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In operations research, bi-level programming is a mathematical modeling which has another optimization problem as a constraint. In the present research, regarding the current intense competition among large manufacturing companies for achieving a greater market share, a bi-level robust optimization model is developed as a leader-follower problem using Stackelberg game in the field of aggregate production planning (APP). The leader company with higher influence intends to produce new products, which can replace the existing products. The follower companies, as rivals, are also seeking more sales, but they do not have the intention and ability to produce such new products. The price of the new products is determined by the presented elasticity relations between the uncertain demand and price. After linearization, using the KKT conditions, the bi-level robust model is transformed into an ordinary uni-level model. Due to the NP-hard nature of the problem, Benders decomposition algorithm (BDA) is proposed for overcoming the computational complexities in large scale. Finally, using the real data of Sarvestan Sepahan Co as a leader company, the validity of the developed model as well as efficiency and convergence of the BDA are investigated. The computational results clearly show the efficiency and effectiveness of the proposed BDA.

Benders Decomposition Algorithm for Robust Aggregate Production Planning Considering Pricing Decisions in Competitive Environment: A Case Study