  Contemporary process industries are constantly confronted with volatile
market conditions that jeopardise their financial sustainability. While mature
markets transition to oligopoly structures, the supply chain operation should
adapt to a more customer-centric focus. Key issues related to the modelling and
impact of the related contractual agreements between firms and customers remain
largely unexplored. In the present work, we examine the problem of fair
customer allocation in oligopolies under different contractual agreements
within a multi-period setting. We consider an ensemble of contract types that
vary in terms of pricing mechanisms and duration. The role of fairness is
examined following the social welfare and Nash bargaining scheme. In the latter
case, the overall problem is formulated as an MINLP. For its efficient solution
we employ a piecewise linearisation strategy based on special-ordered sets. The
impact of the different fairness schemes on the optimal customer allocation is
evaluated via two case studies from the industrial gases market.
