Advances in supply chain operations under uncertainty: game theoretic and global optimisation methods

Supply chains are inherently exposed to uncertainty leading to significant operational disruptions and financial inconsistency. Increasing the resilience and profitability of supply chain operations requires the development of novel methodologies that integrate state-of-the-art optimisation techniques. This thesis addresses this challenge via: (i) the development of global optimisation methodologies to address non-convex problems through the lenses of robust optimisation and (ii) the fair and optimal supply chain planning using a two-stage stochastic framework. For the first part of the thesis, a novel global optimisation algorithm for Quadratically Constrained Quadratic Programming (QCQP) problems is developed. The proposed Robust spatial Branch-and-Bound (RsBB) algorithm integrates Branch-and-Bound and robust cutting plane algorithms. The research hypothesis for this work is that a concurrent robust and optimality search can lead to computational benefits. The performance of the algorithm is evaluated in benchmark pooling problems. The proposed RsBB algorithm results in computational improvements compared to the state-of-the-art methodologies. To further accelerate the performance of the RsBB algorithm, a multi-parametric programming approach is examined. In the multi-parametric variation of the RsBB algorithm, the inner-maximisation problem is replaced by function evaluations resulting in computational time savings of up to 99\% compared to the original algorithm. For the second part of the thesis, the fair and optimal supply chain planning of oligopolistic industrial gases market is evaluated. Initially, a deterministic multi-period model for the supply chain is developed, employing contractual agreements of varying duration and pricing mechanisms. A game-theoretic framework is proposed for the fair profit allocation among the oligopoly firms. Oligopoly markets are susceptible to market uncertainty fluctuations. To address this, a two-stage stochastic model is constructed under product demand and electricity price uncertainty. The stochastic customer allocation increases the resilience of the examined supply chains resulting in higher total profits and more effective utilisation of the oligopoly production plants.