  The knapsack problem is one of the classical problems in combinatorial
optimization: Given a set of items, each specified by its size and profit, the
goal is to find a maximum profit packing into a knapsack of bounded capacity.
In the online setting, items are revealed one by one and the decision, if the
current item is packed or discarded forever, must be done immediately and
irrevocably upon arrival. We study the online variant in the random order model
where the input sequence is a uniform random permutation of the item set.
  We develop a randomized (1/6.65)-competitive algorithm for this problem,
outperforming the current best algorithm of competitive ratio 1/8.06
[Kesselheim et al. SIAM J. Comp. 47(5)]. Our algorithm is based on two new
insights: We introduce a novel algorithmic approach that employs two given
algorithms, optimized for restricted item classes, sequentially on the input
sequence. In addition, we study and exploit the relationship of the knapsack
problem to the 2-secretary problem.
  The generalized assignment problem (GAP) includes, besides the knapsack
problem, several important problems related to scheduling and matching. We show
that in the same online setting, applying the proposed sequential approach
yields a (1/6.99)-competitive randomized algorithm for GAP. Again, our proposed
algorithm outperforms the current best result of competitive ratio 1/8.06
[Kesselheim et al. SIAM J. Comp. 47(5)].
