Mathematical Model of Load Balancing Algorithm in Workshop Systems (Quantitative Study)

Balanced production line in terms of timing and load distribution on machines can improve the important indicators of timely delivery and production, which creates customer satisfaction and competitive advantage for production.Production line balance reduces lost capacity costs and unbalanced lines.Robin Hood algorithm is one of the production balance methods, the most important advantage of which is online production planning and proportional distribution of load on machines, but when the number of work orders is large, this method is not responsive.This paper focuses on optimizing and developing the mathematical model of Robin Hood algorithm so that this model can plan a large number of work orders.Development of the model with two objectives minimizing the maximum load on the production system and minimizing the order completion time Takes place on machines.The problem of production balance is one of the NP-hard problems, and since no Iuick and feasible solution to such problems has been found in a reasonable time, the NSGA algorithm can be found to find close to optimal solutions to the proposed multi-objective mathematical model.-II has been used.The results of the development of the mathematical model in Robin Hood algorithm show that the balance of the production line in the large number of orders and momentary changes in the production plan, using this method can improve production planning.