過去對於專案趕工的問題其求解方法大致上可以分為兩大類:1. 啟發法,2. 最佳法。本研究將重心置於最佳法上,最佳法大部分都是用數學規劃法求解,過去的研究在遇到時間成本互換(time/cost trade-off)的問題時,大多將每單位時間之趕工成本視為常數,因此在趕工時間與成本之關係圖上會呈一直線關係,也就是將趕工成本用平均的概念做計算,即每單位時間的趕工成本皆視為固定,但在現實的專案趕工執行上每單位時間的趕工成本可能是相異的,因此我們在利用數學規劃的方式求解的時候,若可將每單位時間的趕工成本視為變動性的變數,將會更符合現實情況的計算。 但當我們將專案趕工的成本視為變動時,每單位時間的趕工與否都變成是0-1變數,且在設定數學規劃的限制式時,因為每單位時間的趕工具有順序性,必須要先趕工完第一單位時間的趕工才可以進行第二單位時間的趕工,因此會產生具有變數上限值(Variable Upper Bounding, VUB)問題的限制式而增加了計算上的複雜度,本研究擬提供一個新的數學模式轉換法來降低此一計算的困難度,以方便應用於現實的時間成本權衡分析(Time-Cost Trade-off)問題上。
There are two approaches to solve the time-cost tradeoff problem.One is heuristic model, and the other is optimal model. In this research, we foucs on the optimal model. Most of the optimal models were solved with mathematical programming. In the past, it was assumed that the unit time crashing cost is constant for time-cost tradeoff problem. Therefore the relationship between time and cost is linear on its relationship plot. It means that we always use average concept to describe unit time crashing cost. It assumed that each unit time crashing cost is fixed, but it may be different in the real case. If we can assume unit time crashing cost is dynamic for solving time-cost tradeoff problem, it is more suitable for the real case. While we assume unit time crashing cost is dynamic, each unit time crashing variable will become zero-one variable. The unit time crashing cost should occur in order. That means we should complete first crahing unit and then second crashing unit can be started. In order to match the above situation, it will bring a problem of variable upper bounding to increase the complicacy of solving problems while we set up a mathematic model’s constraints.In this research , we want to offer a transformation model to reduce the difficult of solving time-cost tradeoff problem, and it can be used on the real case.