兩階段平行機台考慮工件可分割特性下求解最小完工時間

Two Stage Hybrid Flow Shop Scheduling with Job Splitting Property for Minimizing the Maximum Completion Time

黃少緯(Shao-wei Huang)

指導教授 ： 葉英傑

國立中央大學/管理學院/工業管理研究所/碩士(2014年)

摘要

本論文我們研究一多階段平行機台環境下，有多個工件需要被進行加工處理，且每個工件具有可分割特性的排程問題，我們的目標是決定一最佳排程使得所有工件完工時間最小化。在過去大部分的排程問題都假設每個工件最多只能在一台機台上進行處理，然而在實務上經常會遇到一些情況是多個不同種類的產品，又有各自不同的數量需要在一條生產線上進行加工，在這種狀況下為了使完工時間能夠縮短，我們不會受限於原先的排程假設，我們將允許將相同工件分為多個的批量在不同的機台上同時進行加工，如此來避免機台有閒置的狀況發生。

本研究中我們假設機台環境為兩階段平行機台的排程問題，第一階段有兩台相同平行機台，而第二階段只有單一機台，另外我們假設所有工件之間的整備時間彼此獨立。我們使用分支界限法來尋找此排程問題的最佳解，在演算法中我們提出了下限值和上限值的求算方法以及一些可以刪除不必要的節點法則來提升我們演算法的求解效率。最後我們將此演算法透過JAVA來實現並透過實驗數據來進行分析。

關鍵字

排程 ； 分支界限法 ； 多階段平行機台 ； 工件可分割特性

並列摘要

In this research, we consider the problem of scheduling n jobs on hybrid flow shop with job splitting property, and our objective is to minimize the maximum completion time. In the past, the majority of scheduling studies assumed that each job can be processed on at most one machine at a time. In the real word, there are many cases that have different types of products and each type of products have numbers of units need to go through a production line. In order to make these products finished as soon as possible, it is normal to schedule each unit of the same product on different machines at the same time.

In this research, we assume that there are two identical parallel machines in the first stage and a single machine in second stage, and the setup time of each job are independent. We use a branch and bound algorithm to find the optimal solution for this problem. In this algorithm, we propose the lower bound and upper bound for this scheduling problem and we use some dominance rules to eliminate unnecessary nodes to improve the efficiency of our algorithm. Finally, we implement this algorithm by JAVA, and we conduct the computational analysis.

並列關鍵字

Scheduling ； Branch-and-bound algorithm ； Hybrid flow shop ； Job-splitting property

參考文獻

[1] Fattahi, P. et al. (2013), “A branch and bound algorithm for hybrid flow shop scheduling problem with setup time and assembly operations”, Applied Mathematical Modelling , Vol. 38, pp. 119–134

[2] Brah, Shaukat A. et al. (1991) ”Branch and bound algorithm for the flowshop with multiple processors”, European Journal of Operation Research, Vol.51, pp. 88- 99.

[3] Portmann, M.C. et al. (1997) ”Branch and bound crossed with GA to solve hybrid fowshops”, European Journal of Operation Research, Vol. 107, pp.389-400.

[4] Allaoui, H. et al. (2004) ”Integrating simulation and optimization to schedule a hybrid flowshop with maintenance constraints”, Computers & Industrial Engineering, Vol. 47, pp.431– 450.

[5] Kim, Y.D. et al. (2004) ”Parallel machine scheduling considering a job-splitting property” , International Journal of Production Research, Vol. 42, pp.4531– 4546.