Practicable robust stochastic optimization under divergence measures with an application to equitable humanitarian response planning

We seek to provide practicable approximations of the two-stage robust stochastic optimization (RSO) model when its ambiguity set is constructed with an f-divergence radius. These models are known to be numerically challenging to various degrees, depending on the choice of the f-divergence function. The numerical challenges are even more pronounced under mixed-integer first-stage decisions. In this paper, we propose novel divergence functions that produce practicable robust counterparts, while maintaining versatility in modeling diverse ambiguity aversions. Our functions yield robust counterparts that have comparable numerical difficulties to their nominal problems. We also propose ways to use our divergences to mimic existing f-divergences without affecting the practicability. We implement our models in a realistic location-allocation model for humanitarian operations in Brazil. Our humanitarian model optimizes an effectiveness-equity trade-off, defined with a new utility function and a Gini mean difference coefficient. With the case study, we showcase 1) the significant improvement in practicability of the RSO counterparts with our proposed divergence functions compared to existing f-divergences, 2) the greater equity of humanitarian response that our new objective function enforces and 3) the greater robustness to variations in probability estimations of the resulting plans when ambiguity is considered

Revisiting Gini for equitable humanitarian logistics

Modeling equity in the allocation of scarce resources is a fast-growing concern in the humanitarian logistics field. The Gini coefficient is one of the most widely recognized measures of inequity and it was originally characterized by means of the Lorenz curve, which is a mathematical function that links the cumulative share of income to rank-ordered groups in a population. So far, humanitarian logistics models that have approached equity using the Gini coefficient do not actually optimize its original formulation, but use alternative definitions that do not necessarily replicate that original Gini measure. In this paper, we derive the original Gini coefficient via the Lorenz curve to optimize the effectiveness-equity trade-off in a humanitarian location-allocation problem. We also propose new valid inequalities based on an upper-bounding Lorenz curve to tighten the linear relaxation of our model and develop a clustering-based construction of the Lorenz curve that requires fewer additional constraints and variables than the original one. The computational study, based on the floods and landslides in Rio de Janeiro state, Brazil, reveals that while alternative Gini definitions have interesting properties, they can generate vastly different decisions compared to the original Gini coefficient. In addition, viewed from the perspective of the original Gini coefficient, these decisions can be significantly less equitable

Flexibility and real options analysis in power system generation expansion planning under uncertainty

Over many years, there has been a drive in the electricity industry towards better integration of environmentally friendly and renewable generation resources for power systems. Such resources show highly variable availability, impacting the design and performance of power systems. In this paper, we propose using a stochastic programming approach to optimize generation expansion planning (GEP), with explicit consideration of generator output capacity uncertainty. Flexibility implementation - via real options exercised in response to uncertainty realizations - is considered as an important design approach to the GEP problem. It more effectively captures upside opportunities, while reducing exposure to downside risks. A decision-rule based approach to real options modeling is used, combining conditional-go and finite adaptability principles. The solutions provide decision makers with easy-to-use guidelines with threshold values from which to exercise the options in operations. To demonstrate application of the proposed methodologies and decision rules, a case study situated in the Midwest United States is used. The case study demonstrates how to quantify the value of flexibility, and showcases the usefulness of the proposed approach

Location-allocation models for casualty response planning during catastrophic health events

Catastrophic health events are natural or man-made incidents that result in casualty numbers that overwhelm the immediate response capabilities of healthcare systems. These events overpower hospitals even when the latter trigger contingency capacity surges that are usually sufficient to deal with regular disasters. We seek to build effective location-allocation plans for the overwhelming number of casualties expected in these events by using alternative care facilities to address surge capacity issues and incorporating triage and the movement of self-evacuees for effective treatment allocation. We first tailor and apply our framework in a deterministic location-allocation model for catastrophic radiological incidents, which are events whereby the release of radioactive material leads to significant consequences to people, the environment, and facilities. We formulate a mixed integer linear programming model to locate alternative care facilities, allocate casualties for triage, and allocate triaged casualties for treatment to minimize the total weighted casualty transportation time. The model is applied to the study of two separate radiological dispersal device incidents, both based on Department of Homeland Security's National Planning Scenario 11. We generate the optimal plan for each incident and use sensitivity analyses to draw insights on facility budgeting and triage capacity allocation at hospitals. These insights lead to some response planning rules of thumb. With the above model as a basis, we incorporate data uncertainties, using probabilistically distributed scenarios, and the time sensitivity of information to create a three-stage stochastic programming location-allocation model for general catastrophic health events. In the first stage, the model locates alternative care facilities prior to any scenario realization. In the second stage, it allocates casualties for triage, given initial damage scenarios involving uncertainties in casualty demands, transportation times, and numbers of self-evacuees. In the third stage, it allocates casualties for treatment, given triage scenarios and initial damage scenarios. Model solution time increases exponentially with the number of binary location variables. Given that large solution times are unacceptable in disaster response, we propose an algorithm based on Benders' decomposition to obtain good solutions fast. The algorithm uses valid inequalities to reduce feasibility cuts, flow cover inequalities to generate stronger cuts, and perturbed dual subproblems to reduce the effect of degeneracy. We implement the model and algorithm in the case study of an earthquake situation in the southernmost part of the San Andreas Fault. We compare the effectiveness of our algorithm to classical Benders' decomposition and perform sensitivity analyses on facility budgets and capacities to obtain interesting insights.DOCTOR OF PHILOSOPHY (MAE

Optimization models in emergency logistics : a literature review

Optimization modeling has become a powerful tool to tackle emergency logistics problems since its first adoption in maritime disaster situations in the 1970s. Using techniques of content analysis, this paper reviews optimization models utilized in emergency logistics. Disaster operations can be performed before or after disaster occurrence. Short-notice evacuation, facility location, and stock pre-positioning are drafted as the main pre-disaster operations, while relief distribution and casualty transportation are categorized as post-disaster operations. According to these operations, works in the literature are broken down into three parts: facility location, relief distribution and casualty transportation, and other operations. For the first two parts, the literature is structured and analyzed based on the model types, decisions, objectives, and constraints. Finally, through the content analysis framework, several research gaps are identified and future research directions are proposed

Robust post-disaster route restoration

Route restoration is considered to be a task of foremost priority in disaster relief. In this paper, we propose a robust optimization approach for post-disaster route restoration under uncertain restoration times. We present a novel decision rule based on restoration time ordering that yields optimal restoration sequencing and propose conditions for complexity reduction in the model and prove probability bounds on the satisfaction of these conditions. We implement our models in a realistic study of the 2015 Gorkha earthquake in Nepal.System Engineerin