Large scale multistage stochastic integer programming with applications in electric power systems

Multistage stochastic integer programming (MSIP) is a framework for sequential decision making under uncertainty, where the uncertainty is modeled by a general stochastic process, and the decision space involves integer variables and complicated constraints. Many power system applications, such as generation capacity planning and scheduling under uncertainty stemming from renewable generation, demand variability and price volatility, can be naturally formulated as MSIP problems. In this thesis, we develop general purpose solution methods for large-scale MSIP problems and demonstrate their effectiveness on various power systems applications. In the first part of this thesis, we consider an MSIP approach for electrical power generation capacity expansion problems under demand and fuel price uncertainty. We propose a partially adaptive stochastic mixed integer optimization model in which the capacity expansion plan is fully adaptive to the uncertainty evolution up to a certain period, and is static thereafter. Any solution to the partially adaptive model is feasible to the multistage model and we provide analytical bounds on the quality of such a solution. We propose an algorithm that solves a sequence of partially adaptive models, to recursively construct an approximate solution to the multistage problem. We apply the proposed approach to a realistic generation expansion case study. In the second part of this thesis, we develop decomposition algorithms for general MSIP problems with binary state variables. By exploiting the binary nature of the state variables, we extend the nested Benders decomposition algorithm to this problem class. Key to our developments are new families of cuts that guarantee finite convergence of the proposed algorithm. We also propose a stochastic variant of the nested Benders decomposition algorithm, called Stochastic Dual Dynamic integer Programming (SDDiP), and give a rigorous proof of its finite convergence with probability one to an optimal policy. We provide extensive computational results using the SDDiP approach for generation capacity planning, portfolio optimization, and airline revenue management problems. The final part of this thesis focuses on adapting the SDDiP approach to solve the multistage stochastic unit commitment (MSUC) problem. Unit commitment is a key operational problem in power systems used to determine the optimal generation schedule over the next day or week. Incorporating uncertainty in this already difficult optimization problem imparts severe challenges. We reformulate the MSUC problem such that each stage problem only depends on information from the previous stage and the uncertainty realization. This new formulation is amenable to our SDDiP approach. We propose a variety of computational enhancements to adapt the method to MSUC. Through extensive computational results, we demonstrate the effectiveness of our approach in solving realistic scale MSUC problems.Ph.D

Application of particle swarm optimisation with backward calculation to solve a fuzzy multi-objective supply chain master planning model

Traditionally, supply chain planning problems consider variables with uncertainty associated with uncontrolled factors. These factors have been normally modelled by complex methodologies where the seeking solution process often presents high scale of difficulty. This work presents the fuzzy set theory as a tool to model uncertainty in supply chain planning problems and proposes the particle swarm optimisation (PSO) metaheuristics technique combined with a backward calculation as a solution method. The aim of this combination is to present a simple effective method to model uncertainty, while good quality solutions are obtained with metaheuristics due to its capacity to find them with satisfactory computational performance in complex problems, in a relatively short time period.This research is partly supported by the Spanish Ministry of Economy and Competitiveness projects 'Methods and models for operations planning and order management in supply chains characterised by uncertainty in production due to the lack of product uniformity' (PLANGES-FHP) (Ref. DPI2011-23597) and 'Operations design and Management of Global Supply Chains' (GLOBOP) (Ref. DPI2012-38061-C02-01); by the project funded by the Polytechnic University of Valencia entitled 'Quantitative Models for the Design of Socially Responsible Supply Chains under Uncertainty Conditions. Application of Solution Strategies based on Hybrid Metaheuristics' (PAID-06-12); and by the Ministry of Science, Technology and Telecommunications, government of Costa Rica (MICITT), through the incentive program of the National Council for Scientific and Technological Research (CONICIT) (contract No FI-132-2011).Grillo Espinoza, H.; Peidro Payá, D.; Alemany Díaz, MDM.; Mula, J. (2015). Application of particle swarm optimisation with backward calculation to solve a fuzzy multi-objective supply chain master planning model. International Journal of Bio-Inspired Computation. 7(3):157-169. https://doi.org/10.1504/IJBIC.2015.069557S1571697

