The multi-vehicle cumulative covering tour problem

International audienceThis paper introduces the multi-vehicle cumulative covering tour problem whose motivation arises from humanitarian logistics. The objective is to determine a set of tours that must be followed by a fleet of vehicles in order to minimize the sum of arrival times (latency) at each visited location. There are three types of locations: mandatory, optional, and unreachable. Each mandatory location must be visited, and optional locations are visited in order to cover the unreachable locations. To guarantee the vehicle autonomy, the duration of each tour should not exceed a given time limit. A mixed integer linear formulation and a greedy randomized adaptive search procedure are proposed for this problem. The performance of the algorithm is assessed over a large set of instances adapted from the literature. Computational results confirm the efficiency of the proposed algorithm

Life expectancy associated with different ages at diagnosis of type 2 diabetes in high-income countries: 23 million person-years of observation

Background The prevalence of type 2 diabetes is increasing rapidly, particularly among younger age groups. Estimates suggest that people with diabetes die, on average, 6 years earlier than people without diabetes. We aimed to provide reliable estimates of the associations between age at diagnosis of diabetes and all-cause mortality, cause-specific mortality, and reductions in life expectancy. Methods For this observational study, we conducted a combined analysis of individual-participant data from 19 highincome countries using two large-scale data sources: the Emerging Risk Factors Collaboration (96 cohorts, median baseline years 1961–2007, median latest follow-up years 1980–2013) and the UK Biobank (median baseline year 2006, median latest follow-up year 2020). We calculated age-adjusted and sex-adjusted hazard ratios (HRs) for all-cause mortality according to age at diagnosis of diabetes using data from 1 515 718 participants, in whom deaths were recorded during 23·1 million person-years of follow-up. We estimated cumulative survival by applying age-specific HRs to age-specific death rates from 2015 for the USA and the EU. Findings For participants with diabetes, we observed a linear dose–response association between earlier age at diagnosis and higher risk of all-cause mortality compared with participants without diabetes. HRs were 2·69 (95% CI 2·43–2·97) when diagnosed at 30–39 years, 2·26 (2·08–2·45) at 40–49 years, 1·84 (1·72–1·97) at 50–59 years, 1·57 (1·47–1·67) at 60–69 years, and 1·39 (1·29–1·51) at 70 years and older. HRs per decade of earlier diagnosis were similar for men and women. Using death rates from the USA, a 50-year-old individual with diabetes died on average 14 years earlier when diagnosed aged 30 years, 10 years earlier when diagnosed aged 40 years, or 6 years earlier when diagnosed aged 50 years than an individual without diabetes. Using EU death rates, the corresponding estimates were 13, 9, or 5 years earlier. Interpretation Every decade of earlier diagnosis of diabetes was associated with about 3–4 years of lower life expectancy, highlighting the need to develop and implement interventions that prevent or delay the onset of diabetes and to intensify the treatment of risk factors among young adults diagnosed with diabetes

Life expectancy associated with different ages at diagnosis of type 2 diabetes in high-income countries: 23 million person-years of observation

Background The prevalence of type 2 diabetes is increasing rapidly, particularly among younger age groups. Estimates suggest that people with diabetes die, on average, 6 years earlier than people without diabetes. We aimed to provide reliable estimates of the associations between age at diagnosis of diabetes and all-cause mortality, cause-specific mortality, and reductions in life expectancy. Methods For this observational study, we conducted a combined analysis of individual-participant data from 19 highincome countries using two large-scale data sources: the Emerging Risk Factors Collaboration (96 cohorts, median baseline years 1961–2007, median latest follow-up years 1980–2013) and the UK Biobank (median baseline year 2006, median latest follow-up year 2020). We calculated age-adjusted and sex-adjusted hazard ratios (HRs) for all-cause mortality according to age at diagnosis of diabetes using data from 1 515 718 participants, in whom deaths were recorded during 23·1 million person-years of follow-up. We estimated cumulative survival by applying age-specific HRs to age-specific death rates from 2015 for the USA and the EU. Findings For participants with diabetes, we observed a linear dose–response association between earlier age at diagnosis and higher risk of all-cause mortality compared with participants without diabetes. HRs were 2·69 (95% CI 2·43–2·97) when diagnosed at 30–39 years, 2·26 (2·08–2·45) at 40–49 years, 1·84 (1·72–1·97) at 50–59 years, 1·57 (1·47–1·67) at 60–69 years, and 1·39 (1·29–1·51) at 70 years and older. HRs per decade of earlier diagnosis were similar for men and women. Using death rates from the USA, a 50-year-old individual with diabetes died on average 14 years earlier when diagnosed aged 30 years, 10 years earlier when diagnosed aged 40 years, or 6 years earlier when diagnosed aged 50 years than an individual without diabetes. Using EU death rates, the corresponding estimates were 13, 9, or 5 years earlier. Interpretation Every decade of earlier diagnosis of diabetes was associated with about 3–4 years of lower life expectancy, highlighting the need to develop and implement interventions that prevent or delay the onset of diabetes and to intensify the treatment of risk factors among young adults diagnosed with diabetes