Determining locations and layouts for parcel lockers to support supply chain viability at the last mile.

The pandemic caused by the corona virus SARS-CoV-2 raised many new challenges for humanity. For instance, governments imposed regulations such as lockdowns, resulting in supply chain shocks at different tiers. Additionally, delivery services reached their capacity limits because the demand for mail orders soared temporarily during the lockdowns. We argue that one option to support supply chain viability at the last-mile delivery tier is to use (outdoor) parcel lockers through which customers can collect their orderings 24/7 while ensuring physical distancing. The location planning of such lockers is known to be of utmost importance for their success. Another important topic to address is that the design of the compartment structure of the parcel lockers should meet the (uncertain) customer demand for different commodities. Both of the latter planning issues are combined into one optimization problem in this article. The objective is to maximize a linear function (e.g., expected profits) of the covered demand, given a budget an operator is willing to invest. An integer linear programming formulation is proposed, and a reformulation based on Benders decomposition is derived. It is shown that the Benders cuts can be separated in linear time. The developed algorithms enable solving of large-scale problem instances demonstrated by a performance analysis of computational experiments. The impact of different problem parameters on the obtained solutions is demonstrated by a sensitivity analysis. A case study based on real-world data from Austria is presented. The results show that using parcel lockers can support supply chain viability at the last-mile delivery tier. Moreover, the relatively small investment cost yields promising returns. The results further indicate that small-sized and medium-sized compartments should be preferred over large and x-large ones in the parcel locker compartment design.

Cardiopulmonary Long-Term Sequelae in Patients after Severe COVID-19 Disease.

We aimed to identify cardiopulmonary long-term effects after severe COVID-19 disease as well as predictors of Long-COVID in a prospective registry. A total of 150 consecutive, hospitalized patients (February 2020 and April 2021) were included six months post hospital discharge for a clinical follow-up. Among them, 49% experienced fatigue, 38% exertional dyspnea and 75% fulfilled criteria for Long-COVID. Echocardiography detected reduced global longitudinal strain (GLS) in 11% and diastolic dysfunction in 4%. Magnetic resonance imaging revealed traces of pericardial effusion in 18% and signs of former pericarditis or myocarditis in 4%. Pulmonary function was impaired in 11%. Chest computed tomography identified post-infectious residues in 22%. Whereas fatigue did not correlate with cardiopulmonary abnormalities, exertional dyspnea was associated with impaired pulmonary function (OR 3.6 [95% CI: 1.2-11], p = 0.026), reduced GLS (OR 5.2 [95% CI: 1.6-16.7], p = 0.003) and/or left ventricular diastolic dysfunction (OR 4.2 [95% CI: 1.03-17], p = 0.04). Predictors of Long-COVID included length of in-hospital stay (OR: 1.15 [95% CI: 1.05-1.26], p = 0.004), admission to intensive care unit (OR cannot be computed, p = 0.001) and higher NT-proBNP (OR: 1.5 [95% CI: 1.05-2.14], p = 0.026). Even 6 months after discharge, a majority fulfilled criteria for Long-COVID. While no associations between fatigue and cardiopulmonary abnormalities were found, exertional dyspnea correlated with impaired pulmonary function, reduced GLS and/or diastolic dysfunction.