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When Should you Offer an Upgrade: Online Upgrading Mechanisms for Resource Allocation

Patrick Jaillet, Chara Podimata, Andrew Vakhutinsky, Zijie Zhou

TL;DR

This work study an upgrading scheme for online resource allocation problems and presents a fast algorithm that achieves O(log T) regret, which is a fast algorithm utilizing data akin to those observed in the hospitality industry and estimated to increase the annual revenue by over 17%.

Abstract

In this work, we study an upgrading scheme for online resource allocation problems. We work in a sequential setting, where at each round a request for a resource arrives and the decision-maker has to decide whether to accept it (and thus, offer the resource) or reject it. The resources are ordered in terms of their value. If the decision-maker decides to accept the request, they can offer an upgrade-for-a-fee to the next more valuable resource. This fee is dynamically decided based on the currently available resources. After the upgrade-for-a-fee option is presented to the requester, they can either accept it, get upgraded, and pay the additional fee, or reject it and maintain their originally allocated resource. We take the perspective of the decision-maker and wish to design upgrading mechanisms in a way that simultaneously maximizes revenue and minimizes underutilization of resources. Both of these desiderata are encapsulated in a notion of regret that we define, and according to which we measure our algorithms' performance. We present a fast algorithm that achieves O(log T) regret. Finally, we implemented our algorithm utilizing data akin to those observed in the hospitality industry and estimated our upgrading mechanism would increase the annual revenue by over 17%.

When Should you Offer an Upgrade: Online Upgrading Mechanisms for Resource Allocation

TL;DR

This work study an upgrading scheme for online resource allocation problems and presents a fast algorithm that achieves O(log T) regret, which is a fast algorithm utilizing data akin to those observed in the hospitality industry and estimated to increase the annual revenue by over 17%.

Abstract

In this work, we study an upgrading scheme for online resource allocation problems. We work in a sequential setting, where at each round a request for a resource arrives and the decision-maker has to decide whether to accept it (and thus, offer the resource) or reject it. The resources are ordered in terms of their value. If the decision-maker decides to accept the request, they can offer an upgrade-for-a-fee to the next more valuable resource. This fee is dynamically decided based on the currently available resources. After the upgrade-for-a-fee option is presented to the requester, they can either accept it, get upgraded, and pay the additional fee, or reject it and maintain their originally allocated resource. We take the perspective of the decision-maker and wish to design upgrading mechanisms in a way that simultaneously maximizes revenue and minimizes underutilization of resources. Both of these desiderata are encapsulated in a notion of regret that we define, and according to which we measure our algorithms' performance. We present a fast algorithm that achieves O(log T) regret. Finally, we implemented our algorithm utilizing data akin to those observed in the hospitality industry and estimated our upgrading mechanism would increase the annual revenue by over 17%.
Paper Structure (19 sections, 15 theorems, 58 equations, 3 figures, 1 table, 3 algorithms)

This paper contains 19 sections, 15 theorems, 58 equations, 3 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. Our Contributions and Techniques
  3. Related Work
  4. Model
  5. Model Assumptions and Notations
  6. Algorithm for Two Types of Resources
  7. Benchmark Revenue Upper Bound
  8. Algorithm Description and Regret Analysis
  9. Case 1: $c_1^{(t)}+c_2^{(t)} > (\lambda_1+\lambda_2)(T-t+1)$
  10. Case 2: $c_1^{(t)}+c_2^{(t)} \leq (\lambda_1+\lambda_2)(T-t+1)$
  11. Algorithm for Multiple Types of Resources
  12. Upper Bound on Performance of Any Online Algorithm
  13. Algorithm Description and Regret Analysis
  14. Empirical Study for Hotel Upgrading
  15. Conclusion
  16. ...and 4 more sections

Key Result

Theorem 1

For online resource allocation with $2$ resource types, DynUp-2 incurs regret $O(\log T)$. For online resource allocation with $n$ resource types, DynUp-n incurs regret $O(n \log T)$.

Figures (3)

  • Figure 1: Auxiliary image for the proof sketch. Left: the case where $c_1^{(t)} + c_2^{(t)} < (\lambda_1+\lambda_2) (T-t+1)$. Right: the case where $c_1^{(t)} + c_2^{(t)} \geq (\lambda_1+\lambda_2) (T-t+1)$
  • Figure 2: Left: Distribution of number of requests in each month in 2022. Right: Distribution of a number of requests in each day in November 2022.
  • Figure 3: Left: Daily total revenue of Benchmark and Algorithm DynUp-n in November 2022. Right: Monthly total revenue of Benchmark and Algorithm DynUp-n in 2022.

Theorems & Definitions (15)

  • Theorem 1: Informal
  • Theorem 2
  • Theorem 3
  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • Lemma 5
  • Lemma 6
  • Lemma 7
  • ...and 5 more