Authors:

• Stefano Starita – Sasin School of Management
• Maria Scaparra –  University of Kent, Centre for Logistics and Heuristic Optimisation (CLHO), Kent Business School

This paper examines a mathematical model to improve protection against supply chain disruptions. Supply chains and critical infrastructure systems are vital for the well-being of countries and economies. The need to protect them has been widely recognized by scientists, practitioners, and government agencies alike. Threats such as terrorist attacks, natural disasters, political unrest and, more recently, the Covid-19 pandemic, have highlighted the necessity of mitigation strategies to address disruptive scenarios. Proactive measures to lessen risks and disruptions to essential services have become an imperative agenda for governments and organizations. As a result, expenditures devoted to security and protection efforts have increased significantly over the last decade. However, protection strategies vary depending on the nature of the threat and the infrastructure that needs protecting. For example, a concrete barrier can be built to protect against flooding; hospital capacity can be increased to avoid congestion caused by a pandemic etc. This research focuses on the protection of service or supply facilities in supply systems, where service is provided to customers by their closest facility and efficiency is measured in expected travel costs or distances. The objective of the paper is to answer the following question: how should protective measures be distributed across a supply system which is vulnerable to disruptions, so that the customers’ travel cost is reduced? To answer the question, a mathematical optimization model is introduced, called “the Probabilistic Median Fortification Problem (PMFP)”. This is a non-linear, mixed-integer model and is linearized using probability-chains. A custom GRASP algorithm is also introduced to solve the model. The heuristic is used to highlight numerical difficulties and fine-tune the linearization approach. The paper then applies the PMFP to a real-life problem – a case study using the Toronto general hospital network. This was chosen to highlight how the model can be used to support planning decisions in a healthcare context; a sector particularly in focus due to the COVID-19 pandemic. The study into the hospitals’ network delivers deep insights into how the proposed model can improve healthcare systems. It provides a real-life assessment showing how the hospital could cope better with pressing issues such as high patient demand – a scenario of particular importance during, for example, epidemic or pandemic events. These insights help drive better and more informed decision-making. The case study also shows how robust solutions can be obtained by combining the findings of the model and the findings of a worst-case scenario model in the decision-making process. Being able to show how the model works and its effectiveness in a real-world situation is a key contribution. The paper is published in the Journal of the Operational Research Society. The full article is available for download on Taylor and Francis Online.