Robust Dynamic Staffing with Predictions

2025-10-18

AI Summary

This paper studies the dynamic hiring problem: a decision-maker must sequentially hire workers over a finite horizon to satisfy an unknown demand revealed only at the end. As time progresses, demand forecasts become more accurate, yet worker availability declines—creating a fundamental trade-off between early hiring (risking over-hiring) and late hiring (risking under-hiring). The problem arises in gig-economy settings such as last-mile delivery. We propose a model-agnostic adversarial minimax online algorithm: it models forecasts via uncertainty intervals, formulates the robust optimal cost as a linear program, and designs an efficiently re-solvable online policy. The algorithm accommodates multi-stage demand, hiring reversal costs, and non-uniform prediction intervals. Numerical experiments demonstrate that it outperforms Bayesian heuristic methods in both cost and runtime efficiency, and remains competitive even when compared against computationally expensive optimal benchmarks.

Technology Category

• Search and Optimization: Adversarial Search
• Machine Learning: Online Learning & Bandits
• Planning, Routing, and Scheduling: Scheduling under Uncertainty

Application Category

• Economics, Online Markets and Human Computation: The sharing economy
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We consider a natural dynamic staffing problem in which a decision-maker sequentially hires workers over a finite horizon to meet an unknown demand revealed at the end. Predictions about demand arrive over time and become increasingly accurate, while worker availability decreases. This creates a fundamental trade-off between hiring early to avoid understaffing (when workers are more available but forecasts are less reliable) and hiring late to avoid overstaffing (when forecasts are more accurate but availability is lower). This problem is motivated by last-mile delivery operations, where companies such as Amazon rely on gig-economy workers whose availability declines closer to the operating day. To address practical limitations of Bayesian models (in particular, to remain agnostic to the underlying forecasting method), we study this problem under adversarial predictions. In this model, sequential predictions are adversarially chosen uncertainty intervals that (approximately) contain the true demand. The objective is to minimize worst-case staffing imbalance cost. Our main result is a simple and computationally efficient online algorithm that is minimax optimal. We first characterize the minimax cost against a restricted adversary via a polynomial-size linear program, then show how to emulate this solution in the general case. While our base model focuses on a single demand, we extend the framework to multiple demands (with egalitarian/utilitarian objectives), to settings with costly reversals of hiring decisions, and to inconsistent prediction intervals. We also introduce a practical "re-solving" variant of our algorithm, which we prove is also minimax optimal. Finally we conduct numerical experiments showing that our algorithms outperform Bayesian heuristics in both cost and speed, and are competitive with (approximate or exact) Bayesian-optimal policies when those can be computed.

Problem

• Balancing early hiring against late hiring for optimal staffing
• Addressing adversarial predictions in dynamic worker recruitment
• Minimizing worst-case staffing imbalance costs efficiently

Innovation

• Adversarial prediction intervals for staffing optimization
• Minimax optimal online algorithm with computational efficiency
• Extensible framework supporting reversals and inconsistent predictions