(604a) Multi-Period Game-Theoretic Customer Allocation in Oligopolies Under Contractual Agreements

Contemporary process industries are constantly confronted with volatile market conditions that jeopardise their financial sustainability, leading towards a paradigm shift with the emergence of oligopolies in mature markets [1]. In order to eliminate competition, consolidate their strategic position and secure the stability of these oligopolies, decentralised optimisation schemes that take into account the different, possibly conflicting objectives, are of paramount importance. Lexicographic minimax methods [2], Nash equilibrium approaches [3], Stackelberg games [4] as well as bi-/tri-level programming schemes [5,6] have been proposed in the literature to examine the impact of decentralisation on the optimal decision making within supply chain systems. In this context, the problem of incorporating contracts selection within the process of decision making has been investigated by a few researchers focusing on the procurement of raw material and selling prices [7, 8] from a centralised decision making viewpoint. Notwithstanding, an important problem is concerned with the allocation of customers among different competing companies since it directly impacts operational and strategic decisions of the supply chain. Recently, a static game-theoretic approach for the fair customer allocation within oligopolies was proposed [10]. Different scenarios were explored and it was shown how operational flexibility can affect the negotiation power of the different firms as well as how fairness considerations affect customer allocation among competitors. Nonetheless, key issues related to the modelling and the 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 sales prices and duration. Key decisions include: (i) optimal production, inventory & energy consumption levels of the firms’ plants that comprise the oligopoly, (ii) allocation of customers to firms & (iii) sequencing of contracts with different duration and pricing policies between the firms and the customers. For the sequencing of contracts, we further explore tight MILP formulations so as to enhance computational performance. The role of fairness is investigated via the Nash bargaining approach and the overall problem is formulated as a convex MINLP. For its efficient solution we employ two different solution techniques, i.e. (i) an outer approximation branch & refine global optimisation method [11] and (ii) a piecewise linearisation strategy. The model capabilities and the role of fairness are evaluated through case studies from an industrial liquids market.

References

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