توزیع سود عادلانه در زنجیره تامین پلکانی از طریق قیمت های انتقال Fair profit distribution in multi-echelon supply chains via transfer prices

1. Introduction Over the past decades, supply chains have been reshaped into complex networks involving suppliers, production sites, distribution facilities and markets. The optimisation of supply chains in the process industry has received extensive attention in the literature (Grossmann, 2005; Shah, 2005; Papageorgiou, 2009; Barbosa-P´ovoa, 2012). Many supply chain optimisation models and approaches just consider one supply chain as a whole (Tsiakis & Papageorgiou, 2008; Sousa et al., 2011; Longinidis & Georgiadis, 2011; Liu et al., 2012; Cardoso et al., 2013; Mu˜noz et al., 2015; Gaur et al., 2017). However, in real practice, there are conflicting interests of individual supply chain members that all aim to pursue the most profit and benefit for themselves, which need to be taken into account for optimisation. When the total profit of a supply chain is maximised to enhance its performance, the profit of the whole supply chain is usually distributed to its members in an uneven way, which could lead to negative impacts, including dissatisfaction of members, instability of systems and coalition, disadvantage in competitive edge, loss of markets, increasing costs and reduction in revenue. Thus, a fairer profit distribution is preferred to maintain stability and competitiveness of supply chain networks. The fairness issues have been widely investigated in some fields, e.g. welfare economics (Varian, 1975; Fleurbaey, 2008), telecommunications (Jain et al., 1984; Mazumdar et al., 1991), and supply chain contracting (Cui et al., 2007; Katok & Pavlov, 2013; Ho et al., 2014). The concept, perception and interpretation of fairness vary depending on problems and people involved, and there is no single fairness criterion applicable to all problems. In the literature, there are two widely accepted fairness criteria: proportional fairness and max-min fairness (Bertsimas et al., 2011), which satisfy a set of generally agreed axioms for ideal fairness criterion. This paper aims to develop an optimisation framework for fair profit distribution among supply chain members using transfer prices under these two fairness criteria.