本研究主要探討大型專案所面臨的情況，針對趕工成本及趕工時間加以深入討論有關專案完工時間改變時的最適趕工成本，藉由作業趕工以縮短專案完工時程以符合專案預訂完成時間。本研究將專案趕工問題，建構成一整數非線性規劃INLP (Integer Nonlinear Programming)的數學模型，以不同的專案完工時間下的考量趕工成本最佳化問題，進而提出最適的作業縮短時間。 本研究主要以計劃評核術(Program Evaluation and Review Technique, PERT)與要徑法(Critical Path Method, CPM)來探討大型專案所面臨的情況。本研究不僅討論作業趕工成本的非線性現象以符合真實的現象，並將專案工程進行的各項限制條件，製作成數學問題以求在符合完工時間條件要求下的最適趕工成本的求取。此外本研究運用Lingo 9.0 extended version 語法進行非線性專案趕工模式構建，並採用Lingo 9.0軟體內建之Global Solver 進行其全域最佳解之求解，並利用數值模擬討論在不同專案完工時間要求下之最佳趕工成本與作業趕工策略。綜言之，本研究可視為一具價值之決策支援工具，因其可根據不同專案情境企業僅需對模式進行簡單的修正，即可快速取得最適解。 This paper is mainly aimed to investigate the crashing time and crashing cost of a complicated project for considering the reduction of the time of activities to meet the customer needs as well as to achieve the cost optimality. This study construct the crashing problem of the project to be an Integer Nonlinear Programming (INLP) problem because the crashing cost of each activity is treated as the nonlinear function of the reduction time of each activity. Therefore, this study is focused on the optimal crashing cost under the necessity of finished time of the project for the customer. The Program Evaluation & Review Technique, PERT, and the Critical Path method, CPM, are mainly applied in this paper. The nonlinear relationship between the amount of reduction time of each activity and the crashing cost of each reduction time unit are considered in this study. Thus, the crashing problem of the project is extended to the more practical situation. A nonlinear mathematical model proposed in this paper to meet the entire practical needs of the project is constructed by the syntax of Lingo 9.0 packaged software, and the built-in “global solver” is then selected as the tool for achieving the global optimum solution. A numerical example to execute the program simulation of the different finished time of the project, and the optimal crashing cost as well as the reduction strategy of each activity are also discussed. Actually, this study can be regarded as a valuable decision support tool because it can easily duplicate to solve other project cases by slight changes of the syntax in the main model only.
