Online contention resolution schemes (OCRSs) are effective rounding techniques for online stochastic combinatorial optimization problems. These schemes randomly and sequentially round a fractional solution to a relaxed problem that can be formulated in advance. In this study, we propose OCRSs for online stochastic generalized assignment problems. In the problem of our OCRSs, sequentially arriving items are packed into a single knapsack, and their sizes are revealed only after insertion. The goal of the problem is to maximize the acceptance probability, which is the smallest probability among the items being placed in the knapsack. Since the item sizes are unknown beforehand, a capacity overflow may occur. We consider two distinct settings: the hard constraint, where items that cause overflow are rejected, and the soft constraint setting, where such items are accepted. Under the hard constraint setting, we present an algorithm with an acceptance probability of $1/3$ and prove that no algorithm can achieve an acceptance probability greater than $3/7$. Under the soft constraint setting, we propose an algorithm with an acceptance probability of $1/2$ and demonstrate that this is best possible.

翻译：在线竞争解决机制（OCRS）是解决在线随机组合优化问题的有效舍入技术。这些机制将松弛问题的分数解进行随机化顺序舍入，该松弛问题可预先构建。在本研究中，我们针对在线随机广义分配问题提出了OCRS。在我们的OCRS问题中，依次到达的物品被装入单个背包，其尺寸仅在插入后才会呈现。该问题的目标是最大化接受概率，即所有物品中被装入背包的最小概率。由于物品尺寸事先未知，可能会发生容量溢出。我们考虑两种不同的约束设置：硬约束（导致溢出的物品被拒绝）与软约束（此类物品被接受）。在硬约束设置下，我们提出了一种接受概率为$1/3$的算法，并证明无算法能实现大于$3/7$的接受概率。在软约束设置下，我们提出了一种接受概率为$1/2$的算法，并证明这是最优可达结果。