Robust facility location and fortification considering fortification failure probability

Considering the viability of a supply chain (SC) is the ability to maintain itself and survive in a changing environment through a redesign of structures and replanning of performance with long-term impacts. This paper considers facility location and fortification problem (FLFP) in supply chain network against supply facility disruptions and fortification failure, where the fortification failure probability follows a binomial distribution (BD), a 0-1 uniform distribution (UD), and an unknown distribution but a normal distribution approximation (NDA). Three two-stage robust optimization model with decision-dependent uncertainty (TSRO-DDU) models are developed to model the FLFP problems under failure probability with BD, UD, and NDA. Some theoretical properties are developed to transform TSRO-DDU models equivalently into two-stage optimization models with decision-independent uncertainty (TSRO-DIU). To solve the TSRO-DIU models exactly, an improved column-and-constraint generation algorithm is developed to deal with the bilinear uncertainty of facility disruption and fortification failure. Numerical experiments are conducted to show the importance of considering fortification decisions and fortification failure probability. Furthermore, we demonstrate the flexibility of the TSRO-DDU models under random attack and fortification failure scenarios, compared with the no-fortification model (NFM), the classic successful fortification model (CFM), and the deterministic fortification failure model (DFM). We also extend the models by considering facility recovery decisions after the facility disruption risk. Overall, this work extends the facility location and fortification problems considering the fortification failure probability and can strategically help managers design a resilient and viable supply chain network in a complex and uncertain environment.