Models, Theoretical Properties, and Solution Approaches for Stochastic Programming with Endogenous Uncertainty

In a typical optimization problem, uncertainty does not depend on the decisions being made in the optimization routine. But, in many application areas, decisions affect underlying uncertainty (endogenous uncertainty), either altering the probability distributions or the timing at which the uncertainty is resolved. Stochastic programming is a widely used method in optimization under uncertainty. Though plenty of research exists on stochastic programming where decisions affect the timing at which uncertainty is resolved, much less work has been done on stochastic programming where decisions alter probability distributions of uncertain parameters. Therefore, we propose methodologies for the latter category of optimization under endogenous uncertainty and demonstrate their benefits in some application areas. First, we develop a data-driven stochastic program (integrates a supervised machine learning algorithm to estimate probability distributions of uncertain parameters) for a wildfire risk reduction problem, where resource allocation decisions probabilistically affect uncertain human behavior. The nonconvex model is linearized using a reformulation approach. To solve a realistic-sized problem, we introduce a simulation program to efficiently compute the recourse objective value for a large number of scenarios. We present managerial insights derived from the results obtained based on Santa Fe National Forest data. Second, we develop a data-driven stochastic program with both endogenous and exogenous uncertainties with an application to combined infrastructure protection and network design problem. In the proposed model, some first-stage decision variables affect probability distributions, whereas others do not. We propose an exact reformulation for linearizing the nonconvex model and provide a theoretical justification of it. We designed an accelerated L-shaped decomposition algorithm to solve the linearized model. Results obtained using transportation networks created based on the southeastern U.S. provide several key insights for practitioners in using this proposed methodology. Finally, we study submodular optimization under endogenous uncertainty with an application to complex system reliability. Specifically, we prove that our stochastic program\u27s reliability maximization objective function is submodular under some probability distributions commonly used in reliability literature. Utilizing the submodularity, we implement a continuous approximation algorithm capable of solving large-scale problems. We conduct a case study demonstrating the computational efficiency of the algorithm and providing insights

Decision support system for a reactive management of disaster-caused supply chain disturbances

This research contribution presents the Reactive Disaster and supply chain Risk decision Support System ReDRiSS which supports decision-makers of logistical disaster management in the immediate aftermath of a supply chain disturbance. ReDRiSS suggests a methodology which combines approaches from scenario techniques, operations research and decision theory. Two case studies are provided which focus on decision situations of humanitarian logistics and of business continuity management

Decision support system for a reactive management of disaster-caused supply chain disturbances

This research contribution presents the Reactive Disaster and supply chain Risk decision Support System ReDRiSS which supports decision-makers of logistical disaster management in the immediate aftermath of a supply chain disturbance. ReDRiSS suggests a methodology which combines approaches from scenario techniques, operations research and decision theory. Two case studies are provided which focus on decision situations of humanitarian logistics and of business continuity management

Robust multi-objective optimization of safety barriers performance parameters for NaTech scenarios risk assessment and management

Safety barriers are to be designed to bring the largest benefit in terms of accidental scenarios consequences mitigation at the most reasonable cost. In this paper, we formulate the problem of the identification of the optimal performance parameters of the barriers that can at the same time allow for the consequences mitigation of Natural Technological (NaTech) accidental scenarios at reasonable cost as a Multi-Objective Optimization (MOO) problem. The MOO is solved for a case study of literature, consisting in a chemical facility composed by three tanks filled with flammable substances and equipped with six safety barriers (active, passive and procedural), exposed to NaTech scenarios triggered by either severe floods or earthquakes. The performance of the barriers is evaluated by a phenomenological dynamic model that mimics the realistic response of the system. The uncertainty of the relevant parameters of the model (i.e., the response time of active and procedural barriers and the effectiveness of the barriers) is accounted for in the optimization, to provide robust solutions. Results for this case study suggest that the NaTech risk is optimally managed by improving the performances of four-out-of-six barriers (three active and one passive). Practical guidelines are provided to retrofit the safety barriers design

A Novel Approach to Include Social Costs in Humanitarian Objective Functions

Social cost functions in humanitarian operations are defined as the sum of logistics and deprivation costs. They are widely regarded as appropriate objective functions, even though the way they were introduced requires cautiously formulated deprivation cost functions for the analyzed goods and do not allow decision makers to include their individual preferences. We develop this approach further and introduce a normalized weighted sum approach to increase decision makers\u27 understanding of the tradeoffs between cost and suffering and, therefore, increase transparency significantly. Furthermore, we apply the approach to a case study of a hypothetical water system failure in the city of Berlin. We show that the normalized weighted sum approach significantly improves transparency and leads to a deeper understanding of the tradeoffs during the crisis. Consequently, it proved itself as a powerful tool for decision makers preparing for or navigating through a crisis

An Optimized Resource Allocation Approach to Identify and Mitigate Supply Chain Risks using Fault Tree Analysis

Low volume high value (LVHV) supply chains such as airline manufacturing, power plant construction, and shipbuilding are especially susceptible to risks. These industries are characterized by long lead times and a limited number of suppliers that have both the technical know-how and manufacturing capabilities to deliver the requisite goods and services. Disruptions within the supply chain are common and can cause significant and costly delays. Although supply chain risk management and supply chain reliability are topics that have been studied extensively, most research in these areas focus on high vol- ume supply chains and few studies proactively identify risks. In this research, we develop methodologies to proactively and quantitatively identify and mitigate supply chain risks within LVHV supply chains. First, we propose a framework to model the supply chain system using fault-tree analysis based on the bill of material of the product being sourced. Next, we put forward a set of mathematical optimization models to proactively identify, mitigate, and resource at-risk suppliers in a LVHV supply chain with consideration for a firm’s budgetary constraints. Lastly, we propose a machine learning methodology to quan- tify the risk of an individual procurement using multiple logistic regression and industry available data, which can be used as the primary input to the fault tree when analyzing overall supply chain system risk. Altogether, the novel approaches proposed within this dissertation provide a set of tools for industry practitioners to predict supply chain risks, optimally choose which risks to mitigate, and make better informed decisions with respect to supplier selection and risk mitigation while avoiding costly delays due to disruptions in LVHV supply chains

