Applications of network optimization in cybersecurity and service parts logistics

We develop and analyze novel network-based optimization models for two very important network-related applications: cybersecurity and service parts logistics. We consider one cybersecurity network problem and two service parts logistics network problems. The goal is to find tractable solutions to all three problems by creating carefully designed network-based models. The first problem we consider involves decision making in a cybersecurity environment. The goal here is to find the optimal locations to place defensive investments in a cyber physical system so that the probability of being compromised by a persistent attacker is minimized. We use Markov Decision Processes (MDPs) to show that the problem involves stochastic decision making, and we approach it using a network interdiction model. Initially, we create an MDP to come up with a description of a cyber physical network and try to find the optimal attack strategy for a persistent hacker. We show that the results of our MDP model are the same as those of the so called s-t reliability problem, a well-studied #P network problem. To tackle the exponential increase in the state space and the calculation time of the MDP with respect to the size of the cyber physical network, we create a mixed integer program (MIP) to come up with an attacker’s strategy, and develop it further to include a defender by creating a network interdiction model. We show that the results coming from the MIP and MDP model are the same, thus providing a tractable solution to the cybersecurity problem as well as the related s-t reliability problem. The second problem we consider involves decision making in a Service Parts Logistics (SPL) problem. Modifying the traditional assumption of failure based replacements in post-sales service models, we incorporate Condition Based Replacement (CBR) policies into SPL. We utilize the Internet of Things (IoT) and sensors to operationalize the continuous monitoring of the conditions of the parts in the network. We create a model to decide on strategic network design and spare parts stocking, as well as the customer to network facility allocations. Despite the focused work on high value, low demand logistics models such as SPL in the literature, there has not been a study of integrated SPL problems involving CBR policies. Along with the facility location, customer-to-facility allocation and part stock level decisions for given fill-rate based service levels, the CBR-extended SPL model also finds the optimal conditions to replace the parts at each customer. After a careful development of the part degradation process using a Continuous Time Markov Chain model, we incorporate the CBR policies into the integrated SPL model, which turns out to be a Mixed Integer Program with Quadratic Constraints (MIQCP). Our results show that the CBR flexibility brings in significant savings in the objective function (total costs of the network) when compared to the optimal solutions of the failure-based replacement (FBR) policies. Moreover, in almost all problem instances under a wide variety of conditions, replacing the parts at failure is never optimal even if such policy is allowed as part of CBR. Finally, our results show that the network topology and network design decisions interact with the replacement conditions optimal for each customer. The third problem we consider is an extension of the second problem, SPL problem with CBR, to incorporate on-request 3D printing of spare parts from a common material using Additive Manufacturing (AM) methods. Here we extend the model to include multiple parts as well as the potentially different holding costs and reliability levels for printed parts. Fortunately, we show that the extended model can also be represented as an MIQCP. In our extensive tests with multiple parts and under a wide variety of conditions, AM optimal solutions improve upon those of the traditional SPL model with conventionally manufactured and stocked parts. This additional improvement is on top of the improvements obtained with CBR.