基於資料包絡分析的夏普利值模型在警務人員配置中的應用

Abstract

臺灣警力不足問題存在已久，而現代社會對治安需求的日益提升，進一步加重了基層警力的負擔。派出所基層警員除了維持日常勤務的正常運作以外，如遇有節慶活動或是民眾集會遊行活動等此類需要大量警力來維護公共秩序及保護社會安全的情況，警力問題更顯捉襟見肘，現有警力調度的挑戰愈加急迫。 目前警力的分配與調度大多依賴單位主管或執行業務的承辦人員的經驗判斷或主觀決策，然而此種方法是非理性的，缺乏系統化與科學性，可能導致資源分配不均或效率低下。如何引入科學化方法以妥善分配有限警力資源，降低基層警員的負擔與疲勞度，已成為台灣警界不容忽視及亟待解決的關鍵議題。 本文提出一種基於 DEA (Data Envelopment Analysis) 與 Shapley value 的模型，目的是在有限的警力資源下，對於臨時性或突發性的警力支援需求情形，進行最適化分配，將對日常勤務的影響降至最低。以單一警察局為例，警察局轄下有數個派出所，當需要警力支援的陳情抗議事件發生時，該如何科學性且合理地調度各派出所的人力？我們在此DEA-based Shapley value model中，首先將各派出所視為決策單元 (Decision-Making Units, DMUs)，利用 DEA 模型計算其效率分數，再透過效用函數(Utility Function)將效率分數轉換為代表各單位貢獻能力的效用值 (Utility Value)。接著，將各派出所組成大聯盟 (Grand Coalition) 進行合作賽局，計算 Shapley value，以衡量各派出所在團體合作中的邊際貢獻，藉此進一步推導出各派出所應派遣支援陳抗活動的人力數量。 本研究透過DEA-based Shapley value model，實現科學化、合理化的人力資源分配。我們將結合台灣警界的實務案例，展示此模型在實務操作上的可行性、實用價值及效益。

The issue of insufficient police manpower in Taiwan has persisted for a long time, and the growing demand for public security in modern society has further increased the burden on police officers. In addition to maintaining the routine operation of daily duties, officers are also required to be deployed significant manpower for events such as festive activities or public protests, which are critical for maintaining public order and safety, and promoting social stability. The shortage of police resources has become even more pressing, and the challenge of managing police manpower allocation has become increasingly urgent. The current allocation and scheduling of police manpower largely rely on the judgment or subjective decisions of unit leaders or officers in charge. However, this approach is irrational, lacks systematic and scientific foundations, and may lead to uneven resource distribution or inefficiency. How to introduce scientific methods to properly allocate limited police resources and reduce the burden on police officers has become a pressing concern within Taiwan's police system that requires attention. This paper presents a model based on DEA (Data Envelopment Analysis) and Shapley value, with the aim of optimizing the allocation of police manpower resources for temporary or emergency support needs under limited police resources, while minimizing the impact on routine duties. Taking a police precinct as an example, with several police stations under its jurisdiction, how should manpower be allocated scientifically and reasonably when an event, such as a protest or demonstration requiring police support, occurs? In this DEA-based Shapley value model, each police station is treated as a decision-making unit (DMU), whose efficiency score is derived from the traditional DEA model. Then, the efficiency score is converted into a utility value, representing each unit's independent contribution capacity, through a utility function. Next, the police stations participate in a cooperative game to form a grand coalition, and the Shapley value is calculated to measure how each station contributes marginally to the overall outcome. This allows us to further derive the amount of manpower each police station should dispatch to support the festive activities or public protests. By applying the DEA-based Shapley value model, this study aims to achieve a scientific and rational distribution of manpower resources. A real-world case from the Taiwanese police force is incorporated to demonstrate the proposed model’s practicality and benefits".