7. Conclusions
This work addressed the fair profit distribution problem within a three-echelon supply chain network in the process industry, consisting of AI plants, formulation plants and markets with different bargaining powers. An MILP-based decision framework has been developed for production, distribution and capacity planning of the supply chain network. To achieve a fair profit distribution among all supply chain members involved, game theoretic approaches using Nash bargaining and lexicographic maximin principles were adopted under two different fairness criteria, proportional and max-min fairness. Especially, a tailored computationally efficient hierarchical approach has been proposed for max-min fair solutions. Two examples were examined, and computational results showed that both Nash bargaining and lexicographic maximin approachs can achieve fairer profit distribution, compared to what obtained by maximising total profit, in terms of proportional and max-min fairness, respectively. The effects of bargaining powers of supply chain members on profit distribution were studied. For large instances where the classic iterative lexicographic maximisation approach is highly time consuming, the proposed hierarchical approach is able to find good approximate optimal max-min fair profit distributions with much less computational efforts. At last, through sensitivity analysis, the values of an important parameter in the proposed hierarchical approach was investigated.
As to the future research directions, uncertainties of product demands can be considered and incorporated into the optimisation. In addition, the competition between products in the same group at markets can be studied. More detailed planning and scheduling decisions at plants can also be considered (Liu et al., 2008, 2010a,b, 2012). This work can be further extended to global supply chain networks, considering additional features, e.g., different tax rates and exchange rates.
