Inventory models with lost sales and large lead times have traditionally been considered intractable due to the curse of dimensionality. Recently, Goldberg and co-authors laid the foundations for a new approach to solving these models, by proving that as the lead time grows large, a simple constant-order policy is asymptotically optimal. However, the bounds proven there require the lead time to be very large before the constant-order policy becomes effective, in contrast to the good numerical performance demonstrated by Zipkin even for small lead time values. In this work, we prove that for the infinite-horizon variant of the same lost sales problem, the optimality gap of the same constant-order policy actually converges exponentially fast to zero, with the optimality gap decaying to zero at least as fast as the exponential rate of convergence of the expected waiting time in a related single-server queue to its steady-state value. We also derive simple and explicit bounds for the optimality gap, and demonstrate good numerical performance across a wide range of parameter values for the special case of exponentially distributed demand. Our main proof technique combines convexity arguments with ideas from queueing theory.

Dual-sourcing inventory systems, in which one supplier is faster (i.e. express) and more costly, while the other is slower (i.e. regular) and cheaper, arise naturally in many real-world supply chains. These systems are notoriously difficult to optimize due to the complex structure of the optimal solution and the curse of dimensionality, having resisted solution for over 40 years. Recently, so-called Tailored Base-Surge (TBS) policies have been proposed as a heuristic for the dual-sourcing problem. Under such a policy, a constant order is placed at the regular source in each period, while the order placed at the express source follows a simple order-up-to rule. Numerical experiments by several authors have suggested that such policies perform well as the lead time difference between the two sources grows large, which is exactly the setting in which the curse of dimensionality leads to the problem becoming intractable. However, providing a theoretical foundation for this phenomenon has remained a major open problem.In this paper, we provide such a theoretical foundation by proving that a simple TBS policy is indeed asymptotically optimal as the lead time of the regular source grows large, with the lead time of the express source held fixed. Our main proof technique combines novel convexity and lower-bounding arguments, an explicit implementation of the vanishing discount factor approach to analyzing infinite-horizon Markov decision processes, and ideas from the theory of random walks and queues, significantly extending the methodology and applicability of a novel framework for analyzing inventory models with large lead times recently introduced by Goldberg and co-authors in the context of lost-sales models with positive lead times.

bone-marrow-MSCs have greater in vivo chondrogenic potential than periosteum-, synovium-, adipose- and muscle-MSCs.

In this paper, we propose a risk-based data-driven approach to optimal power flow (DROPF) with dynamic line rating. The risk terms, including penalties for load shedding, wind generation curtailment and line overload, are embedded into the objective function. To hedge against the uncertainties on wind generation data and line rating data, we consider a distributionally robust approach. The ambiguity set is based on second-order moment and Wasserstein distance, which captures the correlations between wind generation outputs and line ratings, and is robust to data perturbation. We show that the proposed DROPF model can be reformulated as a conic program. Considering the relatively large number of constraints involved, an approximation of the proposed DROPF model is suggested, which significantly reduces the computational costs. A Wasserstein distance constrained DROPF and its tractable reformulation are also provided for practical large-scale test systems. Simulation results on the 5-bus, the IEEE 118-bus and the Polish 2736-bus test systems validate the effectiveness of the proposed models.

The aim of the study was to explore the relationship between the concentration of C-telopeptide fragments of type II collagen (CTX-II), Zn2+, and Ca2+ in urine and knee osteoarthritis (KOA).Eighty-two patients with KOA and 20 healthy volunteers were enrolled. Anteroposterior and lateral position x-rays of knee joints were collected. The images were classified according to Kellgren-Lawrence radiographic grading criterion. The patients were divided into group grade I, group grade II, group grade III, and grade IV. The concentration of CTX-II in the urine was detected by enzyme-linked immunosorbent assay. The concentration of Zn2+ and Ca2+ in urine was detected by inductively coupled plasma atomic emission spectrometry.Compared with the healthy individuals, the concentration of CTX-II was significantly higher in KOA patients. The concentration of CTX-II in KOA patients from high to low was as follows: group IV, group III, group II, and group I. There was no significant difference between group I and healthy individuals. The concentration of Zn2+ and Ca2+ in urine of KOA patients was higher than that in healthy individuals. There was no difference in each KOA group.The concentration of CTX-II is instrumental to diagnose the progress of KOA. The concentration of Zn2+ and Ca2+ in urine is helpful for early diagnosis of KOA.