Online Inventory Management with Application to Energy Procurement in Data Centers

Lin Yang; Mohammad H. Hajiesmaili; Ramesh Sitaraman; Enrique Mallada; Wing S. Wong; Adam Wierman

Home/Archive/arXiv

arXiv · 1901.04372

Online Inventory Management with Application to Energy Procurement in Data Centers

Lin Yang·Mohammad H. Hajiesmaili·Ramesh Sitaraman·Enrique Mallada·Wing S. Wong·Adam Wierman

View original source ↗Read source document ↗Export metadata ↓

Abstract

Motivated by the application of energy storage management in electricity markets, this paper considers the problem of online linear programming with inventory management constraints. Specifically, a decision maker should satisfy some units of an asset as her demand, either form a market with time-varying price or from her own inventory. The decision maker is presented a price in slot-by-slot manner, and must immediately decide the purchased amount with the current price to cover the demand or to store in inventory for covering the future demand. The inventory has a limited capacity and its critical role is to buy and store assets at low price and use the stored assets to cover the demand at high price. The ultimate goal of the decision maker is to cover the demands while minimizing the cost of buying assets from the market. We propose BatMan, an online algorithm for simple inventory models, and BatManRate, an extended version for the case with rate constraints. Both BatMan and BatManRate achieve optimal competitive ratios, meaning that no other online algorithm can achieve a better theoretical guarantee. To illustrate the results, we use the proposed algorithms to design and evaluate energy procurement and storage management strategies for data centers with a portfolio of energy sources including the electric grid, local renewable generation, and energy storage systems.

Explore related subjects

cs.DS math.OC

Keep this discovery

BibTeX RIS

Lin Yang, Mohammad H. Hajiesmaili, Ramesh Sitaraman, Enrique Mallada, Wing S. Wong, Adam Wierman. 2019-01-14. Online Inventory Management with Application to Energy Procurement in Data Centers. https://arxiv.org/abs/1901.04372

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Quasi-Monte Carlo Beyond Hardy-Krause II: $(1 + \varepsilon)n$ Samples Suffice

Numerical integration studies how well one can estimate the integral of a function $f$ over $[0,1)^d$ using $n$ sample points. The two classical methods, Monte Carlo (MC) and quasi-Monte Carlo (QMC), have complementary strengths and weaknesses, and a fundamental question is to design an approach that combines the benefits of both. Recently, building on the transference principle in discrepancy theory, Bansal and Jiang~\cite{BJ25a} gave a randomized QMC method that bridges MC and QMC guarantees using only i.i.d.\ samples. Their method also goes beyond the classical Koksma--Hlawka inequality: it achieves integration error $\widetilde{O}_d(\sigma_{\mathsf{SO}}(f)/n)$, where the smoothed-out variation $\sigma_{\mathsf{SO}}(f)$ can be substantially smaller than the Hardy--Krause variation that governs the classical bound. However, their algorithm requires $n^2$ i.i.d.\ samples as input, and this quadratic blowup is inherent to any method based on the transference principle. In this work, we bypass the quadratic blowup: for any constant $\varepsilon > 0$, we show that $(1+\varepsilon)n$ i.i.d.\ samples suffice to both obtain the beyond-Hardy--Krause guarantee of~\cite{BJ25a}, resolving an open problem posed there, and to produce low-discrepancy point sequences. Our algorithms are variants of the online Haar-thinning method of Dwivedi, Feldheim, Gurel-Gurevich, and Ramdas~\cite{DFG+19}.

cs.DS↗

arXiv2026

A deterministic $(1+\varepsilon)^n$ approximation for the permanent of a nonnegative matrix

For every fixed $0<\varepsilon\le1$, we give a deterministic strongly polynomial algorithm that, given a nonnegative matrix $A\in\mathbb{R}_{\ge0}^{n\times n}$, returns $Q$ satisfying $\operatorname{per} A\le Q\le(1+\varepsilon)^n\operatorname{per} A$.

cs.DS↗

arXiv2026

Single-Exponential Algorithms and a Polynomial Kernel for Strong Connectivity Augmentation

Strong Connectivity Augmentation (SCA) asks whether a directed acyclic graph can be made strongly connected by adding at most $k$ prescribed links whose total weight is within a given budget. Klinkby, Misra, and Saurabh (SODA 2021) gave an $O^*(2^{O(k\log k)})$-time algorithm and asked whether the problem admits a single-exponential parameterized algorithm and a polynomial kernel. We answer both questions affirmatively: SCA can be solved in $O^*(9^k)$ time and admits a polynomial kernel with $O(k^4)$ vertices and $O(k^{16})$ bits. For unweighted SCA, we obtain $O^*(4^k)$ time and a kernel with $O(k^3)$ vertices. Our algorithms are based on a particularly simple reduction to Strongly Connected Spanning Subgraph with two edge costs.

cs.DS↗