Gig-work Management System with Chance-Constraints Verification Algorithm

This paper proposes the framework of an efficient gig-work management system. A gig-work management system recommends one-off tasks with information about task hours and wages to gig-workers. To enable effective management, this paper develops a model of gig-workers’ decision-making. Then, based on the model, we formulate an optimization problem to determine the optimal task hours and wages. The formulated problem belongs to the class of chance-constrained model predictive control (CC-MPC) problems. To efficiently solve the CC-MPC problem, we develop an approximate solution algorithm with guaranteed confidence levels. Finally, we develop gig-worker models based on data collected through crowdsourcing.

💡 Research Summary

The paper addresses the emerging need for systematic management of gig‑work platforms, where short‑term, one‑off tasks are offered to a pool of workers with varying preferences. Recognizing that gig‑workers make acceptance decisions probabilistically rather than deterministically, the authors first develop a behavioral model based on the logit (soft‑max) discrete‑choice framework. Each worker i’s utility is modeled as V_i(ŭ, p, ν_i) = κ ŭ + λ p + ν_i, where κ < 0 captures the disutility of longer task duration, λ > 0 reflects the positive effect of higher wages, and ν_i represents individual‑specific factors. The acceptance probability follows Pr(β_i = 1) = 1/(1 + e^{−V_i}), and the probability that at least one worker in the group accepts a task is 1 − ∏_{i=1}^n 1/(1 + e^{V_i}).

The dynamics of the remaining workload are described by a linear discrete‑time system x(k + 1) = A x(k) − β(k) ŭ(k) + d(k), where A captures the natural growth of pending work when no tasks are performed (eigenvalues ≥ 1 in many realistic settings) and d(k) denotes externally added workload. Because the actual control input u(k) = β(k) ŭ(k) is random, the resulting control problem belongs to the class of chance‑constrained model predictive control (CC‑MPC).

The CC‑MPC formulation seeks to minimize the total wage cost over a prediction horizon N while satisfying two chance constraints: (i) the probability that the predicted workload at horizon end exceeds a reference level x_ref must be bounded by η, and (ii) at each step the probability that no worker accepts the offered task must be below ε. Using the logit model, constraint (ii) can be converted into a deterministic inequality ŭ(t) ≤ \bar{u}(p(t); ν_i, ε) (Equation 9). Constraint (i) remains probabilistic and cannot be directly handled with standard convex techniques.

To solve this problem efficiently, the authors adapt the feasibility verification algorithm of Alamo et al. (2015). The key idea is to iteratively solve a deterministic surrogate (Problem 2) where the chance constraint (i) is ignored, while retaining the deterministic surrogate of (ii). The surrogate problem is solved for a given ε, yielding a candidate control pair (ŭ_c, p_c). A statistical verification step then evaluates whether this candidate satisfies the original chance constraint (i) with confidence at least 1 − δ. This is done by repeatedly sampling the stochastic dynamics, applying a binary flag function g that indicates constraint satisfaction, and using bounds derived from the Riemann ζ‑function to compute lower and upper limits (m_l, M_l) on the number of successes. If M_l · ∑