近年來消防機關普遍面臨人力短缺與勤務負荷高漲之挑戰，救災與救護勤務具有高度不確定性，需消防人員於 24 小時內保持機動待命，這種「待命狀態」雖未產生實質勤務輸出，卻是消防戰力不可或缺的組成部分，本研究定義此類為維持應變量能存在、具隨機性且不可或缺的待命負荷為「虛工」。實務上各分隊人力配置多依主管經驗法則，且多僅以「實質勤務量」作為評估標準，缺乏量化之客觀依據。此舉常造成部分分隊長期負擔較重、勤務分配不均、各單位對人力需求之主觀認知落差顯著，甚至引發跨單位的人力競逐，影響整體消防戰力。本研究係以某縣市政府消防局某大隊所轄三個分隊（Ａ、Ｂ、Ｃ）為研究範圍，依據過去之歷史勤務統計，考量救災、救護、空跑勤務、交通時間與人員結構等，建構一套整數規劃最佳化模式。模型以「各消防員於研究週期內之疲勞度差異最小化」為目標，並考量幹部與隊員不同勤務限制、女性消防員配置條件、各分隊最低人力門檻、交通時間對救護勤務之影響等因素，以求得公平而合理的分隊人力分配方案。 本研究使用 LINGO 20.0 進行求解，並搭配 Excel 驗證與分析。範例結果顯示，最佳化模式之公平性指標顯著優於現行人工配置，能有效縮小分隊間的勤務負擔差異。並透過導入「虛工」機制納入考量，更能精確算出各分隊在達致整體勞逸均衡時所具備之「閒置量能」或「調節韌性」。此外，透過敏感度分析針對總員額變動、勤務量增減及權重參數設定進行探討，驗證了模式在面對外部環境變動時的系統韌性，並標定出運作邊界與關鍵限制因子。本研究成果不僅可提供消防機關於分隊人力調整與增補評估之決策支援，其模型之「各分隊虛工數據」，更可填補實務管理之空白，作為決策者指派非例行性臨時勤業務（如專案公差、大型宣導等）之關鍵客觀依據，為有限的消防人力資源提供兼顧公平與彈性的最佳化管理工具。;In recent years， fire departments have faced significant challenges due to personnel shortages and increasing workloads. Emergency rescue and medical services are characterized by high uncertainty， requiring personnel to maintain 24-hour standby readiness. Although this "standby state" does not produce tangible service output， it remains an indispensable component of firefighting combat power. This study defines the stochastic and essential standby load required to maintain response capacity as "Virtual Work." In practice， the allocation of personnel across fire stations often relies on the rule of thumb of supervisors and is primarily evaluated based on "actual workload，" lacking a quantitative and objective basis. This frequently leads to long-term overburdening of certain stations， uneven duty distribution， and significant subjective gaps in perceived manpower needs， which may even trigger inter-unit competition for personnel and affect overall operational effectiveness. This research focuses on three stations (A， B， and C) under a specific fire bureau division. Based on historical duty statistics and considering factors such as fire suppression， emergency medical services (EMS)， false alarms， transit times， and personnel structure， an Integer Programming optimization model is constructed. The model aims to "minimize the variance in fatigue levels among firefighters" within the research cycle. It incorporates constraints such as duty limitations for officers versus firefighters， female personnel allocation requirements， minimum staffing thresholds for each station， and the impact of transit time on EMS， seeking a fair and rational manpower distribution scheme. The model was solved using LINGO 20.0 and validated through Excel analysis. Results indicate that the optimization model’s fairness index is significantly superior to current manual allocations， effectively narrowing the workload gap between stations. By incorporating the "Virtual Work" mechanism， the model not only allocates actual duties but also accurately calculates the "buffer capacity" or "regulatory resilience" of each station when overall labor-leisure equilibrium is achieved. Furthermore， through sensitivity analysis of total staffing changes， workload fluctuations， and weight parameter settings， the system′s resilience to external environmental changes was verified， identifying operational boundaries and key limiting factors. The findings of this study provide decision-making support for personnel adjustment and recruitment evaluation in fire departments. Additionally， the "Virtual Work" data fills a gap in practical management， serving as an objective basis for assigning non-routine tasks (such as special projects or public outreach)， thereby providing an optimized management tool that balances fairness and flexibility for limited firefighting resources.
