An inventory management problem is addressed for a make-to-order supply chain that has inventory holding and/or manufacturing locations at each node. The lead times between nodes and production capacity limits are heterogeneous across the network. This study focuses on a single product, a multi-period centralized system in which a retailer is subject to an uncertain stationary consumer demand at each time period. Two sales scenarios are considered for any unfulfilled demand: backlogging or lost sales. The daily inventory replenishment requests from immediate suppliers throughout the network are modeled and optimized using three different approaches: (1) deterministic linear programming, (2) multi-stage stochastic linear programming, and (3) reinforcement learning. The performance of the three methods is compared and contrasted in terms of profit (reward), service level, and inventory profiles throughout the supply chain. The proposed optimization strategies are tested in a stochastic simulation environment that was built upon the open-source OR-Gym Python package. The results indicate that, of the three approaches, stochastic modeling yields the largest increase in profit, whereas reinforcement learning creates more balanced inventory policies that would potentially respond well to network disruptions. Furthermore, deterministic models perform well in determining dynamic reorder policies that are comparable to reinforcement learning in terms of their profitability.
The spatial profile of a magnetically self-confined plasma formed by a magneto-plasma compressor is measured in radial and axial direction with an array of Faraday cups, and radiation with a wavelength as short as extreme ultraviolet is detected. A Gaussian distribution approximates the radial profile of the ion current density. Along the axis, the ion current density remains approximately constant up to 2.25 inner anode radii from the electrodes end, before diverging. The plasma stream is further compressed by the addition of an external magnetic field. The external magnetic field is measured and is close to the self-induced magnetic field. The measurements of the profile show an increase in the ion current density after the inlet into the external magnetic field. The ion current density at 3.25 inner anode radii from the end of the electrodes doubles, and the width of the plasma stream decreases. Estimations show that the increase of the ion current density is also due to an increase of around 25% of the mean ion charge, hence to a temperature increase of around 50% enhancing photon emission at shorter wavelength. A design guideline is presented to dimensionalize the amplitude of the external magnetic field depending on the wanted temperature increase in the plasma stream.
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