Motivated by many interesting real-world applications in logistics and online advertising, we consider an online allocation problem subject to lower and upper resource constraints, where the requests arrive sequentially, sampled i.i.d. from an unknown distribution, and we need to promptly make a decision given limited resources and lower bounds requirements. First, with knowledge of the measure of feasibility, i.e., $\alpha$, we propose a new algorithm that obtains $1-O(\frac{\epsilon}{\alpha-\epsilon})$ -competitive ratio for the offline problems that know the entire requests ahead of time. Inspired by the previous studies, this algorithm adopts an innovative technique to dynamically update a threshold price vector for making decisions. Moreover, an optimization method to estimate the optimal measure of feasibility is proposed with theoretical guarantee at the end of this paper. Based on this method, if we tolerate slight violation of the lower bounds constraints with parameter $\eta$, the proposed algorithm is naturally extended to the settings without strong feasible assumption, which cover the significantly unexplored infeasible scenarios.

翻译：在物流和在线广告中许多令人感兴趣的现实应用的推动下,我们考虑在线分配问题,但资源限制较低,资源限制较高。 在这种情况下,请求是按顺序、抽样(i.d.d.d.)从未知的分布中获得的,我们需要迅速作出决定,因为资源有限和限制要求较低。首先,我们了解可行性的衡量标准,即$\alpha$,我们提议一种新的算法,获得$-O(frac hipsilon-hepsilon-alpha-epsilon)$($-epsilon)美元($-ephalpha-elslon})-对了解整个请求的离线问题的竞争比率。在以往研究的启发下,这一算法采用了一种创新技术,以动态方式更新决策的临界阈值矢量。此外,在本文末尾提出了一种最优化的方法,在理论保证下估算最佳可行性。根据这种方法,如果我们容忍以美元参数轻微违反较低约束,拟议的算法自然扩展到各种环境,而没有强有力的可行假设,涵盖重大不可行的假设。