本研究發展多目標數學模式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方法(Point-wise Fluid-Based Approximation Approach)來描述此動態等候系統(dynamic queuing system)中的顧客等候長度變化,接著將此等候系統與最佳化數學規劃模型整合,以最小化顧客等候成本與醫院的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,且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:最佳化模式所求得之人力配置,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;而當整體抵達率增加,服務人力與等候人數將會隨之增加;當整體服務率增加,服務人力與等候人數將會隨之減少;當營運成本權重增加,同時減少等候成本權重,批價及配藥處的服務人力將會減少,而等候人數將會增加。求解結果可提供給大型醫院作批價與領藥人力配置決策之參考。
This study presents a multi-objective model to determine the optimal numbers of cashiers and dispensaries in a large hospital. The objectives are to minimize the total expected weighted waiting cost and the service cost. A point-wise fluid-based approximation approach is adopted to construct a dynamic queuing system that describes the expected queue length of customer. The dynamic queuing system 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.