A game-theoretic optimisation approach to fair customer allocation in oligopolies
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A game‑theoretic optimisation approach to fair customer allocation in oligopolies Vassilis M. Charitopoulos1,2 · Vivek Dua1 · Jose M. Pinto3 · Lazaros G. Papageorgiou1 Received: 3 July 2019 / Revised: 20 December 2019 / Accepted: 21 December 2019 © The Author(s) 2020
Abstract Under the ever-increasing capital intensive environment that contemporary process industries face, oligopolies begin to form in mature markets where a small number of companies regulate and serve the customer base. Strategic and operational decisions are highly dependent on the firms’ customer portfolio and conventional modelling approaches neglect the rational behaviour of the decision makers, with regards to the problem of customer allocation, by assuming either static competition or a leader-follower structure. In this article, we address the fair customer allocation within oligopolies by employing the Nash bargaining approach. The overall problem is formulated as mixed integer program with linear constraints and a nonlinear objective function which is further linearised following a separable programming approach. Case studies from the industrial liquid market highlight the importance and benefits of the proposed game theoretic approach. Keywords Game theory · Supply chain optimisation · Oligopoly · Nash equilibrium · Customer allocation List of symbols Sets b Outsourcing tiers c Customers cf(c,f ) Set of existing firm’s customers cti(c,t,i) Set of customer’s tanks for product i * Lazaros G. Papageorgiou [email protected] 1
Department of Chemical Engineering, Centre for Process Systems Engineering, University College London, Torrington Place, London WC1E 7JE, UK
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Cambridge Judge Business School, University of Cambridge, Trumpington St, Cambridge CB2 1AG, UK
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Linde.Digital, Linde PLC., 10 Riverview Drive, Danbury, CT 06810, USA
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f Oligopoly firms i Liquid products k Grid points t Customer tanks Parameters 𝛼f Negotiation power of firm f f 𝛿i Short-cut model parameters dependent on the design of the ASU plant (–) 𝜂ff ′ Inter-firm swaps premium 𝛾bL , 𝛾bU Lower and upper bounds of the tiers b for outsourcing product demand (m3) f V LOX Upper limit on the volumetric rate flow of liquid oxygen in the ASU of firm f (m3/h) sq 𝜋f Status quo profit of firm f prior to the fair allocation of the customers ($) 𝜋̃fk Profit of firm f at grid point k ($) f
V air , V air Lower and upper limits on the volumetric rate flow of air in the f
ASU of firm f (m3/h) and upper limits on the volumetric rate flow of gaseous nitrogen in the liquefier of ASU of firm f (m3/h) f f V GNI Pip , V GNI Pip Lower and upper limits on the volumetric rate flow of gaseous nitrogen send to product pipeline by firm f (m3/h) Dict Product demand of customer c for tank t (m3) DCictf Delivery cost of demand of product i for customer c and tank t served by firm f ($) Ecf 1, if customer c is initially contracted to firm f; 0, otherwise EPC Electricity price ($/MWh) FDCcf Fixed cost of firm
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