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Alvarez-Miranda, E., & Pereira, J. (2017). Designing and constructing networks under uncertainty in the construction stage: Definition and exact algorithmic approach. Comput. Oper. Res., 81, 178–191.
Abstract: The present work proposes a novel Network Optimization problem whose core is to combine both network design and network construction scheduling under uncertainty into a single two-stage robust optimization model. The first-stage decisions correspond to those of a classical network design problem, while the second-stage decisions correspond to those of a network construction scheduling problem (NCS) under uncertainty. The resulting problem, which we will refer to as the Two-Stage Robust Network Design and Construction Problem (2SRNDC), aims at providing a modeling framework in which the design decision not only depends on the design costs (e.g., distances) but also on the corresponding construction plan (e.g., time to provide service to costumers). We provide motivations, mixed integer programming formulations, and an exact algorithm for the 2SRNDC. Experimental results on a large set of instances show the effectiveness of the model in providing robust solutions, and the capability of the proposed algorithm to provide good solutions in reasonable running times. (C) 2017 Elsevier Ltd. All rights reserved.
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Guevara, E., Babonneau, F., Homem-de-Mello, T., & Moret, S. (2020). A machine learning and distributionally robust optimization framework for strategic energy planning under uncertainty. Appl. Energy, 271, 18 pp.
Abstract: This paper investigates how the choice of stochastic approaches and distribution assumptions impacts strategic investment decisions in energy planning problems. We formulate a two-stage stochastic programming model assuming different distributions for the input parameters and show that there is significant discrepancy among the associated stochastic solutions and other robust solutions published in the literature. To remedy this sensitivity issue, we propose a combined machine learning and distributionally robust optimization (DRO) approach which produces more robust and stable strategic investment decisions with respect to uncertainty assumptions. DRO is applied to deal with ambiguous probability distributions and Machine Learning is used to restrict the DRO model to a subset of important uncertain parameters ensuring computational tractability. Finally, we perform an out-of-sample simulation process to evaluate solutions performances. The Swiss energy system is used as a case study all along the paper to validate the approach.
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Pereira, J. (2016). The robust (minmax regret) single machine scheduling with interval processing times and total weighted completion time objective. Comput. Oper. Res., 66, 141–152.
Abstract: Single machine scheduling is a classical optimization problem that depicts multiple real life systems in which a single resource (the machine) represents the whole system or the bottleneck operation of the system. In this paper we consider the problem under a weighted completion time performance metric in which the processing time of the tasks to perform (the jobs) are uncertain, but can only take values from closed intervals. The objective is then to find a solution that minimizes the maximum absolute regret for any possible realization of the processing times. We present an exact branch-and-bound method to solve the problem, and conduct a computational experiment to ascertain the possibilities and limitations of the proposed method. The results show that the algorithm is able to optimally solve instances of moderate size (25-40 jobs depending on the characteristics of the instance). (c) 2015 Elsevier Ltd. All rights reserved.
Keywords: Scheduling; Single machine; Uncertainty; Robust optimization; Branch-and-bound
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Pereira, J. (2018). The robust (minmax regret) assembly line worker assignment and balancing problem. Comput. Oper. Res., 93, 27–40.
Abstract: Line balancing aims to assign the assembly tasks to the stations that compose the assembly line. A recent body of literature has been devoted to heterogeneity in the assembly process introduced by different workers. In such an environment, task times depend on the worker performing the operation and the problem aims at assigning tasks and workers to stations in order to maximize the throughput of the line. In this work, we consider an interval data version of the assembly line worker assignment and balancing problem (ALWABP) in which it is assumed that lower and upper bounds for the task times are known, and the objective is to find an assignment of tasks and workers to the workstations such that the absolute maximum regret among all of the possible scenarios is minimized. The relationship with other interval data minmax regret (IDMR) problems is investigated, the inapplicability of previous approximation methods is studied, regret evaluation is considered, and exact and heuristic solution methods are proposed and analyzed. The results of the proposed methods are compared in a computational experiment, showing the applicability of the method and the theoretical results to solve the problem under study. Additionally, these results are not only applicable to the problem in hand, but also to a more general class of problems. (C) 2018 Elsevier Ltd. All rights reserved.
Keywords: Production; Line balancing; Robust optimization; Minmax regret
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Pereira, J., & Alvarez-Miranda, E. (2018). An exact approach for the robust assembly line balancing problem. Omega-Int. J. Manage. Sci., 78, 85–98.
Abstract: This work studies an assembly line balancing problem with uncertainty on the task times. In order to deal with the uncertainty, a robust formulation to handle changes in the operation times is put forward. In order to solve the problem, several lower bounds, dominance rules and an enumeration procedure are proposed. These methods are tested in a computational experiment using different instances derived from the literature and then compared to similar previous approaches. The results of the experiment show that the method is able to solve larger instances in shorter running times. Furthermore, the cost of protecting a solution against uncertainty is also investigated. The results highlight that protecting an assembly line against moderate levels of uncertainty can be achieved at the expense of small quantities of additional resources (stations). (C) 2017 Elsevier Ltd. All rights reserved.
Keywords: Line balancing; Robust optimization; Lower bounds; Branch-and-bound
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Reus, L., & Fabozzi, F. J. (2021). Robust Solutions to the Life-Cycle Consumption Problem. Comput. Econ., 57, 481–499.
Abstract: This paper demonstrates how the well-known discrete life-cycle consumption problem (LCP) can be solved using the Robust Counterpart (RC) formulation technique, as defined in Ben-Tal and Nemirovski (Math Oper Res 23(4):769-805, 1998). To do this, we propose a methodology that involves applying a change of variables over the original consumption before deriving the RC. These transformations allow deriving a closed solution to the inner problem, and thus to solve the LCP without facing the curse of dimensionality and without needing to specify the prior distribution for the investment opportunity set. We generalize the methodology and illustrate how it can be used to solve other type of problems. The results show that our methodology enables solving long-term instances of the LCP (30 years). We also show it provides an alternative consumption pattern as to the one provided by a benchmark that uses a dynamic programming approach. Rather than finding a consumption that maximizes the expected lifetime utility, our solution delivers higher utilities for worst-case scenarios of future returns.
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