本研究將重心置於數學線性規劃求解,過去的研究在面對時間/成本權衡問題時,大多將單位時間趕工成本視為一固定常數,因此單位時間趕工成本與趕工時間呈現直線關係;然而,在專案實際的執行過程中,趕工單位時間成本並不一定會相同,其常會隨著壓縮的時間而增加,因此本研究為能更符合實際情況,將單位時間的趕工成本視為遞增的。而實際上,為了保障權益,通常會在專案合約中訂下逾期罰金的相關事項,因此本研究同時考量單位時間趕工成本與逾期罰金的情況進行分析。 本研究發展出一套運作模式,使專案在約定期限前,若發現單位時間趕工成本高於逾期罰金時,專案將會停止趕工,並將剩餘時間支付逾期罰金,使趕工成本最小化,避免多支付單位時間趕工成本與逾期罰金之間的差額。
In this research, we focus on the build up of a linear programming model to solve the time/cost trade-off problem with penalty consideration. In the past, it was assumed that the unit time crash cost for a project activity is constant. Therefore the relationship between crash time and crash cost is linear. In practice, when a project is executed, activity crash cost may be different at different times. As a project activity crashes further its crash cost often increases. Moreover, in most cases, penalty is likely to be imposed in the project contract in order to protect the right of project client. This research assumes unit time crash cost is incremental and penalty exists when solving the time/cost trade-off problem. Through this research we develop an operational model so that when the unit time crash cost if higher than penalty, the project will stop crashing. This will realize the benefit exists in the difference between the crash cost and penalty so as to achieve the minimum crash cost objectives.