Bin covering algorithms in the second stage of the lot to order matching problem

Evaluation of heuristics for a class-constrained lot-to-order matching problem in semiconductor manufacturing

“…In fact, no literature could be found regarding its specific formulation or solution methodology, despite the extensive collection of packing problem variations. Three papers and one PhD dissertation of the same lineage, however, do look at the lot-to-order matching problem (LOMP), where only one class of product is allowed (Knutson 1998, Knutson et al 1999, Fowler et al 2000, Carlyle et al 2001. The problem we solve in this paper, the CLOMP, is a generalized version of Knutson's LOMP, because multiple classes of product are present in the customer orders and factory lots.…”

“…Refer to Boushell et al (2005) for a detailed discussion of the cutting and packing family of problems. As stated above, the most relevant set of papers in our review specifically deal with the Lot-to-Order Matching problem (LOMP) (Knutson 1998, Knutson et al 1999, Fowler et al 2000, Carlyle et al 2001. The LOMP can be described as the assignment of orders into a capacity-constrained factory, while simultaneously assigning factory lots of different sizes into those customer orders.…”

“…The origin of the first fit decreasing algorithm (FFD) used in this paper is Knutson (1998), Knutson et al (1999), Fowler et al (2000) and Carlyle et al (2001), where it was referred to as FFD(S i ). The FFD(S i ) heuristic is based on the first fit decreasing algorithm described by Dyckhoff (1990) and was determined to yield the best results among four heuristics tested in Knutson (1998) and Carlyle et al (2001). For each Stage 2 order covering, the FFD heuristic splits the lots into two classes, with each group of lots arranged in order of non-increasing size, based on the number of class A or B die in the lot, respectively.…”

Comparison and evaluation of lot-to-order matching policies for a semiconductor assembly and test facility

“…The two bin-covering algorithms are compared in this analysis: (i) ® rst in ® rst out (FIFO) ; and (ii) ® rst ® t decreasing [FFD1(S i )] algorithms. These algorithms were compared to several other bin-covering algorithms in Carlyle et al (1999), and in this analysis FFD1(S i ) had the best overall performance. In this current paper we expand on the previous analysis to compare the performance of the FIFO and the FFD1(S i ) algorithms in the context of the overall system in a more realistic setting.…”

“…This is the reason why heuristics are most often used in solving this type of problem. Carlyle et al (1999) has shown that bin covering is, in the language of computational complexity, NP-hard. Theoretically, optimal solutions to the problem can be found through enumerative procedures , but this is practical only for cases containing not more than a few items and bins.…”