A robust-fuzzy-probabilistic optimization model for the multi-objective problem of a sustainable green integrated production system under uncertainty

The design of a problem involving a sustainable integrated production system under uncertainty are covered in this article. The presented model aims to create an integrated production system that will lower costs across the board and greenhouse gas emissions. The robust-fuzzy-probabilistic (RFP) optimization method is used to control the non-deterministic parameters of the problem. The model's exact solution yielded calculation results that demonstrate that as greenhouse gas emissions have decreased, the production system's costs have increased as a result of changes in the number of machines and their technological capabilities. The outcome also demonstrates that as the uncertainty rate rises, the production system's level of demand also rises, which results in a rise in production. Costs and greenhouse gas emissions rise as a result of this increase in production. Additionally, the findings demonstrate that raising the average recycling rate improves the production system's stability. Because this is an NP-hard issue, many different optimization strategies have been tried, including the multi objective grey wolf optimizer (MOGWO) and the Non-dominated Sorting Genetic II (NSGA II). looking at the numerical examples of various sizes reveals that these algorithms have near-optimal solutions much more quickly and with much higher efficiency than the exact method.