A Heuristic Procedure for Linear Dynamics and Quadratic Criteria Manpower Planning Model

人力規劃數學模式之啟發式解法

張保隆(Pao-Long Chang)

《管理科學學報》 2卷2期 (1985/11) Pp. 247-254

https://doi.org/10.6504/JOMS.1985.02.02.08

摘要

一般文獻上所探討的人力規劃數學模式，在求解上經常是相當複雜且費時的。針對這個問題，本文提出一新的求解方法。這個方法只利用到矩陣的運算，而不需要其他艱深的尋優技術。因此在分析人力的僱用、訓練及升遷等問題時，將有所助益。

並列摘要

Among the various manpower planning models developed in the past decade, many of them can be used to analyze the influence of recruitment and transition behavior on the size and the relative structure of organizations. However, they often lead to mathematical programs which are difficult to solve.
The aim of this paper is first to determine the optimal value function and the recruiting level for each grade by applying dynamic programming arguments on a linear-quadratic optimal control problem when transition matrices are considered to be constant. We then develop a heuristic prodecure in a iterative process to improve the optimal value by varying the transition rates within some limits. Computationally, our algorithm has one important advantage. That is, it involves only matrix manipulations and no sophisticated optimization technique is needed. Furthermore, it can be applied to the planning of hiring and training of personnel in an organization. If a training budget is available for the entire planning horizon, our algorithm could also be used to determine how much of the training budget should be distributed to each period, and then determine the appropriate number of people moving from grades to grades.