In this paper, we introduce a unified mathematical formulation for the Capacitated Vehicle Routing Problem (CVRP) and for the Capacitated Location Routing Problem (CLRP), adopting radiality constraints in order to guarantee valid routes and eliminate subtours. This idea is inspired by formulations already employed in electric power distribution networks, which requires a radial topology in its operation. The results show that the proposed formulation greatly improves the convergence of the solver.
This paper introduces a new bi-objective vehicle routing problem that integrates the Open Location Routing Problem (OLRP), recently presented in the literature, coupled with the growing need for fuel consumption minimization, named Green OLRP (G-OLRP). Open routing problems (ORP) are known to be NP-hard problems, in which vehicles start from the set of existing depots and are not required to return to the starting depot after completing their service. The OLRP is a strategic-level problem involving the selection of one or many depots from a set of candidate locations and the planning of delivery radial routes from the selected depots to a set of customers. The concept of radial paths allows us to use a set of constraints focused on maintaining the radiality condition of the paths, which significantly simplifies the set of constraints associated with the connectivity and capacity requirements and provides a suitable alternative when compared with the elimination problem of sub-tours traditionally addressed in the literature. The emphasis in the paper will be placed on modeling rather than solution methods. The model proposed is formulated as a bi-objective problem, considering the minimization of operational costs and the minimization of environmental effects, and it is solved by using the epsilon constraint technique. The results illustrate that the proposed model is able to generate a set of trade-off solutions leading to interesting conclusions about the relationship between operational costs and environmental impact.
The generalized exponential distribution could be a good option to analyse lifetime data, as an alternative for the use of standard existing lifetime distributions as exponential, Weibull or gamma distributions. Assuming different non-informative prior distributions for the parameters of the model, we introduce a Bayesian analysis using Markov Chain Monte Carlo (MCMC) methods. Some numerical illustrations considering simulated and real lifetime data are presented to illustrate the proposed methodology, especially the effects of different priors on the posterior summaries of interest.
The use of saturated two-level designs is very popular, especially in industrial applications where the cost of experiments is too high. Standard classical approaches are not appropriate to analyze data from saturated designs, since we could only get the estimates of the main factor effects and we would not have degrees of freedom to estimate the variance of the error. In this paper, we propose the use of empirical Bayesian procedures to get inferences for data obtained from saturated designs. The proposed methodology is illustrated assuming a simulated data set.
In this paper, we present a Bayesian analysis of a data set selected from a Brazilian food company. This data set represents the times taken for different quality control analysts to test manufactured products arriving at the company’s quality control department. The samples selected from each batch contain mixtures of different products, which may be submitted to quality testing taking different times. From preliminary analysis of the data, it was observed that the histograms presented two clusters, indicating a mixture of distributions. A mixture of parametrical distributions was thus assumed in the presence of a covariate in order to analyze the data set and to establish standards to be used by the company for the times taken by the analysts. Inferences and predictions are obtained using a Bayesian approach with standard existing Markov Chain Monte Carlo (MCMC) methods.
In this paper, we address the problem of scheduling jobs in a no-wait flowshop problem with sequence-dependent setup times with the objective of minimizing makespan. This problem is well-known for being nondeterministic polynomial-time hard, and small contribution to the problem has been made. We propose a new constructive heuristic named GAPH based on a structural property. The effectiveness of the structural property is crucial given that it is responsible for 100% of the success rate of the total problems tested. The computational results demonstrate that the proposed approach is superior than three of the best-know methods in the literature such as the twos by Bianco, Dell’Olmo and Giordani (INFOR Journal: 37 (1), 3-19, 1999) and TRIPS heuristic adapted for sequence-dependent setup times objective by Brown, Mcgarvey and Ventura (Journal of the Operational Research Society, 55 (6), 614-621, 2004) in terms of the solution quality and that it requires less computational effort.