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Notification Timing for On-Demand Personnel Scheduling

Prakash Gawas, Antoine Legrain, Louis-Martin Rousseau

TL;DR

The paper studies how to schedule on demand shifts by notifying senior employees first while allowing them to bump juniors under constraints, framing this as the Notification Timing Problem (NTP). It proves $NP$-hardness for offline variants via a subset sum reduction and develops a two-stage stochastic DNTP to capture uncertainty in response delays, complemented by threshold based policy function approximations (PFAs). The authors show offline solutions can nearly eliminate bumps, and they propose the ONP threshold policy which, when validated on real data, outperforms the current practice and closely matches stochastic performance while keeping vacancies under a 0.3% target. Practically, the work provides a scalable methodology for data driven notification timing that improves staffing reliability and reduces disruptions in on-demand platforms, with clear guidance on implementing offline learned thresholds and policy choices.

Abstract

Modern business models have enabled service systems to leverage a large pool of casual employees with flexible hours, paid based on piece rates, to fulfill on-demand work. These systems have been successfully implemented in sectors such as ride-sharing, delivery services, and microtasks. However, because casual employees engage infrequently and may lack experience, maintaining service quality remains a key challenge. We introduce a novel scheduling system designed to provide experienced casual employees to service companies, optimizing their operations through a dynamic, data-driven approach. Similar to traditional on-call systems, it contacts casual personnel in order of seniority to inform them about available work. However, our system offers greater flexibility, allowing employees to take time to decide and freely select from available shifts. Senior employees can also replace (bump) junior employees from the schedule if no other preferred shift is available, subject to certain conditions. While permitted, these replacements create disruptions and dissatisfaction among employees. The management aims to efficiently assign all shifts while minimizing bumps. However, uncertainty arises regarding when an employee will select a shift. The key challenge is determining the optimal timing to notify employees to reduce disruptions. We first establish that this problem is $\mathcal{NP}$-complete even with perfect information. To address this, we propose a two-stage stochastic formulation for the dynamic problem and develop a heuristic algorithm that approximates the optimal policy using a threshold-based structure. These policies are fine-tuned using offline solutions with pre-known uncertainty, allowing for optimization. Testing on real-world data demonstrates that our approach outperforms the current strategy used by our industry partner.

Notification Timing for On-Demand Personnel Scheduling

TL;DR

The paper studies how to schedule on demand shifts by notifying senior employees first while allowing them to bump juniors under constraints, framing this as the Notification Timing Problem (NTP). It proves -hardness for offline variants via a subset sum reduction and develops a two-stage stochastic DNTP to capture uncertainty in response delays, complemented by threshold based policy function approximations (PFAs). The authors show offline solutions can nearly eliminate bumps, and they propose the ONP threshold policy which, when validated on real data, outperforms the current practice and closely matches stochastic performance while keeping vacancies under a 0.3% target. Practically, the work provides a scalable methodology for data driven notification timing that improves staffing reliability and reduces disruptions in on-demand platforms, with clear guidance on implementing offline learned thresholds and policy choices.

Abstract

Modern business models have enabled service systems to leverage a large pool of casual employees with flexible hours, paid based on piece rates, to fulfill on-demand work. These systems have been successfully implemented in sectors such as ride-sharing, delivery services, and microtasks. However, because casual employees engage infrequently and may lack experience, maintaining service quality remains a key challenge. We introduce a novel scheduling system designed to provide experienced casual employees to service companies, optimizing their operations through a dynamic, data-driven approach. Similar to traditional on-call systems, it contacts casual personnel in order of seniority to inform them about available work. However, our system offers greater flexibility, allowing employees to take time to decide and freely select from available shifts. Senior employees can also replace (bump) junior employees from the schedule if no other preferred shift is available, subject to certain conditions. While permitted, these replacements create disruptions and dissatisfaction among employees. The management aims to efficiently assign all shifts while minimizing bumps. However, uncertainty arises regarding when an employee will select a shift. The key challenge is determining the optimal timing to notify employees to reduce disruptions. We first establish that this problem is -complete even with perfect information. To address this, we propose a two-stage stochastic formulation for the dynamic problem and develop a heuristic algorithm that approximates the optimal policy using a threshold-based structure. These policies are fine-tuned using offline solutions with pre-known uncertainty, allowing for optimization. Testing on real-world data demonstrates that our approach outperforms the current strategy used by our industry partner.
Paper Structure (33 sections, 33 theorems, 32 equations, 8 figures, 10 tables, 2 algorithms)

This paper contains 33 sections, 33 theorems, 32 equations, 8 figures, 10 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. On-Demand Labor Platforms
  3. On-Demand Shift Scheduling System
  4. Research Contribution
  5. Problem Description and Computational Complexity
  6. Problem Description
  7. Offline NTP Formulation
  8. Employee Preferences
  9. MIP Model
  10. Preliminaries
  11. Example:
  12. Reduction
  13. Example:
  14. Intuition
  15. Proof
  16. ...and 18 more sections

Key Result

Theorem 1

Given an instance $I = \{H, M, \mathbf{r}\}$, let $S^*_\mathcal{X}$ denote an optimal schedule with preferences $\mathcal{X}$ such that $\mathcal{X} = \{{\mathcal{X}_i}\}_{i \in \mathcal{E}}$. Also, let $S^*_p$ be the schedule that minimizes the total potential bumps for this instance, and $S^*_I$ b

Figures (8)

  • Figure 1: (a) NBS : $\mathbf{C_0^* = 11}$, (b) $\mathbf{S_1^*}$ : $\mathbf{B(S_1^*) = 1}$ and $\mathbf{C(S_1^*) = 10}$, (c) $\mathbf{S_2^*}$ : $\mathbf{B(S_2^*) = 1}$ and $\mathbf{C(S_2^*) = 10}$
  • Figure 2: (a) NBS : $C^{*}_{0} = 24$ (b) $\mathbf{S^*}$ : $\mathbf{B(S^*) = 5}$ and $C(S^*) = 19$;
  • Figure 3: CDF plot of Response Delay
  • Figure 4: Cumulative Notifications Sent
  • Figure 5: Train vs Test performance of ${\textbf{MIP}_{\textbf{DNTP-S}}}$ - Average Bumps
  • ...and 3 more figures

Theorems & Definitions (34)

  • Theorem 1
  • Corollary 1
  • Proposition 1
  • Definition 1
  • Proposition 2
  • Proposition 3
  • Proposition 4
  • Proposition 5
  • Proposition 6
  • Corollary 2
  • ...and 24 more