物流中心之檢貨系統與汽車測試中心之測試作業皆為一開放式排程，開放式排程之別於流程式與變序式排程乃是其各工作之操作順序無限制。本研究嘗試以數學規劃模式來描述一n件貨品工作訂單，m步操作作業程序之開放式排程中遲延罰金成本最小化，再以擴張樹之網路結構簡化數學規劃模式，並發展一閒置時間法則作為排程決策評估選擇之基準。本研究嘗試採用貨品工作訂單數、操作作業程序數、貨品工作訂單遲延因數和預定交貨期分布情況不同之十五種實驗組合中7,200個案，來比較本研究發展之啟發式解法與最小作業時間作業先排法、最小預定交貨期作業先排法、最小總寬裕工作作業時間作業先排法、最小寬裕作業時間作業先排法四種派工法之績效。實驗結果顯示本研究發展之啟發式解法比另四種派工法好出甚多，本研究發展之啟發式解法非常適用於多工作、多機和高遲延因數之開放式排程。貨品工作訂單遲延因數是此啟發式解法績效之主要影響因素，預定交貨期分布則較為次之。

This open-shop schedule has no restriction on the processing order of the jobs. The problem for minimizing the total tardy cost in an m-machine nonpreemptive open-shop is NP-hard. A network structure based on the spanning tree is constructed in this work to simplify the mathematical model of a nonpreemptive open-shop problem whose objective is to minimize total tardy cost. The idle time rule developed in this work serves as the decision criterion to test the performance. The proposed Heuristic A is compared with SPT, EDD, SLACK, and MWSTR/EST (Minimum Weighted Slack Time Remaining rule and Early Starting Time rule) methods using 7,200 cases, which are constructed by different features. Experimental results indicate that Heuristic A performs much better than the other four methods under the total tardy cost criterion and even better for complex problems. The results also reveal that the tardiness factor has significant influence on Heuristic A, and the due-date range has minor influence.