-II). The proposed algorithm has been applied on a tri-objective problem for a two echelon serial supply chain. The objectives considered are: (1) minimization of the total cost of a two-echelon serial supply chain and (2) minimization of the variance of order quantity and (3) minimization of the total inventory. The variance of order quantity is an important factor to consider since the variance of order quantity is used to measure the bullwhip effect which is one of the performance measures of a supply chain. The supply chain under consideration is assumed to consist of buyers and supplier. The production process at the supplier is an imperfect production process and thus produces defective items. A percentage of defective items are sold at a secondary market and the remaining defective items are repaired. We have introduced a mutation algorithm which has been embedded in the proposed algorithm. Since the proposed mutation algorithm is performed over the entire population, thus the mutation algorithm has caused the modification of the parts of the original NSGA-II. The results of the modified algorithm have been compared with those of the original NSGA-II and SPEA2 (Strength Pareto Evolutionary Algorithm 2) evolutionary algorithms for varying values of probability of crossover. The experimental results show that the proposed algorithm performs significantly better than the original NSGA-II and SPEA2.