本研究主要探討雙機流程工廠(Two-machine Flow shop)群組排程(Group Scheduling)總完工時間最小化之問題,且考慮了工作順序相依整備時間(Sequence-Dependent Setup Times)、工作順序相依拆卸時間(Sequence-Dependent Removal Times)及工作轉換時間(Transportation Times)等。群組排程問題是屬於NP-hard問題,而本研究的群組排程問題較之傳統群組排程問題更具一般性。 本研究提出一種新的粒子群演算法(Particle Swarm Optimization, PSO)編碼方式來求解雙機群組流程工廠排程問題,可同時求解群組與群組之間的排序以及群組內工作的排序,我們測試了162個隨機產生的測試問題,測試問題群組數最大為15,群組內的工作數最多為10,為了衡量所提PSO解題品質,本研究亦提出三種下界(Lower Bound)做為比對基準。從有限的數值模擬結果顯示,PSO於求解各種規模問題,解題品質相當良好,且本研究所提出三種下界亦能有效的作為衡量基準。
This paper investigates the two-machine flow shop group scheduling problem with job transportation times between machines, sequence-dependent setup and removal times. The objective is to minimize the total completion time. As known, this problem is a NP-hard problem that generalizes the typical two-machine group scheduling problems. In this paper, a PSO based algorithm with an effective coding scheme is proposed to effectively solve various 162 instances with group numbers up to 15. Note that the proposed coding scheme simultaneously determines the sequence of jobs in each group and the sequence of groups. In addition, three different lower bounds are developed to evaluate the effectiveness of the PSO algorithm. Limited numerical results show that the proposed PSO algorithm performs well for all test problems.