Three time-based scale formulations for the two-stage lot sizing and scheduling in process industries

In this paper, we propose three novel mathematical models for the two-stage lot-sizing and scheduling problems present in many process industries. The problem shares a continuous or quasi-continuous production feature upstream and a discrete manufacturing feature downstream, which must be synchronized. Different time-based scale representations are discussed. The first formulation encompasses a discrete-time representation. The second one is a hybrid continuous-discrete model. The last formulation is based on a continuous-time model representation. Computational tests with state-of-the-art MIP solver show that the discrete-time representation provides better feasible solutions in short running time. On the other hand, the hybrid model achieves better solutions for longer computational times and was able to prove optimality more often. The continuous-type model is the most flexible of the three for incorporating additional operational requirements, at a cost of having the worst computational performance. Journal of the Operational Research Society (2012) 63, 1613-1630. doi:10.1057/jors.2011.159 published online 7 March 2012

Tuberculosis and latent tuberculosis in prison inmates

OBJECTIVE: To estimate the prevalences of tuberculosis and latent tuberculosis ill inmates. METHODS: Observational study was carried out with inmates of a prison and a jail in the State of Sao Paulo, Southeastern Brazil, between March and December of 2008. Questionnaires were used to collect sociodemographic and epidemiological data. Tuberculin skin testing was administered (PPD-RT23-2TU/0.1 mL), and the following laboratory tests were also performed: sputum smear examination, sputum culture, identification of strains isolated and drug susceptibility testing. The variables were compared using Pearson's chi-square (chi(2)) association test, Fisher's exact test and the proportion test. RESULTS: Of the 2,435 inmates interviewed, 2,237(91.9%) agreed to submit to tuberculin skin testing and of these, 73.0% had positive reactions. The prevalence of tuberculosis was 830.6 per 100,000 inmates. The coefficients of prevalence were 1,029.5/100,000 for inmates of the prison and 525.7/100,000 for inmates of the jail. The sociodemographic characteristics of the inmates in the two groups studied were similar; most of the inmates were young and single with little schooling. The epidemiological characteristics differed between the prison units, with the number of cases of previous tuberculosis and of previous contact with the disease greater in the prison and coughing, expectoration and smoking more common in the jail. Among the 20 Mycobacterium tuberculosis strains identified, 95.0% were sensitive to anti-tuberculosis drugs, and 5.0% were resistant to streptomycin. CONCLUSIONS: The prevalences of tuberculosis and latent tuberculosis were higher in the incarcerated population than in the general population, and they were also higher in the prison than in the jail.