Optimization and Analysis of Protection Strategies for Supply Chains: Comparing Regret and Expected Models

The inherent and growing complexity characterizing today's infrastructure systems has considerably increased their vulnerability to external disruptions. Recent world events have demonstrated how the damage of one or more infrastructure components can result in disastrous political, social and economical effects. This, in turn, has fostered the development of sophisticated quantitative methods that identify cost-effective ways of strengthening supply systems in the face of disruption. Stochastic and robust optimization can be used for this purpose. An example of a protection model which explicitly takes into account the uncertainty characterizing the extent of disruptive events is the Stochastic R-Interdiction Median Problem with Fortification (S-RIMF) [26]. The objective of this model is to optimally protect facilities in a supply system so as to minimize the expected operational costs resulting from the loss of an uncertain number of system components. In this article, we analyze how protection strategies vary when using different measures of optimization under uncertainty. We propose two regret models

and show how to solve them by extending the bounds based approach developed for S-RIMF. Also, we discuss how to build a reliability envelope for the models considered,

which can be used to identify the range of possible impacts associated with different protection strategies. The new regret models and the original S-RIMF are tested on a

new data set which was built using the Census 2001 data of the United Kingdom. We analyze and compare the protection plans generated by the models, and provide some useful insights related to the robustness of the different modeling approaches.