Fair profit distribution in multi-echelon supply chains via transfer prices

The total profit maximisation of a supply chain may result in an uneven and impractical profit distribution among the members. This work addresses the fair profit distribution within a multi-echelon supply chain using transfer prices. A mixed integer linear programming (MILP) model framework is proposed for the optimal production, distribution and capacity planning of a supply chain of an active ingredient (AI), consisting of AI plants, formulation plants and markets. The transfer prices of the AI from AI plants to formulation plants, and those of products from formulation plants to markets are to be optimised. The proportional and max-min fairness criteria are adopted to define fair profit distributions. Considering bargaining powers of supply chain members, game theoretic solution approaches are developed for fair solutions using Nash bargaining and lexicographic maximin principles. Especially, a hierarchical approach is developed to obtain an approximate optimal fair solution efficiently. The applicability and efficiency of the proposed approaches are demonstrated by two examples, including a real world agrochemical supply chain.