Spontaneous Volunteer Task Assignment in the Acute Phase of Disaster Response: A Rolling-Horizon MIP Approach

This paper presents a dynamic multi-period mixed-integer programming model for the Disaster Volunteer Task Assignment Problem (DVTAP) that advances the humanitarian logistics literature through an integrated treatment of features that have previously appeared only in isolation. Unlike prior formulations that assume volunteer surplus or steady-state conditions, our model reflects the acute-phase reality where tasks far exceed available volunteers and new task arrivals diminish over time as the disaster stabilizes. We incorporate makespan as an optimization objective alongside deprivation-weighted response time, skill matching, workload balance, and volunteer reliability. Ideal-nadir normalization ensures that all objective components contribute meaningfully regardless of their native units. The approach proceeds in two stages. First, we formulate and solve a single-period baseline MIP under volunteer surplus using the CBC solver at four scales (10 to 500 tasks). All four instances are solved to proven optimality, achieving 80 to 100% task coverage with skill-matching rates of 76.9 to 99.6%. Second, we develop a rolling-horizon algorithm that decomposes the multi-period problem into sequential epoch-level MIPs with state transitions, non-homogeneous Poisson task arrivals, fatigue accumulation, and task surplus conditions where the initial task-to-volunteer ratio exceeds 3:1. Computational experiments on three dynamic scenarios (up to 559 mean cumulative tasks) demonstrate that the algorithm achieves mean task completion rates of 84.21 ± 1.92% (Large-Dynamic), 93.74 ± 2.07% (Small-Dynamic), and 94.59 ± 2.03% (Medium-Dynamic) (mean ± standard deviation across 30 Monte Carlo replications) within a 15 h planning horizon, with per-epoch skill-matching rates of 11 to 20% (substantially lower than the static baseline due to triage-mode epochs that force all-volunteer assignment regardless of skill fit). The results reveal a clear regime transition: early epochs operate under severe task surplus where triage dominates, while later epochs transition to volunteer surplus where optimization of secondary objectives becomes feasible. Comparison against a skill-aware greedy heuristic confirms that the MIP’s advantage lies in global multi-objective coordination. This research contributes both a validated mathematical framework and a practical algorithmic approach for multi-period volunteer assignment under demand decay, extending prior work by Sperling and Schryenthrough explicit Poisson dynamics, fatigue state modeling, and makespan optimization.