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Sequential testing of k-out-of-n systems with imperfect tests ; Coolen, Kris ; et al E-print/Working paper (2015) A k-out-of-n system configuration requires that, for the overall system to be functional, at least k out of the total of n components be working. We consider the problem of sequentially testing the ... [more ▼] A k-out-of-n system configuration requires that, for the overall system to be functional, at least k out of the total of n components be working. We consider the problem of sequentially testing the components of a k-out-of-n system in order to learn the state of the system, when the tests are costly and when the individual component tests are imperfect, which means that a test can identify a component as working when in reality it is down, and vice versa. Each component is tested at most once. Since tests are imperfect, even when all components are tested the state of the system is not necessarily known with certainty, and so reaching a lower bound on the probability of correctness of the system state is used as a stopping criterion for the inspection. We define different classes of inspection policies and we examine global optimality of each of the classes. We find that a globally optimal policy for diagnosing k-out-of-n systems with imperfect tests can be found in polynomial time when the predictive error probabilities are the same for all the components. Of the three policy classes studied, the dominant policies always contain a global optimum, while elementary policies are compact in representation. The newly introduced class of so-called `interrupted block-walking' policies combines these merits of global optimality and of compactness. [less ▲] Detailed reference viewed: 31 (4 ULg)Revealed preference tests of collectively rational consumption behavior: formulations and algorithms ; ; Crama, Yves et al E-print/Working paper (2013) This paper focuses on revealed preference tests of the collective model of household consumption. We start by showing that the decision problems corresponding to testing collective rationality are {\sc np ... [more ▼] This paper focuses on revealed preference tests of the collective model of household consumption. We start by showing that the decision problems corresponding to testing collective rationality are {\sc np}-complete. This makes the application of these tests problematic for (increasingly available) large(r) scale data sets. We then present two approaches to overcome this negative result. First, we introduce exact algorithms based on mixed-integer programming ({\sc mip}) formulations of the collective rationality tests, which can be usefully applied to medium sized data sets. Next, we propose simulated annealing heuristics, which allow for efficient testing of the collective model in the case of large data sets. We illustrate our methods by a number of computational experiments based on Dutch labor supply data. [less ▲] Detailed reference viewed: 78 (9 ULg)Algorithms for testing the collective consumption model ; ; Crama, Yves et al Conference (2012, November 09) In this talk, we discuss an extension of the strong axiom of revealed preferences to collective households. The question that we address is whether a set of observed consumption baskets can be decomposed ... [more ▼] In this talk, we discuss an extension of the strong axiom of revealed preferences to collective households. The question that we address is whether a set of observed consumption baskets can be decomposed in such a way that each of the derived data sets reflects the choices of a “rational” (i.e., utility-maximizing) individual member of the household. Although testing revealed preference axioms on data generated by a single decisionmaker can be done in polynomial time, the extension to two-member households is NP-complete. We propose two algorithms for testing the collective consumption model on large data sets. The first one is an exact algorithm based on a new mixed-integer programming formulation, whereas the second one is a heuristic based on a simulated annealing procedure that solves a global optimization formulation of the problem. Computational experiments are performed on real-life data. [less ▲] Detailed reference viewed: 19 (0 ULg) |
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