Barrera, J., Carrasco, R. A., Mondschein, S., Canessa, G., & Rojas-Zalazar, D. (2020). Operating room scheduling under waiting time constraints: the Chilean GES plan. Ann. Oper. Res., 286(1-2), 501–527.
Abstract: In 2000, Chile introduced profound health reforms to achieve a more equitable and fairer system (GES plan). The reforms established a maximum waiting time between diagnosis and treatment for a set of diseases, described as an opportunity guarantee within the reform. If the maximum waiting time is exceeded, the patient is referred to another (private) facility and receives a voucher to cover the additional expenses. This voucher is paid by the health provider that had to do the procedure, which generally is a public hospital. In general, this reform has improved the service for patients with GES pathologies at the expense of patients with non-GES pathologies. These new conditions create a complicated planning scenario for hospitals, in which the hospital's OR Manager must balance the fulfillment of these opportunity guarantees and the timely service of patients not covered by the guarantee. With the collaboration of the Instituto de Neurocirugia, in Santiago, Chile, we developed a mathematical model based on stochastic dynamic programming to schedule surgeries in order to minimize the cost of referrals to the private sector. Given the large size of the state space, we developed an heuristic to compute good solutions in reasonable time and analyzed its performance. Our experimental results, with both simulated and real data, show that our algorithm performs close to optimum and improves upon the current practice. When we compared the results of our heuristic against those obtained by the hospital's OR manager in a simulation setting with real data, we reduced the overtime from occurring 21% of the time to zero, and the non-GES average waiting list's length from 71 to 58 patients, without worsening the average throughput.
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Barrera, J., Homem-De-Mello, T., Moreno, E., Pagnoncelli, B. K., & Canessa, G. (2016). Chance-constrained problems and rare events: an importance sampling approach. Math. Program., 157(1), 153–189.
Abstract: We study chance-constrained problems in which the constraints involve the probability of a rare event. We discuss the relevance of such problems and show that the existing sampling-based algorithms cannot be applied directly in this case, since they require an impractical number of samples to yield reasonable solutions. We argue that importance sampling (IS) techniques, combined with a Sample Average Approximation (SAA) approach, can be effectively used in such situations, provided that variance can be reduced uniformly with respect to the decision variables. We give sufficient conditions to obtain such uniform variance reduction, and prove asymptotic convergence of the combined SAA-IS approach. As it often happens with IS techniques, the practical performance of the proposed approach relies on exploiting the structure of the problem under study; in our case, we work with a telecommunications problem with Bernoulli input distributions, and show how variance can be reduced uniformly over a suitable approximation of the feasibility set by choosing proper parameters for the IS distributions. Although some of the results are specific to this problem, we are able to draw general insights that can be useful for other classes of problems. We present numerical results to illustrate our findings.
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Canessa, G., Gallego, J. A., Ntaimo, L., & Pagnoncelli, B. K. (2019). An algorithm for binary linear chance-constrained problems using IIS. Comput. Optim. Appl., 72(3), 589–608.
Abstract: We propose an algorithm based on infeasible irreducible subsystems to solve binary linear chance-constrained problems with random technology matrix. By leveraging on the problem structure we are able to generate good quality upper bounds to the optimal value early in the algorithm, and the discrete domain is used to guide us efficiently in the search of solutions. We apply our methodology to individual and joint binary linear chance-constrained problems, demonstrating the ability of our approach to solve those problems. Extensive numerical experiments show that, in some cases, the number of nodes explored by our algorithm is drastically reduced when compared to a commercial solver.
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Canessa, G., Moreno, E., & Pagnoncelli, B. K. (2021). The risk-averse ultimate pit problem. Optim. Eng., 22, 2655–2678.
Abstract: In this work, we consider a risk-averse ultimate pit problem where the grade of the mineral is uncertain. We derive conditions under which we can generate a set of nested pits by varying the risk level instead of using revenue factors. We propose two properties that we believe are desirable for the problem: risk nestedness, which means the pits generated for different risk aversion levels should be contained in one another, and additive consistency, which states that preferences in terms of order of extraction should not change if independent sectors of the mine are added as precedences. We show that only an entropic risk measure satisfies these properties and propose a two-stage stochastic programming formulation of the problem, including an efficient approximation scheme to solve it. We illustrate our approach in a small self-constructed example, and apply our approximation scheme to a real-world section of the Andina mine, in Chile.
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