A decomposition strategy for decision problems with endogenous uncertainty using mixed-integer programming

Despite methodological advances for modeling decision problems under uncertainty, faithfully representing endogenous uncertainty still proves challenging, both in terms of modeling capabilities and computational requirements. A novel framework called Decision Programming provides an approach for solving such decision problems using off-the-shelf mathematical optimization solvers. This is made possible by using influence diagrams to represent a given decision problem, which is then formulated as a mixed-integer linear programming problem. In this paper, we focus on the type of endogenous uncertainty that received less attention in the introduction of Decision Programming: conditionally observed information. Multi-stage stochastic programming (MSSP) models use conditional non-anticipativity constraints (C-NACs) to represent such uncertainties, and we show how such constraints can be incorporated into Decision Programming models. This allows us to consider the two main types of endogenous uncertainty simultaneously, namely decision-dependent information structure and decision-dependent probability distribution. Additionally, we present a decomposition approach that provides significant computational savings and also enables considering continuous decision variables in certain parts of the problem, whereas the original formulation was restricted to discrete variables only. The extended framework is illustrated with two example problems. The first considers an illustrative multiperiod game and the second is a large-scale cost-benefit problem regarding climate change mitigation. Neither of these example problems could be solved with existing frameworks.Comment: 26 pages, 10 figure

Leveraging Decision Diagrams to Solve Two-stage Stochastic Programs with Binary Recourse and Logical Linking Constraints

Two-stage stochastic programs with binary recourse are challenging to solve and efficient solution methods for such problems have been limited. In this work, we generalize an existing binary decision diagram-based (BDD-based) approach of Lozano and Smith (Math. Program., 2018) to solve a special class of two-stage stochastic programs with binary recourse. In this setting, the first-stage decisions impact the second-stage constraints. Our modified problem extends the second-stage problem to a more general setting where logical expressions of the first-stage solutions enforce constraints in the second stage. We also propose a complementary problem and solution method which can be used for many of the same applications. In the complementary problem we have second-stage costs impacted by expressions of the first-stage decisions. In both settings, we convexify the second-stage problems using BDDs and parametrize either the arc costs or capacities of these BDDs with first-stage solutions depending on the problem. We further extend this work by incorporating conditional value-at-risk and we propose, to our knowledge, the first decomposition method for two-stage stochastic programs with binary recourse and a risk measure. We apply these methods to a novel stochastic dominating set problem and present numerical results to demonstrate the effectiveness of the proposed methods

Enumerative Branching with Less Repetition

We can compactly represent large sets of solutions for problems with discrete decision variables by using decision diagrams. With them, we can efficiently identify optimal solutions for different objective functions. In fact, a decision diagram naturally arises from the branch-and-bound tree that we could use to enumerate these solutions if we merge nodes from which the same solutions are obtained on the remaining variables. However, we would like to avoid the repetitive work of finding the same solutions from branching on different nodes at the same level of that tree. Instead, we would like to explore just one of these equivalent nodes and then infer that the same solutions would have been found if we explored other nodes. In this work, we show how to identify such equivalences—and thus directly construct a reduced decision diagram—in integer programs where the left-hand sides of all constraints consist of additively separable functions. First, we extend an existing result regarding problems with a single linear constraint and integer coefficients. Second, we show necessary conditions with which we can isolate a single explored node as the only candidate to be equivalent to each unexplored node in problems with multiple constraints. Third, we present a sufficient condition that confirms if such a pair of nodes is indeed equivalent, and we demonstrate how to induce that condition through preprocessing. Finally, we report computational results on integer linear programming problems from the MIPLIB benchmark. Our approach often constructs smaller decision diagrams faster and with less branching

08421 Abstracts Collection -- Uncertainty Management in Information Systems

From October 12 to 17, 2008 the Dagstuhl Seminar 08421 \u27`Uncertainty Management in Information Systems \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. The abstracts of the plenary and session talks given during the seminar as well as those of the shown demos are put together in this paper

Solving Multi-objective Integer Programs using Convex Preference Cones

Esta encuesta tiene dos objetivos: en primer lugar, identificar a los individuos que fueron víctimas de algún tipo de delito y la manera en que ocurrió el mismo. En segundo lugar, medir la eficacia de las distintas autoridades competentes una vez que los individuos denunciaron el delito que sufrieron. Adicionalmente la ENVEI busca indagar las percepciones que los ciudadanos tienen sobre las instituciones de justicia y el estado de derecho en Méxic

Development of a system-dynamics-based methodology for comprehensive community energy planning

Global trends are leading to a rise in Energy Planning (EP) at the community-level, and Distributed Energy Resources at the residential-level, while seeking a more sustainable future; EP involves decision-making about energy systems. Whilst Community Energy Planning (CEP) aims to be holistic and participatory, it comprises multiple disjointed methods that lead to two challenges. The first challenge is hindrance to a holistic approach and understanding of the energy system, while the second challenge is hindrance to participation from diverse stakeholders. However, System Dynamics (SD), which is a methodology for mental and simulation models, looks promising as a basis for a comprehensive CEP methodology that would lead to a more holistic and participatory CEP. Consequently, the research question of the thesis is: is a System Dynamics approach an effective and comprehensive methodology for sustainable Community Energy Planning? The research aims were broken down into specific objectives which are addressed in specific chapters. The objectives that required creating simulation models were addressed as case-study chapters, and arranged such that later chapters build on models created in earlier chapters, culminating in the combination of multiple earlier models. Drawing on the literature of Sustainability Assessment (SA) and the methods used in CEP, it is argued that CEP is a form of SA because it utilises Sustainability Indicators to appraise models of planned energy systems. Furthermore, a comprehensive CEP methodology is proposed that is centred around SD, which addresses some of the challenges of CEP. Subsequently, gaps were identified in the demonstration of SD among the methods of the proposed CEP methodology, which was found to be in the area of bottom-up simulation models. The case-study chapters are the first attempts in the following, while utilising SD from the bottom-up: a valid supply-side model; use of the supply-side model in decision-making analyses; a valid demand-side model; use of the demand-side model in decision-making analyses; and combination of supply-side models, and with a demand-side model. Additionally, there are other significant contributions from the case-studies. In conclusion, it is argued that SD could be an effective basis for a more comprehensive CEP methodology, and that this research can be considered a step towards that aim

Intergenerational Transmission of Inflation Aversion: Theory and Evidence

We study the evolution of inflation aversion preferences across generations. In the theoretical part of the paper, we analyze the dynamics of such preferences in an overlapping-generations model with heterogenous mature agents characterized by different degrees of inflation aversion. We show how the stability of a society’s degree of inflation aversion depends on the strength and speed of changes in the structure of the population. The empirical part then proposes two applications in support of the theoretical results. We first link demographic structures to inflation aversion, and then proceed by looking at the relations between income (in)equality and measures of inflation aversion.Intergenerational transmission, evolving preferences, inflation aversion, central bank independence, demographic change, income inequality