A New Bi-objective Mathematical Model to Optimize Reliability and Cost of Aggregate Production Planning System in a Paper and Wood Company

In this research, a bi-objective model is developed to deal with a supply chain including multiple suppliers, multiple manufacturers, and multiple customers, addressing a multi-site, multi-period, multi-product aggregate production planning (APP) problem. This bi-objective model aims to minimize the total cost of supply chain including inventory costs, manufacturing costs, work force costs, hiring, and firing costs, and maximize the minimum of suppliers' and producers' reliability by the considering probabilistic lead times, to improve the performance of the system and achieve a more reliable production plan. To solve the model in small sizes, a ε-constraint method is used. A numerical example utilizing the real data from a paper and wood industry is designed and the model performance is assessed. With regard to the fact that the proposed bi-objective model is NP-Hard, for large-scale problems one multi-objective harmony search algorithm is used and its results are compared with the NSGA-II algorithm. The results demonstrate the capability and efficiency of the proposed algorithm in finding Pareto solutions.