A Bi-Level Robust Optimization Model in Production Planning by Consideration of Pricing Decisions for Satisfying the Demand in a Competitive Environment: a Case Study

Bi-level programming is a mathematical programming, which there is another optimization problem at its constraints. According to the current fierce competition between large production companies to obtain a greater share of the market, this study develops a bi-level robust optimization model as the leader and the follower using Stackelberg game in the field of production planning. The leader company with higher leverage has decided to produce some new products that can be replaced with the existing products. The follower companies as a competitor, similar to the leader company, are looking to sell more. The follower companies do not have any intent and ability to produce such new products. Prices of the new products are determined using the tensile relations, which presented between the uncertain demand and price, creating the game between two levels of the model. After the linearization, the bi-level robust model is transformed to standard single-level model using conditions of Karush–Kuhn–Tucker (KKT). Finally, the accuracy and efficiency of the developed model have been verified by using the real data of Sarvestan Sepahan Company in Isfahan as the leader in the competitive market.