Optimal allocation of fire-safety training instructors for municipalities in Taiwan

Personnel-scheduling research has addressed duty rosters, staffing levels, and academic workload allocation, but the allocation of instructors to tiered instructional roles within recurring safety-training programs remains underexplored, particularly where workload equity must hold among personnel of comparable qualification rather than across the pool as a whole. This study formulates fire-safety training instructor allocation as a mixed-integer programme. The objective minimises the sum of within-tier teaching-hour ranges, subject to asymmetric role eligibility, per-slot coverage requirements, assignment exclusivity, and designated-day gender-representation and leadership-presence obligations, together with a secondary term that consolidates assignments into fewer instructor-days. The model is applied to a 15-day municipal training programme in Taiwan involving 30 instructors across three tiers and solved using LINGO 17.0. Relative to the archived manual schedule, the sum of within-tier ranges falls from 50 to 2 h and planning time from approximately 7200 to 100 s; within the junior tier, Jain's fairness index rises from 0.575 to 0.988. Sensitivity analyses across tier composition, policy-group size, and the consolidation coefficient identify a feasibility boundary at three senior instructors. The findings support fairness-oriented optimisation as a decision-support approach for municipal fire-safety training, subject to local recalibration and further validation under dynamic availability and explicit fatigue constraints.