Dynamic Robust Transmission Expansion Planning

Recent breakthroughs in Transmission Network Expansion Planning (TNEP) have demonstrated that the use of robust optimization, as opposed to stochastic programming methods, renders the expansion planning problem considering uncertainties computationally tractable for real systems. However, there is still a yet unresolved and challenging problem as regards the resolution of the dynamic TNEP problem (DTNEP), which considers the year-by-year representation of uncertainties and investment decisions in an integrated way. This problem has been considered to be a highly complex and computationally intractable problem, and most research related to this topic focuses on very small case studies or used heuristic methods and has lead most studies about TNEP in the technical literature to take a wide spectrum of simplifying assumptions. In this paper an adaptive robust transmission network expansion planning formulation is proposed for keeping the full dynamic complexity of the problem. The method overcomes the problem size limitations and computational intractability associated with dynamic TNEP for realistic cases. Numerical results from an illustrative example and the IEEE 118-bus system are presented and discussed, demonstrating the benefits of this dynamic TNEP approach with respect to classical methods.Comment: 10 pages, 2 figures. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPWRS.2016.2629266, IEEE Transactions on Power Systems 201

Optimal management of bio-based energy supply chains under parametric uncertainty through a data-driven decision-support framework

This paper addresses the optimal management of a multi-objective bio-based energy supply chain network subjected to multiple sources of uncertainty. The complexity to obtain an optimal solution using traditional uncertainty management methods dramatically increases with the number of uncertain factors considered. Such a complexity produces that, if tractable, the problem is solved after a large computational effort. Therefore, in this work a data-driven decision-making framework is proposed to address this issue. Such a framework exploits machine learning techniques to efficiently approximate the optimal management decisions considering a set of uncertain parameters that continuously influence the process behavior as an input. A design of computer experiments technique is used in order to combine these parameters and produce a matrix of representative information. These data are used to optimize the deterministic multi-objective bio-based energy network problem through conventional optimization methods, leading to a detailed (but elementary) map of the optimal management decisions based on the uncertain parameters. Afterwards, the detailed data-driven relations are described/identified using an Ordinary Kriging meta-model. The result exhibits a very high accuracy of the parametric meta-models for predicting the optimal decision variables in comparison with the traditional stochastic approach. Besides, and more importantly, a dramatic reduction of the computational effort required to obtain these optimal values in response to the change of the uncertain parameters is achieved. Thus the use of the proposed data-driven decision tool promotes a time-effective optimal decision making, which represents a step forward to use data-driven strategy in large-scale/complex industrial problems.Peer ReviewedPostprint (published version

Modelling and solving healthcare decision making problems under uncertainty

The efficient management of healthcare services is a great challenge for healthcare managers because of ageing populations, rising healthcare costs, and complex operation and service delivery systems. The challenge is intensified due to the fact that healthcare systems involve various uncertainties. Operations Research (OR) can be used to model and solve several healthcare decision making problems at strategic, tactical and also operational levels. Among different stages of healthcare decision making, resoure allocation and capacity planning play an important role for the overall performance of the complex systems. This thesis aims to develop modelling and solution tools to support healthcare decision making process within dynamic and stochastic systems. In particular, we are concerned with stochastic optimization problems, namely i) capacity planning in a stem-cell donation network, ii) resource allocation in a healthcare outsourcing network and iii) real-time surgery planning. The patient waiting times and operational costs are considered as the main performance indicators in these healthcare settings. The uncertainties arising in patient arrivals and service durations are integrated into the decision making as the most significant factors affecting the overall performance of the underlying healthcare systems. We use stochastic programming, a collection of OR tools for decision-making under uncertainty, to obtain robust solutions against these uncertainties. Due to complexities of the underlying stochastic optimization models such as large real-life problem instances and non-convexity, these models cannot be solved efficiently by exact methods within reasonable computation time. Thus, we employ approximate solution approaches to obtain feasible decisions close to the optimum. The computational experiments are designed to illustrate the performance of the proposed approximate methods. Moreover, we analyze the numerical results to provide some managerial insights to aid the decision-making processes. The numerical results show the benefits of integrating the uncertainty into decision making process and the impact of various factors in the overall performance of the healthcare systems