評選多項計畫的組合之高效能方法

Abstract

已知多個計畫的期望績效以多指標用來評量，從這些計畫之中選取若干項計畫所成的每個子集均被視為一個計畫組合。若對於包含24個計畫評選的問題，利用傳統的資料包絡分析法(DEA)對全部可能的計畫組合評量其相對效率，需要超過一天來求得績效高的計畫組合；本研究發展出一個計算程序降低了計算時間，僅需要37秒。對於包含37個計畫的2^37個計畫組合的超大型問題，若直接使用傳統的DEA，目前任何的數學規劃軟體均不能處理；以本研究之計算程序，能在一天內求解。本研究的第二個目的是評量每一個績效高的計畫組合的穩定度，穩定度是指使該計畫組合仍維持高績效時，其中各項計畫在各指標可容忍惡化的程度。

We are selecting several projects out of a set of projects. Every subset of these projects is treated as a portfolio. Multiple indices are used to measure the expected performance of those projects. We employ Data Envelopment Analysis (DEA) to measure the relative efficiency of each portfolio against all the possible portfolios. Our research has two major objectives. The first objective is to develop an algorithm to reduce problem complexity and the required computation time. The conventional DEA needs to generate all the possible portfolios first and then measure each portfolio’s efficiency against all the portfolios. For the problem with 24 projects, it needs more than one day to obtain the efficient portfolios while our procedure needs only 37 seconds only. For our algorithm, a selection problem with 37 projects could be solved within one day in a personal computer. It is impossible to solve the problem with more than 2^37 decision variables by any existing mathematical programming software if conventional DEA program is used. The second objective is to measure the stability of each identified efficient portfolio. The tolerance of its each individual index becomes worse could be measured for keeping its efficiency.