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Cho, A. D., Carrasco, R. A., & Ruz, G. A. (2022). Improving Prescriptive Maintenance by Incorporating Post-Prognostic Information Through Chance Constraints. IEEE Access, 10, 55924–55932.
Abstract: Maintenance is one of the critical areas in operations in which a careful balance between preventive costs and the effect of failures is required. Thanks to the increasing data availability, decision-makers can now use models to better estimate, evaluate, and achieve this balance. This work presents a maintenance scheduling model which considers prognostic information provided by a predictive system. In particular, we developed a prescriptive maintenance system based on run-to-failure signal segmentation and a Long Short Term Memory (LSTM) neural network. The LSTM network returns the prediction of the remaining useful life when a fault is present in a component. We incorporate such predictions and their inherent errors in a decision support system based on a stochastic optimization model, incorporating them via chance constraints. These constraints control the number of failed components and consider the physical distance between them to reduce sparsity and minimize the total maintenance cost. We show that this approach can compute solutions for relatively large instances in reasonable computational time through experimental results. Furthermore, the decision-maker can identify the correct operating point depending on the balance between costs and failure probability.
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Homem-de-Mello, T., Kong, Q. X., & Godoy-Barba, R. (2022). A Simulation Optimization Approach for the Appointment Scheduling Problem with Decision-Dependent Uncertainties. INFORMS J. Comput., Early Access.
Abstract: The appointment scheduling problem (ASP) studies how to manage patient arrivals to a healthcare system to improve system performance. An important challenge occurs when some patients may not show up for an appointment. Although the ASP is well studied in the literature, the vast majority of the existing work does not consider the well-observed phenomenon that patient no-show is influenced by the appointment time, the usual decision variable in the ASP. This paper studies the ASP with random service time (exogenous uncertainty) with known distribution and patient decision-dependent no-show behavior (endogenous uncertainty). This problem belongs to the class of stochastic optimization with decision-dependent uncertainties. Such problems are notoriously difficult as they are typically nonconvex. We propose a stochastic projected gradient path (SPGP) method to solve the problem, which requires the development of a gradient estimator of the objective function-a nontrivial task, as the literature on gradient-based optimization algorithms for problems with decision-dependent uncertainty is very scarce and unsuitable for our model. Our method can solve the ASP problem under arbitrarily smooth show-up probability functions. We present solutions under different patterns of no-show behavior and demonstrate that breaking the assumption of constant show-up probability substantially changes the scheduling solutions. We conduct numerical experiments in a variety of settings to compare our results with those obtained with a distributionally robust optimization method developed in the literature. The cost reduction obtained with our method, which we call the value of distribution information, can be interpreted as how much the system performance can be improved by knowing the distribution of the service times, compared to not knowing it. We observe that the value of distribution information is up to 31% of the baseline cost, and that such value is higher when the system is crowded or/and the waiting time cost is relatively high.
Summary of Contribution: This paper studies an appointment scheduling problem under time-dependent patient no-show behavior, a situation commonly observed in practice. The problem belongs to the class of stochastic optimization problems with decision-dependent uncertainties in the operations research literature. Such problems are notoriously difficult to solve as a result of the lack of convexity, and the present case requires different techniques because of the presence of continuous distributions for the service times. A stochastic projected gradient path method, which includes the development of specialized techniques to estimate the gradient of the objective function, is proposed to solve the problem. For problems with a similar structure, the algorithm can be applied once the gradient estimator of the objective function is obtained. Extensive numerical studies are presented to demonstrate the quality of the solutions, the importance of modeling time-dependent no-shows in appointment scheduling, and the value of using distribution information about the service times.
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Lagos, T., Armstrong, M., Homem-de-Mello, T., Lagos, G., & Saure, D. (2021). A framework for adaptive open-pit mining planning under geological uncertainty. Optim. Eng., 72, 102086.
Abstract: Mine planning optimization aims at maximizing the profit obtained from extracting valuable ore. Beyond its theoretical complexity-the open-pit mining problem with capacity constraints reduces to a knapsack problem with precedence constraints, which is NP-hard-practical instances of the problem usually involve a large to very large number of decision variables, typically of the order of millions for large mines. Additionally, any comprehensive approach to mine planning ought to consider the underlying geostatistical uncertainty as only limited information obtained from drill hole samples of the mineral is initially available. In this regard, as blocks are extracted sequentially, information about the ore grades of blocks yet to be extracted changes based on the blocks that have already been mined. Thus, the problem lies in the class of multi-period large scale stochastic optimization problems with decision-dependent information uncertainty. Such problems are exceedingly hard to solve, so approximations are required. This paper presents an adaptive optimization scheme for multi-period production scheduling in open-pit mining under geological uncertainty that allows us to solve practical instances of the problem. Our approach is based on a rolling-horizon adaptive optimization framework that learns from new information that becomes available as blocks are mined. By considering the evolution of geostatistical uncertainty, the proposed optimization framework produces an operational policy that reduces the risk of the production schedule. Our numerical tests with mines of moderate sizes show that our rolling horizon adaptive policy gives consistently better results than a non-adaptive stochastic optimization formulation, for a range of realistic problem instances.
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