A multi-objective stochastic programming approach with untrusted suppliers for green supply chain design by uncertain demand, shortage, and transportation costs

In recent decades, people are paying more attention to protecting the environment and biological resources. One of the most important issues of environmental pollution is air pollution, with production and transportation contributing a significant number of emissions. Considering the various warnings about the excessive increase in the amount of carbon dioxide on the planet, it is necessary to investigate the solutions to reduce the emission of carbon dioxide. On the other hand, in the production cycle, providing more comprehensive models and finding more optimal designs will play a significant role in reducing energy consumption and increasing profitability. Models with the most uncertain parameters are more practical and closer to the real world. In this paper, we consider a multi-objective stochastic programming approach for green supply chain design under uncertainty. Demands, supplies, processing, transportation, shortage, and capacity expansion costs are all considered uncertain parameters. At the same time, environmental approaches to reduce air pollution, (specifically reducing carbon dioxide emissions), are presented. Our multi-objective model includes the minimization of the sum of the total cost, the minimization of the variance of the total cost, the minimization of the financial risk or the probability of not meeting a certain budget, and the minimization of the amount of pollution consequent of production and transportation machines. In the following case study, a three-tier supply chain with four suppliers, four production centers, and three product distribution centers with uncertain demand, suppliers, processing, transportation, cost shortages, and capacity development are examined. To solve the model, two meta-heuristic algorithms (multi-objective genetics with faulty sorting and particle swarming) have been developed. The computational results and optimal designs of the supply set were obtained after the implementation of the algorithms, and finally, by performing Sensitivity Analysis and statistical tests, showed that there are two algorithms with good performance and in most cases, the Non-dominated Sorting Genetic Algorithm (NSGA-II) is superior to the Multi-Objective Particle Swarm Optimization (MOPSO).