We study the problem of online peak minimization under inventory constraints. It is motivated by the emerging scenario where large-load customers utilize energy storage to reduce the peak procurement from the grid, which accounts for up to 90 \% of their electric bills. The problem is uniquely challenging due to (i) the coupling of online decisions across time imposed by the inventory constraints and (ii) the noncumulative nature of the peak procurement. In this paper, we develop an optimal online algorithm for the problem that attains the best possible competitive ratio (CR) among all deterministic and randomized algorithms. We show that the optimal CR can be computed in polynomial time, by solving a linear number of linear-fractional problems. We also generalize our approach to develop an anytime-optimal online algorithm that achieves the best possible CR at any epoch, given the inputs and online decisions so far. The algorithm retains the optimal worst-case performance and achieves adaptive average-case performance. Simulation results based on real-world traces show that our algorithms improve peak reduction by more than 19\% as compared to baseline alternatives. \\%DIF > of their electric bills. The problem is uniquely challenging due to (i) the coupling of online decisions across time imposed by the inventory constraints and (ii) the noncumulative nature of the peak procurement. In this paper, we develop an optimal online algorithm for the problem, attaining the best possible competitive ratio (CR) among all deterministic and randomized algorithms. We show that the optimal CR can be computed in polynomial time, by solving a linear number of linear-fractional problems. More importantly, we generalize our approach to develop an anytime-optimal online algorithm that achieves the best possible CR at any epoch, given the inputs and online decisions so far. The algorithm retains the optimal worst-case performance and achieves adaptive average-case performance. Simulation results based on real-world traces show that, under typical settings, our algorithms improve peak reduction by over 19\\% as compared to baseline alternatives.
We study the problem of online peak-demand minimization under energy storage constraints. It is motivated by an increasingly popular scenario where large-load customers utilize energy storage to reduce the peak procurement from the grid, which accounts for up to 90 \\%DIF > of their electric bills. The problem is uniquely challenging due to (i) the coupling of online decisions across time imposed by the inventory constraints and (ii) the noncumulative nature of the peak procurement. In this paper, we develop an optimal online algorithm for the problem, attaining the best possible competitive ratio (CR) among all deterministic and randomized algorithms. We show that the optimal CR can be computed in polynomial time, by solving a linear number of linear-fractional problems. More importantly, we generalize our approach to develop an anytime-optimal online algorithm that achieves the best possible CR at any epoch, given the inputs and online decisions so far. The algorithm retains the optimal worst-case performance and achieves adaptive average-case performance. Simulation results based on real-world traces show that, under typical settings, our algorithms improve peak reduction by over 19\\% as compared to baseline alternatives.
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peak minimization under inventory
peak-demand minimization under energy storage
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the emerging
an increasingly popular
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\% of their electric bills. The problem is uniquely challenging due to (i) the coupling of online decisions across time imposed by the inventory constraints and (ii) the noncumulative nature of the peak procurement. In this paper, we develop an optimal online algorithm for the problem that attains the best possible competitive ratio (CR) among all deterministic and randomized algorithms. We show that the optimal CR can be computed in polynomial time, by solving a linear number of linear-fractional problems. We also generalize our approach to develop an anytime-optimal online algorithm that achieves the best possible CR at any epoch, given the inputs and online decisions so far. The algorithm retains the optimal worst-case performance and achieves adaptive average-case performance. Simulation results based on real-world traces show that our algorithms improve peak reduction by more than 19\% as compared to baseline alternatives.