Scheduling Hybrid Flowshops in Printed Circuit Board Assembly Lines*

Abstract

We treat a three-stage hybrid flowshop for the production of printed circuit boards (PCB), suggested to us by a real-life production situation. The problem is to determine a schedule that minimizes the makespan for a given demand profile over a finite planning horizon. We propose a global procedure that utilizes genetic algorithms and three subproblems. The performance of the procedure is evaluated via experimentation over thousands of problem realizations that are randomly generated. The experimental results show the efficiency of the global procedure and provides qualitative answers to the allocation of machines to the various stages. (HYBRID FLOWSHOPS; SCHEDULING; PRINTED CIRCUIT BOARD ASSEMBLY; HEURIS-TICS) insertion machines for s ϭ 1, 2, 3. Therefore this problem may be viewed as a three-stage MHFS scheduling problem. There are n types of PCBs to be scheduled without preemption; each type has to be assembled serially through the three stages. The setup between different types of PCBs is conducted off-line, and the setup time can be neglected. Finally, the objective is to find an optimal schedule that minimizes the makespan. Review of LiteratureThe general MHFS is an S-stage flowshop environment with m s parallel identical machines in each stage, s ϭ 1, 2, . . . , S. We denote the MHFS scheduling problem as Fs(Pm 1 , Pm 2 , . . . , Pm S )͉ Ϫ ͉C max . The literature on the MHFS scheduling problem has only considered simple cases. If S Ն 2 and m s ϭ 1 for s ϭ 1, 2, . . . , S, then the problem becomes the standard flowshop problem. If S ϭ 1 and m 1 Ն 2, the problem reduces to the standard parallel machine problem. If S ϭ 2 and m 1 ϭ m 2 ϭ 1, the problem is solvable to optimality by the Johnson algorithm (Johnson 1954). For S ϭ 2, more general cases have been discussed by the following authors. Arthanary and Ramaswamy (1971) considered the case m 1 ϭ m, m 2 ϭ 1, and proposed a branch and bound procedure that can solve small-sized instances. Gupta, Hariri, and Potts (1997) discussed the same problem and proposed several heuristics. Gupta and Tunc (1991) developed two polynomially bounded heuristics for the m 1 ϭ 1, m 2 ϭ m case. Langston (1987), Sriskandarajah and Sethi (1989), and Deal and Hunsucker (1991) developed heuristics for a more general case, m 1 ϭ m 2 ϭ m. Lee andVairaktarakis (1994), andGuinet, Solomon, Kedia, andDussauchoy (1996) devised their heuristic algorithms for the most general case, the F2(Pm 1 , Pm 2 )͉ Ϫ ͉C max problem. Of more recent vintage is the work of Soewandi (1998), who treated the two-and three-stage hybrid flowshop problem with identical and uniform machines, and Riane, Artiba, and Elmaghraby (1998a), who treated a special hybrid flowshop composed only of two stages, in which the first stage had only one machine and the second stage had two dedicated machines. Haouari and M'Hallah (1997) proposed a tabu search (TS)-based heuristic and a simulated annealing (SA)-based heuristic. For S ϭ 3, Vignier, Commandeur, and Proust (1997) proposed a branch and bound procedure that can solve s...

The hybrid flow shop scheduling problem

“…In these two papers, the authors study a linear combination of the makespan and the number of tardy jobs as an objective. Another real world application is given in [87], where a real printed circuit board manufacturing system modeled as a 3-stage HFS is approached with GA. The HFS with multiprocessor tasks is studied for the makespan criterion by [175] and by [139] and approached with GA. A GA and a SA were proposed for a fairly complex cyclic scheduling flexible flow line with lot sizing in [85].…”

“…))||non-regular MPF, heuristics, photographic film production [45] F Hm, ((P M (k) ) m k=1 ))|pmtn, prec|Cmax polynomial algorithm for special case of prec ( [78]) [64] F Hm, ((P M (k) ) m k=1 ))||Ē u +T v +C w +d z heuristic, assignable due dates, controllable processing times [73] F H2, ((1 (1) , P m (2) ))|assembly (2) |Cmax MPF, heuristics [87] F H3, ((P M (k) ) 3 k=1 ))||Cmax GA, printed circuit boards [157] F H2, ((1 (1) , Q2 (2) ))||Cmax MPF, DP, heuristics, NP-complete proof…”

“…HFS is found in all kinds of real world scenarios including the electronics [217], [218], [118], [87], paper, [177] and textile, [55], industries. Examples are also found in the production of concrete, [143], the manufacturing of photographic film, [197,4], and others, [2,42,3,116,20,224,159].…”

Lot Processing in Hybrid Flow Shop Scheduling Problem

“…HFSs have important applications in flexible manufacturing systems (FMS), such as electronics and furniture manufacturing, process industries such as chemical, textile, metallurgical, semiconductors, printed circuit board assembly lines, pharmaceutical, oil, food, automobile manufactures, steel making systems, etc. -see, e.g., Tang et al (2002), Jin et al (2002), Mathirajan & Sivakumar (2006) and Yaurima et al (2009)-. Therefore, HFS scheduling has attracted interest by scientific community, being reflected in literature contributions dealing with this particular problem; however the issue of lot processing in this type of shops has not gained sufficient attention.…”

Heuristics and metaheuristics for heavily constrained hybrid flowshop problems

“…The computational results show the superiority of the GA for these problems. Jin et al (2002) model a real-world application of a printed circuit board manufacturing system as a three-stage hybrid flowshop problem. The objective they aim to optimise is the makespan value.…”