Mathematical model and exact algorithm for the home care worker scheduling and routing problem with lunch break requirements

<p>Home health care or home care (HHC/HC) refers to the delivery of social, medical and paramedical services to clients in their own homes. Each day, care workers start from the HHC/HC centre, visit some clients and return to the centre. During the service delivery process, there is usually a lunch break for each worker. In this paper, we address a real-life home care worker scheduling and routing problem with the consideration of lunch break requirements. A three-index mathematical model is constructed for the problem. The problem is decomposed into a master problem and several pricing sub-problems, and is optimally solved by a branch-and-price (B&P) algorithm. Specifically, a sophisticated label-correcting algorithm is designed to address lunch break constraints in pricing sub-problems; some cutting-edge acceleration strategies are applied during the column generation process. Experimental results show that the proposed B&P algorithm is able to produce satisfied solutions within an acceptable runtime and outperforms the mixed integer programming solver CPLEX.</p

Highly Efficient Carbon Dots with Reversibly Switchable Green–Red Emissions for Trichromatic White Light-Emitting Diodes

Carbon dots (CDs) have potentials to be utilized in optoelectronic devices, bioimaging, and photocatalysis. The majority of the current CDs with high quantum yield to date were limited in the blue light emission region. Herein, on the basis of surface electron-state engineering, we report a kind of CDs with reversible switching ability between green and red photoluminescence with a quantum yield (QY) of both up to 80%. Highly efficient green and red solid-state luminescence is realized by doping CDs into a highly transparent matrix of methyltriethoxysilane and 3-triethoxysilylpropylamine to form CDs/gel glasses composites with QYs of 80 and 78%. The CDs/gel glasses show better transmittance in visible light bands and excellent thermal stability. A blue-pumped CDs/gel glasses phosphor-based trichromatic white light-emitting diode (WLED) is realized, whose color rendering index is 92.9. The WLED gets the highest luminous efficiency of 71.75 lm W^–1 in CDs-based trichromatic WLEDs. This work opens a door for developing highly efficient green- and red-emissive switching CDs which were used as phosphors for WLEDs and have the tendency for applications in other fields, such as sensing, bioimaging, and photocatalysis