Modeling Supply Chain Disruptions: A Network Flow Approach

Globalization, outsourcing and cost optimization have all contributed to increased supply chain vulnerability, yet our understanding of effective mitigation strategies remains limited. In our research, we study the effects of disruptions on supply chain networks. To do so, we develop in the first research project a bilevel optimization model to analyze supply chain disruptions in a production setting. This results in a convex network flow problem in which total production cost is minimized under a chance constraint. This chance constraint imposes a bound on the regret of disrupted scenarios with high pre-determined probability, where this regret is defined as a cost surplus which results from a comparison between a reactive setting, where we consider the disruption unknown until it occurs, and an anticipative setting, which assumes the disruption scenario to be known at the beginning of the planning horizon. A generalized Benders decomposition approach which makes use of the problem structure is developed to solve the problem efficiently. In the second research project we study a similar model in which an additional chance constraint on service level is introduced to account for demand uncertainty. We derive an approximation of this model and derive a bound on the approximation error. This approximation model is then solved with the same Benders decomposition procedure as the first model discussed. We obtain managerial insights from both models by means of numerical experimentation. We demonstrate a relationship between the stochastic demand and service level requirements. Moreover, we observe that unused production capacity is a key driver for mitigation inventory. In the last research project we shift our focus towards gaining a more holistic understanding of the supply chain network disruption literature. The number of articles written in the area has increased significantly in the last few years, and with the advent of the Covid-19 pandemic the interest in the area has expanded even further. We perform a literature review with a particular focus on recognizing research gaps. We observe a surprising lack of articles studying assembly supply chains, despite their ubiquity in real world applications. A similar lack of articles is observed in the area of multi-product supply chains as well. Finally, in light of the ongoing Covid-19 pandemic we shift our attention towards the disruptive effect of pandemics on supply chains. We observe that most of the mathematical models of supply chain networks under disruptions discussed in the literature are incapable of accounting for the fact that pandemics disrupt several aspects of supply chain networks simultaneously. Moreover, we observe that a large number of articles studies problems stemming directly from real world applications. The resulting models are often challenging to solve mathematically, so we perform a comprehensive study of solution methods used in the supply chain network literature and highlight multi-objective optimization as an area of utmost importance for current and future research.