A new MILP model proposal in feed formulation and using a hybrid-linear binary PSO (H-LBP) approach for alternative solutions

Large-scale feed factories may have multiple production and storage facilities. Any production facility uses its own available raw materials while performing feed formulation. However, ensuring a reasonable cost is achieved, and the desired quality criteria are met, may require obtaining a certain amount of raw material from other facilities. Selecting a specific amount of raw materials among many raw materials in different facilities requires many combinations to be tried out. Providing solutions, especially when there is a large amount of the raw material, may be costly and take more time. A new mixed-integer linear programming (MILP) model that specifies the type of material and the amount of the material to be selected from external facilities has been proposed in this study. When deterministic methods like MILP are used, only one solution result is obtained. However, when the decision-maker would like to see alternative results, solution constraints can be mitigated and a solution provided within the same or similar time. A new method named hybrid-linear binary PSO (H-LBP) has been proposed in this study for the problems that the decision-maker had limited time for and for which the solution results were required in a shorter time. Continuous particle swarm optimization, which works as a hybrid with linear programming, has been used in this method. The new model proposed in this study was tested on the mixed feeds for sheep, cattle and rabbit species by using both MILP and the proposed H-LBP methods. Raw materials determined by the model were added to the mixture, and the cost in each of the three species was observed to go down. In addition, different alternative solutions at reasonable cost and similar quality were presented to the producer/decision-maker in a shorter time.