A Model for Preliminary Estimation and Continual Updates of Project S-curve

[[abstract]]S曲線是一個工程專案從開始至結束的累計進度的圖形表達，專案之進度控管一般以該曲線為工具。傳統上S曲線的產生方法為先考慮專案屬性因素從事專案排程計算進度，但其作法是很費時的，且在專案執行過程又常須再檢討排程，又因主觀之條件也常使排程可能存在不合理而又不自知之情形，因此若能運用過去已完成之案例資料，可便捷又能考量影響因子的S曲線預估模式，對於了解傳統排程所得S曲線之可行與否應有輔助作用。多年來，已有許多文獻提出運用歷史案例資料擬合S曲線以為預估基礎之研究模式，但有其應用上的缺失；本研究先提出一個新的數學公式來擬合S曲線，經以案例資料計算擬合並與其他公式比較，顯示精度可被接受。本研究另蒐集已完工的第二高速公路工程標案實際進度資料，先計得每一案例擬合曲線之參數值為發展預估模式所需之輸出數據，再將對每一標案做屬性定義與分類為輸入數據；運用類神經網路計得每一獨特案例之專屬早期預估專案S曲線，且經過驗證比其他方法有較高預估之精度。再者，本研究再提出專案進行中之持續更新進度模式，就執行中專案已施工之即時實際進度值，從歷史案例資料庫擷取進度值相似度高之案例，從而得到持續更新之S曲線。最後整合類神經網路之早期預估與持續更新模式為專案S曲線更新進度之整合模式。經過驗證發現使用此整合模式在專案執行期初或期中即可產生高準確性之S曲線，可應用於專案執行期間求得預估S曲線，並可與傳統排程進度比較，以了解排程進度相對於完成案例是否合理，可為專案管理進度管控之輔佐參考。[[abstract]]The S-curve is a graphical representation of a construction project’s cumulative progress from start to finish and commonly used as a tool for project progress control, but the traditional forecasting method by calculating the cumulative progress at each time point from a schedule is time-consuming and it would be beneficial for project progress management if the forecast can be assisted by faster methods. While S-curves for project control during construction should be estimated analytically based on a schedule of activity times, empirical estimation methods using various mathematical S-curve formulas have been developed for initial planning at pre-design stages, with the mean for past similar projects often used as the basis of prediction. In an attempt to make an improvement, a succinct cubic polynomial function for generalizing S-curves is proposed and a comparison with existing formulas shows its advantages of accuracy and simplicity. Then, based on an analysis of the attributes and actual progress of 101 projects, four factors, i.e. contract amount, duration, type of work, and location, are used as the inputs of a model developed for estimating S-curves as represented by the polynomial parameters. For model development, it is proposed to use neural networks for their ability to perform complex nonlinear mapping. The neural network model is compared with statistical models with respect to modeling and testing accuracy. The results show that the presented methodology can achieve error reduction consistently, thereby being potentially useful for owners and contractors in early financial planning and checking schedule-based estimates. Based on the obtained initial forecast, this research proposes a model for continually updating project progress for a project during execution. For the actual progress of the completed parts of a project, the model uses the matching method in case-based reasoning to retrieve cases of high similarity from progress data of historical cases in order to obtain a subsequent S-curve forecast. The initial forecast from the neural network and the subsequent forecast from the matching method are assigned different weights depending on the percentage project time and the weighted average result will be the model output. Tests found that using such a combination can produce highly accurate S-curve forecasts in the beginning or middle of a project, indicating that the model can perform continual progress forecast for a project and can be used for assisting the traditional schedule-based progress control in project management