Stay or Switch: Competitive Online Algorithms for Energy Plan Selection in Energy Markets with Retail Choice

TL;DR

The paper tackles online decision-making for energy plan selection in retail-choice markets by modeling the problem as a metrical task system with temporally dependent switching costs. It introduces a two-state simplification (variable-rate vs fixed-rate) and develops both a deterministic online algorithm with a $3$-competitive ratio and a randomized online algorithm with a $2$-competitive ratio, along with an offline optimum for benchmarking. The approach extends to linearly decreasing cancellation fees, proposing a heuristic with a conjectured bound, and is validated on real-world demand, pricing, and contract data, showing substantial cost savings close to offline optimum for online methods. The practical impact is to enable cost-effective, automated plan selection in dynamic energy markets, potentially boosting residential participation and tightening competition among retailers.

Abstract

Energy markets with retail choice enable customers to switch energy plans among competitive retail suppliers. Despite the promising benefits of more affordable prices and better savings to customers, there appears subsided participation in energy retail markets from residential customers. One major reason is the complex online decision-making process for selecting the best energy plan from a multitude of options that hinders average consumers. In this paper, we shed light on the online energy plan selection problem by providing effective competitive online algorithms. We first formulate the online energy plan selection problem as a metrical task system problem with temporally dependent switching costs. For the case of constant cancellation fee, we present a 3-competitive deterministic online algorithm and a 2-competitive randomized online algorithm for solving the energy plan selection problem. We show that the two competitive ratios are the best possible among deterministic and randomized online algorithms, respectively. We further extend our online algorithms to the case where the cancellation fee is linearly proportional to the residual contract duration. Through empirical evaluations using real-world household and energy plan data, we show that our deterministic online algorithm can produce on average 14.6% cost saving, as compared to 16.2% by the offline optimal algorithm, while our randomized online algorithm can further improve cost saving by up to 0.5%.

Figures (7)

• Figure 1: An example of $\Delta(t)$, $\text{OFA}_s$, $\text{gCHASE}_s$, and $\text{gCHASE}_s^r$. The solutions of running Algorithm 1, 2, and 3 are shown in the last three rows, where $s_t^{\mathcal{A}}$ denotes the state at time $t$ in algorithm ${\mathcal{A}}$, and Pr$[\cdot]$ is the probability notation.
• Figure 2: A worst-case $\Delta(t)$ of $\text{gCHASE}^r_s$ and rCHASErchase. The solutions of running Algorithm 1, 3, and rCHASE are shown in the last three rows, where $\mathbb{E}[\cdot]$ is the expectation notation.
• Figure 3: Constant Cancellation Fee -- cost ratio of online algorithms comparing to the offline algorithm under three demand types for all families.
• Figure 4: Linear Decreasing Cancellation Fee -- cost ratio of online algorithms comparing to the offline algorithm under three demand types for all families.
• Figure 5: Change of Constant Cancellation Fee Under Base Demand Type -- cost ratio of online algorithms comparing to the offline algorithm for all families.

Theorems & Definitions (13)

• Proposition 1
• Definition 1
• Definition 2
• Theorem 1
• Theorem 2
• Theorem 3
• Lemma 1
• Theorem 4
• Definition 3
• Lemma 2