大型醫院批價與領藥服務人力配置之最佳化模型

Abstract

本研究利用數學規劃方法求解大型醫院批價與領藥服務人力配置問題。研究中首先以 逐點流體基礎近似法 (point-wise fluid-based approximation approach) 來描述此動態等候網路 (dynamic queuing networks) 中的顧客等候長度變化，接著將此等候網路與最佳化建模整合， 以最小化顧客等候成本與醫院營運成本作為求解目標，建構批價與領藥服務人力配置最佳化模型，所求解之服務人力數量必須介於各等候處所規定的人力數量配置上限以及最少所需的人力數量配置下限。本研究根據台北市某一大型教學中心醫院之資料產生接近實際狀況之測 試例題，利用 GAMS 的 MINOS 求解器求解此測試例題之最佳批價與領藥服務人力配置，並 調整顧客抵達率、服務率與目標式各成本項權重來探討各成本項對服務人力及等候人數的影響。研究結果發現最佳化模型所求得之人力配置，有明顯的改善效益，每天可為醫院節省約 15%的營運成本，同時也可降低約 91.6%的顧客等候成本。本研究所建立之模型可提供大型醫 院作為批價與領藥人力配置決策之參考。

This paper presents a mathematical programming model to determine the optimal numbers of cashiers and dispensaries in a large hospital. The objective of this model is to minimize customers’ total waiting cost and the hospital’s operational cost. A point-wise fluid-based approximation approach is adopted to construct a dynamic queuing network that describes the expected queue length of customer. The dynamic queuing network is then encapsulated in an optimization model that determines optimal time-varying numbers of cashier and dispensary servers per time unit and subject to the minimal and maximal server requirements set by the hospital. A test problem instance was designed based on a large hospital in Taipei city, and the MINOS solver of GAMS was applied to solve for the optimal time-varying cashier and dispensary servers. The sensitivity analyses were also conducted to examine the impacts of customer arrival rates, service rates, and weights of the cost components in the objective function on the waiting cost and operational cost. Numerical results showed that the proposed optimization model can provide an optimal strategy of the manpower allocation to reduce the waiting cost and operational cost.