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We introduce and study a general version of the fractional online knapsackproblem with multiple knapsacks, heterogeneous constraints on which items canbe assigned to which knapsack, and rate-limiting constraints on the assignmentof items to knapsacks. This problem generalizes variations of the knapsackproblem and of the one-way trading problem that have previously been treatedseparately, and additionally finds application to the real-time control ofelectric vehicle (EV) charging. We introduce a new algorithm that achieves acompetitive ratio within an additive factor of one of the best achievablecompetitive ratios for the general problem and matches or improves upon thebest-known competitive ratio for special cases in the knapsack and one-waytrading literatures. Moreover, our analysis provides a novel approach to onlinealgorithm design based on an instance-dependent primal-dual analysis thatconnects the identification of worst-case instances to the design ofalgorithms. Finally, we illustrate the proposed algorithm via trace-basedexperiments of EV charging.

Competitive Algorithms for the Online Multiple Knapsack Problem with Application to Electric Vehicle Charging