Synchronizing inventory and transport within supply chain management

The problem considers synchronized optimization of inventory and transport, and focuses on producer-distributor relations. Particular attention is paid to developing a mathematical model and an optimization problem that can be used to minimize the overall distribution cost by an appropriate placement of warehouses and cross-docking points. Solutions to this problem are explored using genetic algorithms and ideas from graph/network theory. Note: there are three separate reports contained within the uploaded .pdf file

Dynamical simulations of polaron transport in conjugated polymers with the inclusion of electron-electron interactions

Dynamical simulations of polaron transport in conjugated polymers in the presence of an external time-dependent electric field have been performed within a combined extended Hubbard model (EHM) and Su-Schrieffer-Heeger (SSH) model. Nearly all relevant electron-phonon and electron-electron interactions are fully taken into account by solving the time-dependent Schr\"{o}dinger equation for the $\pi$-electrons and the Newton's equation of motion for the backbone monomer displacements by virtue of the combination of the adaptive time-dependent density matrix renormalization group (TDDMRG) and classical molecular dynamics (MD). We find that after a smooth turn-on of the external electric field the polaron is accelerated at first and then moves with a nearly constant velocity as one entity consisting of both the charge and the lattice deformation. An ohmic region (3 mV/$\text{\AA}$ $\leq E_0\leq$ 9 mV/$\text{\AA}$) where the stationary velocity increases linearly with the electric field strength is observed for the case of $U$=2.0 eV and $V$=1.0 eV. The maximal velocity is well above the speed of sound. Below 3 mV/$\text{\AA}$ the polaron velocity increases nonlinearly and in high electric fields with strength $E_0\geq$ 10.0 mV/$\text{\AA}$ the polaron will become unstable and dissociate. The relationship between electron-electron interaction strengths and polaron transport is also studied in detail. We find that the the on-site Coulomb interactions $U$ will suppress the polaron transport and small nearest-neighbor interactions $V$ values are also not beneficial to the polaronic motion while large $V$ values favor the polaron transport