An efficient controlled elitism non-dominated sorting genetic algorithm for multi-objective supplier selection under fuzziness

Supplier selection and order allocation constitute vital strategic decisions that must be made by managers within supply chain management environments. In this paper, we propose a multi-objective fuzzy model for supplier selection and order allocation in a two-level supply chain with multi-period, multi-source, and multi-product characteristics. The supplier evaluation objectives considered in this model include cost, delay, and electronic-waste (e-waste) minimization, as well as coverage and weight maximization. A signal function is used to model the price discount offered by the suppliers. Triangular fuzzy numbers are used to deal with the uncertainty of delay and e-waste parameters while the fuzzy Technique for Order Performance by Similarity to Ideal Solution (TOPSIS) is used to obtain the weights of the suppliers. The resulting NP-hard problem, a Pareto-based meta-heuristic algorithm called controlled elitism non-dominated sorting genetic algorithm (CENSGA), is developed. The Non-dominated Sorting Genetic Algorithm (NSGA-II) and Multi-Objective Particle Swarm Optimization (MOPSO) are used to validate the applicability of the CENSGA algorithm and the Taguchi technique to tune the parameters of the algorithms. The results are analysed using graphical and statistical comparisons illustrating how the proposed CENSGA dominates NSGA-II and MOPSO in terms of mean ideal solution distance (MID) and spacing metrics.