Alvaro E. Cordero-Franco

Solving the Bilevel Facility Location Problem under Preferences by a Stackelberg-Evolutionary Algorithm

This research highlights the use of game theory to solve the classical problem of the uncapacitated facility location optimization model with customer order preferences through a bilevel approach. The bilevel model provided herein consists of the classical facility location problem and an optimization of the customer preferences, which are the upper and lower level problems, respectively. Also, two reformulations of the bilevel model are presented, reducing it into a mixed-integer single-level problem. An evolutionary algorithm based on the equilibrium in a Stackelberg’s game is proposed to solve the bilevel model. Numerical experimentation is performed in this study and the results are compared to benchmarks from the existing literature on the subject in order to emphasize the benefits of the proposed approach in terms of solution quality and estimation time.

A Self-Starting CUSUM Chart Combined with a Maximum Likelihood Estimator for the Time of a Detected Shift in the Process Mean

Detection of a special cause of variation and the identification of the time it occurs are two important activities in any quality improvement strategy. Detection of changes in a process can be done using control charts. One of these charts, the self-starting CUSUM chart, was created to detect small sustained changes and be implemented without a Phase I or a priori knowledge of the parameters of the process. To estimate the time of a detected change, a CUSUM-based change-point estimator can be used, but experiments show that the corresponding MLE has smaller bias and standard error. This paper proposes the sequential use of the self-starting CUSUM chart and the MLE of a change point in series of independent normal observations. Performance is studied with Monte Carlo simulations showing that the use of the MLE reduces the bias of the change-point estimation. It is also shown how extra observations after a change is detected can be used to improve estimation of the change-point time. Copyright

The cumulative capacitated vehicle routing problem: New formulations and iterated greedy algorithms

Abstract In this work, we address the Cumulative Capacitated Vehicle Routing Problem (CCVRP), a variant of the classical CVRP, which aims to minimize the sum of the arrival times to customers instead of the total traveled distance. This problem is relevant due to its applications in fields such as emergency logistics, transportation, wireless network and computing, among others. This paper presents the first two tractable integer formulations capable of solving instances with up to 44 nodes and two versions of an Iterated Greedy procedure for dealing with larger instances. Experimental results show that both formulations obtain optimal solutions in a reasonable amount of computational time. Regarding the two metaheuristic procedures, they were able to reach optimal and best known solutions and, in some cases, outperform the bounds obtained by exact methods for tested instances with up to 199 customers. Using larger instances, the proposed metaheuristics showed competitive results when compared to the best known values reported in the literature, with a significant reduction in computational time.

The sequential normal scores transformation

ABSTRACT The sequential analysis of series often requires nonparametric procedures, where the most powerful ones frequently use rank transformations. Reranking the data sequence after each new observation can become too intensive computationally. This led to the idea of sequential ranks, where only the most recent observation is ranked. However, difficulties finding, or approximating, the null distribution of the statistics may have contributed to the lack of popularity of these methods. In this article, we propose transforming the sequential ranks into sequential normal scores that are independent and asymptotically standard normal random variables. Thus, original methods based on the normality assumption may be used. A novel approach permits the inclusion of a priori information in the form of quantiles. It is developed as a strategy to increase the sensitivity of the scoring statistic. The result is a powerful convenient method to analyze non normal data sequences. Also, four variations of sequential normal scores are presented using examples from the literature. Researchers and practitioners might find this approach useful to develop nonparametric procedures to address new problems extending the use of parametric procedures when distributional assumptions are not met. These methods are especially useful with large data streams where efficient computational methods are required.

A control chart for variance based on squared ranks

ABSTRACT A nonparametric control chart for variance is proposed. The chart is constructed following the change-point approach through the recursive use of the squared ranks test for variance. It is capable of detecting changes in the behaviour of individual observations with performance similar to a self-starting CUSUM chart for scale when normality is assumed, and a relatively better power when assessing nonnormal observations. A comparison is also made with two equivalent nonparametric charts based on Mood and Ansari-Bradley statistics. When dealing with symmetrical distributions, the proposed chart shows smaller (better) out-of-control average run length (ARL), and a competing performance otherwise. In addition, sensitivity to changes in mean and variance at the same time was tested. Extensive Monte Carlo simulation was used to measure performance, and a practical example is provided to illustrate how the proposed control chart can be implemented in practice.