# Online Inventory Management with Application to Energy Procurement in Data Centers

arXiv: Data Structures and Algorithms, Volume abs/1901.04372, 2019.

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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. T...More

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Introduction

- Online optimization and decision making under uncertainty is a fundamental topic that has been studied using a wide range of theoretical tools and in a broad set of applications.
- Motivated by storage management problem for data centers procuring energy from the electricity market, this paper studies a generalization of the classical online optimization formulation: online linear programming with inventory management (OLIM).
- In this problem, in each slot, a decision maker should satisfy d(t) units of an asset, e.g., energy demand, as her demand, either from a market with time-varying price or from her own inventory, e.g., energy storage system.
- A formal statement of the problem is presented in § 2

Highlights

- Online optimization and decision making under uncertainty is a fundamental topic that has been studied using a wide range of theoretical tools and in a broad set of applications
- Motivated by storage management problem for data centers procuring energy from the electricity market, this paper studies a generalization of the classical online optimization formulation: online linear programming with inventory management (OLIM)
- We develop a online algorithms for online linear programming with inventory management and show that the algorithm achieves the minimal competitive ratio achievable by an online algorithm
- We developed two competitive algorithms for online linear programming with inventory management constraints
- We proved that both algorithms achieve the best possible competitive ratio
- We evaluated the proposed algorithms using extensive data-traces from the application of energy procurement in data centers

Methods

- The authors perform trace-based simulations with extensive data traces. The authors use Akamai traces for the energy demand, four different electricity market for the energy prices, and nearby renewable generations to evaluate the results with more uncertainty from renewable generation.
- Basic online algorithm (§3.1) Online algorithm with rate constraints (§3.3) A simple data-driven approach to use optimal solution for the previous day for the current day.
- ▷ (OPT) Optimal offline algorithm with storage by solving OLIM in §2.
- Since OPT represents the best achievable cost for the given inputs, all other algorithms are evaluated by computing empirical cost ratio which is the ratio of the cost of the algorithm with the cost of OPT.
- The cost ratio is always greater than equal to 1 and lower the cost ratio of an algorithm, the better the performance

Results

- To evaluate the performance of the second algorithm BatManRate, the authors consider identical charging and discharge rates, i.e., ρc = ρd , and normalize it against the storage capacity.
- The authors define ρ = ρc /B as a measure of the rate at which an energy storage is charged/discharged relative to its capacity.
- For Flywheels, there is no rate constraints and it reduces to BatMan. the authors investigate the performance of BatManRate for the first three technologies, and report the results in Table 3

Conclusion

- The authors developed two competitive algorithms for online linear programming with inventory management constraints.
- The authors proved that both algorithms achieve the best possible competitive ratio.
- The authors evaluated the proposed algorithms using extensive data-traces from the application of energy procurement in data centers.
- The authors plan to extend the results and tackle maximization version of the problem, and general convex cost function

Summary

## Introduction:

Online optimization and decision making under uncertainty is a fundamental topic that has been studied using a wide range of theoretical tools and in a broad set of applications.- Motivated by storage management problem for data centers procuring energy from the electricity market, this paper studies a generalization of the classical online optimization formulation: online linear programming with inventory management (OLIM).
- In this problem, in each slot, a decision maker should satisfy d(t) units of an asset, e.g., energy demand, as her demand, either from a market with time-varying price or from her own inventory, e.g., energy storage system.
- A formal statement of the problem is presented in § 2
## Methods:

The authors perform trace-based simulations with extensive data traces. The authors use Akamai traces for the energy demand, four different electricity market for the energy prices, and nearby renewable generations to evaluate the results with more uncertainty from renewable generation.- Basic online algorithm (§3.1) Online algorithm with rate constraints (§3.3) A simple data-driven approach to use optimal solution for the previous day for the current day.
- ▷ (OPT) Optimal offline algorithm with storage by solving OLIM in §2.
- Since OPT represents the best achievable cost for the given inputs, all other algorithms are evaluated by computing empirical cost ratio which is the ratio of the cost of the algorithm with the cost of OPT.
- The cost ratio is always greater than equal to 1 and lower the cost ratio of an algorithm, the better the performance
## Results:

To evaluate the performance of the second algorithm BatManRate, the authors consider identical charging and discharge rates, i.e., ρc = ρd , and normalize it against the storage capacity.- The authors define ρ = ρc /B as a measure of the rate at which an energy storage is charged/discharged relative to its capacity.
- For Flywheels, there is no rate constraints and it reduces to BatMan. the authors investigate the performance of BatManRate for the first three technologies, and report the results in Table 3
## Conclusion:

The authors developed two competitive algorithms for online linear programming with inventory management constraints.- The authors proved that both algorithms achieve the best possible competitive ratio.
- The authors evaluated the proposed algorithms using extensive data-traces from the application of energy procurement in data centers.
- The authors plan to extend the results and tackle maximization version of the problem, and general convex cost function

- Table1: Summary of algorithms that are evaluated
- Table2: The empirical cost ratio of different algorithms in different markets and different seasons
- Table3: Comparison of different algorithms using different energy storage technologies
- Table4: Summary of data center locations, markets, and nearby solar and wind power plants used in experiments

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