Development of a Heuristic Method for Solving the Problem of Optimizing a Feed Mixture Production Plan with Fuzzy Constraints

The compilation of optimal production plans often requires consideration of the fuzziness in certain initial information. Therefore, a pertinent issue in the theory and practice is the solution of production plan optimization problems under conditions of fuzzy information using mathematical models and tools of fuzzy sets. The research aims to develop various formulations for optimization problems of production plans using the example of a feed production plan. The problem is addressed based on a modified model considering fuzzy constraints by adapting various optimality principles. The research focuses on the processes of feed mixture production at the Makinsk poultry farm, characterized by fuzzy constraints on feed composition. New formulations of optimization problems under fuzzy constraints are obtained in the form of fuzzy mathematical programming problems, and heuristic methods for their solution are proposed. Various scenarios are considered, where the original multi-criteria optimization problem can be reduced to a single-criterion problem. For each formulation of the optimization problem, modifications of Pareto optimality methods and the main criterion are applied, ensuring the effective utilization of expert information and the decision maker’s knowledge during the optimization process and the selection of the best solution.