The release of flammable and toxic chemicals in petrochemical facilities is a major concern when designing modern process safety systems. While the proper selection of the necessary types of gas detectors needed is important, appropriate placement of these detectors is required in order to have a well-functioning gas detection system. However, the uncertainty in leak locations, gas composition, process and weather conditions, and process geometries must all be considered when attempting to determine the appropriate number and placement of the gas detectors. Because traditional approaches are typically based on heuristics, there exists the need to develop more rigorous optimization based approaches to handling this problem. This work presents several mixed-integer programming formulations to address this need. First, a general mixed-integer linear programming problem is presented. This formulation takes advantage of precomputed computational fluid dynamics (CFD) simulations to determine a gas detector placement that minimizes the expected detection time across all scenarios. An extension to this formulation is added that considers the overall coverage in a facility in order to improve the detector placement when enough scenarios may not be available. Additionally, a formulation considering the Conditional-Value-at-Risk is also presented. This formulation provides some control over the shape of the tail of the distribution, not only minimizing the expected detection time across all scenarios, but also improving the tail behavior. In addition to improved formulations, procedures are introduced to determine confidence in the placement generated and to determine if enough scenarios have been used in determining the gas detector placement. First, a procedure is introduced to analyze the performance of the proposed gas detector placement in the face of “unforeseen” scenarios, or scenarios that were not necessarily included in the original formulation. Additionally, a procedure for determine the confidence interval on the optimality gap between a placement generated with a sample of scenarios and its estimated performance on the entire uncertainty space. Finally, a method for determining if enough scenarios have been used and how much additional benefit is expected by adding more scenarios to the optimization is proposed. Results are presented for each of the formulations and methods presented using three data sets from an actual process facility. The use of an off-the-shelf toolkit for the placement of detectors in municipal water networks from the EPA, known as TEVA-SPOT, is explored. Because this toolkit was not designed for placing gas detectors, some adaptation of the files is necessary, and the procedure for doing so is presented.

This study proposes several decision-making tools utilizing optimization and machine learning frameworks to assess and improve the safety of the workplaces. The first chapter of this study presents a novel mathematical model to optimally locate a set of detectors to minimize the expected number of casualties in a given threat area. The problem is formulated as a nonlinear binary integer programming model and then solved as a linearized branch-and-bound algorithm. Several sensitivity analyses illustrate the model's robustness and draw key managerial insights. One of the prevailing threats in the last decades, Active Shooting (AS) violence, poses a serious threat to public safety. The second chapter proposes an innovative mathematical model which captures several essential features (e.g., the capacity of the facility and individual choices, heterogeneity of individual behavioral and choice sets, restriction on choice sets depending on the location of the shooter and facility orientation, and many others) which are essential for appropriately characterizing and analyzing the response strategy for civilians under an AS exposed environment. We demonstrate the applicability of the proposed model by implementing the effectiveness of the RUN.HIDE.FIGHT.® (RHF) program in an academic environment. Given most of the past incidents took place in built environments (e.g., educational and commercial buildings), there is an urgent need to methodologically assess the safety of the buildings under an active shooter situation. Finally, the third chapter aims to bridge this knowledge gap by developing a learning technique that can be used to model the behavior of the shooter and the trapped civilians in an active shooter incident. Understanding how the civilians responded to different simulated environments, a number of actions could have been undertaken to bolster the safety measures of a given facility. Finally, this study provides a customized decision-making tool that adopts a tailored maximum entropy inverse reinforcement learning algorithm and utilizes safety measurement metrics, such as the percentage of civilians who can hide/exit in/from the system, to assess a workplace's safety under an active shooter incident.