Facility Location Problem: Modeling Joint Disruptions Using Subordination

We study the facility location problem with disruptions where the objective is to choose a set of locations that minimizes the sum of expected servicing and setup costs. Disruptions can affect multiple locations simultaneously and are caused by multiple factors like geography, supply chain characteristics, politics, and ownership. Accounting for the various factors when modeling disruptions is challenging due to a large number of required parameters, the lack of calibration methodologies, the sparsity of disruption data, and the number of scenarios to be considered in the optimization. Because of these reasons, existing models neglect dependence or prespecify the dependence structures. Using partially subordinated Markov chains, we present a comprehensive approach that starts from disruption data, models dependencies, calibrates the disruption model, and optimizes location choices. We construct a metric and a calibration algorithm that learns from the data the strength of dependence, the number of necessary factors (subordinators), and the locations each subordinator affects. We prove that our calibration approach yields consistent estimates of the model parameters. Then, we introduce a variant of the standard approach to the underlying optimization problem, which leverages partially subordinated Markov chains to solve it quickly and precisely. Finally, we demonstrate the efficacy of our approach using twelve different disruption data sets. Our calibrated parameters are robust, and our optimization algorithm performs better than the simulation-based algorithm. The solutions from our model for disruptions have lower costs than those from other disruption models. Our approach allows for better modeling of disruptions from historical data and can be adapted to other problems in logistics, like the hub location, capacitated facility location, and so on., with joint disruptions.