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

A practical assessment of risk-averse approaches in production lot-sizing problems

This paper presents an empirical assessment of four state-of-the-art risk-averse approaches to deal with the capacitated lot-sizing problem under stochastic demand. We analyse two mean-risk models based on the semideviation and on the conditional value-at-risk risk measures, and alternate first and second-order stochastic dominance approaches. The extensive computational experiments based on different instances characteristics and on a case-study suggest that CVaR exhibits a good trade-off between risk and performance, followed by the semideviation and first-order stochastic dominance approach. For all approaches, enforcing risk-aversion helps to reduce the cost-standard deviation substantially, which is usually accomplished via increasing production rates. Overall, we can say that very risk-averse decision-makers would be willing to pay an increased price to have a much less risky solution given by CVaR. In less risk-averse settings, though, semideviation and first-order stochastic dominance can be appealingalternatives to provide significantly more stable production planning costs with a marginal increase of the expected costs.Peer reviewe

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

Brazilian disaster datasets and real-world instances for optimization and machine learning

We present comprehensive datasets of Brazilian disasters from January 2003 to February 2021 as well as real-world optimization instances built up from these data. The data were gathered through a series of open available reports obtained from different government and institutional sources. Afterwards, data consolidation and summarization were carried out using Excel and Python. The datasets include 9 types of disaster, such as flash floods, landslides and droughts, and the corresponding number of affected people during an 18-year or a 218-month observation period for 5,402 Brazilian municipalities, totaling more than 65,000 observations. Data on relevant geographical, demographic and socioeconomic aspects of the affected municipalities are also provided. These encompass geographic coordinates, regions, population, income, development indicators, amongst other information. From a statistical point of view, the data on disasters can address a number of applications using both supervised and unsupervised machine learning techniques such as, for time series analysis or other dynamic models using socioeconomic data as explanatory variables, i.e. data on the size of the poor population, income, education and general development. The geographic dataset can be useful for aggregating analyses concerning the various forms of territorial organization and allows for the visualization of data in maps. All the aforementioned data can be also used to devise realistic optimization instances related to diverse humanitarian logistics and/or disaster management problems, such as facility location, location-allocation, vehicle routing, and so forth. In particular, we describe two real-world instances for the location-allocation problem studied in [1]. For that purpose, we partially use the given datasets and included other information such as costs and distances relevant to the optimization model. Although using real-world cases to test optimization approaches is a common and encouraged practice in Operations Research, comprehensive datasets and practical optimization instances, as presented in this article, are rarely described and/or available in the academic literature

Insights from two-stage stochastic programming in emergency logistics

ABSTRACT This paper discusses the practical aspects and resulting insights of the results of a two-stage mathematical network flow model to help make the decisions required to get humanitarian aid quickly to needy recipients as part of a disaster relief operation. The aim of model is to plan where to best place aid inventory in preparation for possible disasters, and to make fast decisions about how best to channel aid to recipients as fast as possible. Humanitarian supply chains differ from commercial supply chains in their greater urgency of response and in the poor quality of data and increased uncertainty about important inputs such as transportation resources, aid availability, and the suddenness and degree of "demand". The context is usually more chaotic with poor information feedback and a multiplicity of decision-makers in different aid organizations. The model attempts to handle this complexity by incorporating practical decisions, such as pre-allocation of emergency goods, transportation policy, fleet management and procurement, in an uncertainty environment featured by a scenario-based approach. Preliminary results based on the floods and landslides disaster of the Mountain Region of Rio de Janeiro state, Brazil, point to how to cope with these challenges by using the mathematical model