A new mathematical approach to supporting group technology

Abstract

This paper presents a mathematical approach which can be successfully applied in different group technology problems. The method is originated from formal concept analysis (FCA). We produce some particular extent partitions of a formal context which encodes the relationship between given technical objects and their attributes. We show how to define the part type notions and also how to solve the cell formation problem by means of these extent partitions. The main focus of the paper is a solution method for the determination of master parts. The method is based on notions defined by modal operators analogously to formal concepts and uses the extent partitions of the complementary context. It follows from the nature of the problem that several solutions can exist; a consistency measure is introduced in order to rank them. [

The Enhancement of the Overall Group Technology Efficacy using Clustering Algorithm for Cell Formation

“…For each part, 𝑁𝑁𝑁𝑁 𝑖𝑖𝑖𝑖 and 𝑁𝑁𝑁𝑁 𝑖𝑖𝑖𝑖 for each machine cell are calculated to assign the part to the specific MC with the smallest sum of 𝑁𝑁𝑁𝑁 𝑖𝑖𝑖𝑖 and 𝑁𝑁𝑁𝑁 𝑖𝑖𝑖𝑖 . Finally, two part families are generated, including (3,5,6) and (1,2,4) according to two machine cells.…”

“…The processing time for all operations is assumed to be the same. According to the calculation of the 𝑆𝑆𝐶𝐶 matrix, the machine pairs (8, 3), (6,4), (9,6), and (7, 10) have highest SC value. Therefore, the machine pair (8,3) should be assigned to the first MC and the machine pair (6,4) assigned to the second MC since the merging condition at step 3d is not satisfied.…”

“…The next highest 𝑆𝑆𝐶𝐶 is for machine pair (9,6). Machine 6 has already been assigned to the second MC.…”

“…For over three decades, various production-oriented methods have been introduced for cell formation problems such as mathematical programming, heuristic and (meta-) heuristic algorithm, graph partitioning, and most commonly hierarchical method. The mathematical programming methods focus on developing the model to maximize the total operations in each cell and/or to minimize the moves between cells [5,6]. Some studies addressed heuristic algorithms based on flow-matrix to solve cell formation problems (CFP) and machine layout generation [7][8][9].…”

An incremental method for the construction of the box extents of a context

“…The notion of the box extents of a context and the box elements of a concept lattice are related to the application of Formal Concept Analysis [1] in data classification by defining partitions of a universe putting its elements with similar attributes into the same class, see [4,6] and [2]. This task transparently appears in some clustering problems originating in database analysis, as well as in the engineering discipline Group Technology, see, e.g., [9] or [8]. This discipline exploits the similarities between technological objects and divides them into (relatively) homogeneous groups in order to optimize the manufacturing processes.…”