DECISION ANALYTICAL METHODS FOR ROBUST WATER INFRASTRUCTURE PLANNING UNDER DEEP UNCERTAINTY

Deep uncertainties resulting from climate change, demographic pressures, and rapidly evolving socioeconomic conditions are challenging the way that water planners design and operate large-scale infrastructure systems. Conventionally, water infrastructures have been developed using stationary methods, assuming that the underlying uncertainties can be derived from historical data or experience. However, these methods are less useful under deeply uncertain climate and socioeconomic conditions, in which the future can be substantially different from the past and cannot be expressed by well-defined probability distributions. The recognition of deep uncertainties in long-term water resources planning has led to the development of “decision-analytical” frameworks that do not require predictions or prior probabilistic inference about the future. Instead, these approaches seek for alternatives that perform well across a broad range of conditions (robust) and can adapt to changing conditions (flexible). This dissertation aims to develop three new decision-analytical frameworks that build upon the previous work. The first study presents a generalized framework for water infrastructure design under climate change using regret-based robustness criterion and compares the findings to more conventional, predict-then-act based analyses of infrastructure design. The method is demonstrated for the design of a run-of-the-river hydropower system in Malawi. The second study further develops the framework by considering multiple climatic, demographic, and socioeconomic uncertainties in the context of a water supply design project in the Coastal Kenya. This improved framework incorporates a Bayesian belief network to blend multiple sources of subjective information from model projections and expert opinions elicited from stakeholder workshops. The third framework develops a decision-analytical approach for flexible river basin planning under climate change and applies to the problem of long-term water supply and irrigation planning in the Niger River Basin. The framework makes use of a stochastic programming model to search for optimal planning pathways under a wide range of scenarios that represent both natural climate variability and climate changes. In this process, the framework explores uncertain beliefs associated with the probability weights assigned to each scenario and identifies “belief dominant” pathways that are insensitive to underlying probabilistic assumptions and are more promising based on climate projections

Screening robust water infrastructure investments and their trade-offs under global change: A London example

We propose an approach for screening future infrastructure and demand management investments for large water supply systems subject to uncertain future conditions. The approach is demonstrated using the London water supply system. Promising portfolios of interventions (e.g., new supplies, water conservation schemes, etc.) that meet London’s estimated water supply demands in 2035 are shown to face significant trade-offs between financial, engineering and environmental measures of performance. Robust portfolios are identified by contrasting the multi-objective results attained for (1) historically observed baseline conditions versus (2) future global change scenarios. An ensemble of global change scenarios is computed using climate change impacted hydrological flows, plausible water demands, environmentally motivated abstraction reductions, and future energy prices. The proposed multi-scenario trade-off analysis screens for robust investments that provide benefits over a wide range of futures, including those with little change. Our results suggest that 60 percent of intervention portfolios identified as Pareto optimal under historical conditions would fail under future scenarios considered relevant by stakeholders. Those that are able to maintain good performance under historical conditions can no longer be considered to perform optimally under future scenarios. The individual investment options differ significantly in their ability to cope with varying conditions. Visualizing the individual infrastructure and demand management interventions implemented in the Pareto optimal portfolios in multi-dimensional space aids the exploration of how the interventions affect the robustness and performance of the system

Facility Location Planning in Relief Logistics: Decision Support for German Authorities

Disasters have devastating impacts on societies, affecting millions of people and businesses each year. The delivery of essential goods to beneficiaries in the aftermath of a disaster is one of the main objectives of relief logistics. In this context, selecting suitable locations for three different types of essential facilities is central: warehouses, distribution centers, and points of distribution. The present dissertation aims to improve relief logistics by advancing the location selection process and its core components. Five studies published as companion articles address substantial aspects of relief logistics. Despite the case studies\u27 geographical focus on Germany, valuable insights for relief logistics are derived that could also be applied to other countries. Study A addresses the importance of public-private collaboration in disasters and highlights the significance of considering differences in resources, capabilities, and strategies when using logistical models. Moreover, power differences, information sharing, and partner selection also play an important role. Study B elaborates on the challenges to identify candidate locations for warehouses, which are jointly used by public and private actors, and suggests a methodology to approach the collaborative warehouse selection process. Study C investigates the distribution center selection process and highlights that including decision-makers\u27 preferences in the objective function of location selection models helps to raise awareness of the implications of location decisions and increases transparency for decision-makers and the general population. Study D analyzes the urban water supply in disasters using a combination of emergency wells and mobile water treatment systems. Selected locations of mobile systems change significantly if vulnerable parts of the population are prioritized. Study E highlights the importance of accurate information in disasters and introduces a framework that allows determining the value of accurate information and the planning error due to inaccurate information. In addition to the detailed results of the case studies, four general recommendations for authorities are derived: First, it is essential to collect information before the start of the disaster. Second, training exercises or role-playing simulations with companies will help to ensure that planned collaboration processes can be implemented in practice. Third, targeted adjustments to the German disaster management system can strengthen the country\u27s resilience. Fourth, initiating public debates on strategies to prioritize parts of the population might increase the acceptance of the related decision and the stockpiling of goods for the people who know in advance that they will likely not receive support. The present dissertation provides valuable insights into disaster relief. Therefore, it offers the potential to significantly improve the distribution of goods in the aftermath of future disasters and increase disaster resilience