In recebt years,the exploration of organizational ptoblems using
mathematic model has been receiving mord and mord concern from the
academic circles. Certain problems in organization,especially the
inter-relation of cause and effect among the variables of the
organizational structure through the indication of mathematical
equation,may be sudstantially discussed. As a result,it may serve as a
reference to the management for their decision-making.
Taking an organization as a production system to observe the organization
function with input-output concept is a new topic that is worthy of our
further studies.In 1982,M.J.Beckmann,with the same viewpoints,executed the
production function in organizations doing case work based on "output
timing effect "as a considering factor;yet the rate of output and the
arrival of case work are deemed homothetic that can not be completely
applied to otganizations doing case work whick takes "work timing effect
"as the key-point of consideration,in addition to the arrival of case work
that bears non-selectivity.
In this paper,we further generalize the hierarchical model of organization
doing case work,establishing probuction function orientated by "work case
work ,establishing probuction function orientated by "work timing
effect",while the item of input is the personnel at various levels of the
hierarchy and the item of output is the service criterion of the objective
index.Hence,based on the idea that the minimum cost in the industrial
economics is the optimal,we set up the cost function of the organization
doing case work;calculating it under certain service criterion,cost is the
minimal and most suitable for the personnel arrangement in the
gierarchical structure.With production function of the organizations doing
case work ,cost function and the optimal personnel layout,we discuss and
compare properties of function specifically with the relevant functions in
the industrial economics;then perform analyses on sensitivity of the key
variables in all functions.
We also analyze the unoccupied and busy condition on work of the personnel
at each level through cross section of the organization doing case
work;analyze the waiting and service condidtion of a case wofk into the
hierarchical system through longitudinal sdction there-of;thus searching
for the inter-connection of time and cost factors.Henceforth,to analyze
organizations doing case work with homogeneous attributde and branching
approach,working from the angle of cost or the time length being employed
of the personnel at various levels in the hierarchical structure.
This study enables us to see clearly the inter-action of all the variables
in the organizations doing case work.Likewise,it presents to the
decision-maker as a reference for designing and organizing personnel
structure in the industrial hierarchy by means of the current analysis of
the said organtion.
論文提要內容：
近年來利用數量化模式，探討組織問題，已逐漸受到學者的重視；組織中的某些問題
，尤其是組織結構中變數間的因果關係，藉由數學算式的表示，可以更脤體地被討論
，其結果將可提供舌理者做決策的參考。
將組織看成一估生產系統，從投入一產出的概念來觀察一個組織的功能，是值得我們
探討的新課題。1982年，M.J.Beckmann依此此觀點建立執行個案組織（Organization
s Doing Case
Work）的生產函數，即是以〞產出時效〞來考慮；但其將產出率與個案到達率視為相
同的論點，並不能完全適用於以〞工作時效〞為考量重點，且個案到達率無選擇性的
執行個案組織﹖
本文進一步將執行個案組織的層級模式一般化，建構以〞工作時效〞為導向的生產函
數，其投入項為各層級的人員，產出項為客觀性指標的服務水準。再從業經濟學中成
本最小為最佳化的想法，建立執個案組織的成本函數；並求算在某一服務水準之下，
成本為最小的最適成員配置。就描述執行個案組織功能的生產函數成本、蚱本函數及
最適成員配置，分別討論函數性質，一一與產業經濟學中有關的函數做比較；並對各
函數的主要變數做敏感分析。
我們也從執行個案組織的棋部面，分析各層級人員閒置及工作忙碌的情形；從縱剖面
分析一個個案進入體系的等候及服務情形；且以時間及成本因素尋求相關性。再者，
分析二個工作屬性相同，服務水準一樣的執行個案組織，就成本或各層級人員被雇用
時間的角度，探討執行個案組織合併與分設的優劣情形。
本研究讓我們清楚地瞭解到執行個案組織中各變數的互動關係，藉由該類型組織的現
況分析，以做為提示決策者設計組織成員結構的參考。