The quality, manufacturing lead times, utilization of resources and

The paper deals with the machine-part cell formation problem (CFP) in cellular manufacturing system (CMS). CMS makes use of application of group technology. The objective of CFP in CMS is to identify part families and machine cells in order to minimize the intercellular movement as well as to maximize the machine utilization within a cell. Previous studies on CFP generally focused on maximizing grouping efficacy (GC) by minimizing exceptional elements as well as void elements. In this paper, a genetic algorithm heuristic is presented to maximize the grouping efficacy for the CFP. Computational experiments were carried considering 36 benchmark problem sets from the literature. Computational results show that the proposed heuristic has shown to produce solutions in terms of GC that are either better than or competitive with the existing algorithms.Keywords: Cellular manufacturing system; group technology; grouping efficacy; genetic algorithm; machine-part cell formation1 IntroductionGrouping technology (GT) 1-2 deals with the grouping of similar parts that are identified based on their similarities in design and production, resulting in improved efficiencies of a cellular manufacturing system (CMS). The application of GT in a CMS improves productivity, product quality, manufacturing lead times, utilization of resources and on the other hand, it reduces work in process inventory, setup time, and material handling cost 3-5.  The machine-part cell formation problem (CFP) usually seeks to obtain a solution with formation of completely independent machine cells where each cell is assigned with independent part families so that a machine cell can carry out all operations of that particular part family. But in actual practice, it is sometimes difficult to execute all the operations of a part family following a particular machine cell. Therefore, the principal objective of applying GT in CMS is to minimize intercellular movements of parts and to maximize utilization of machines 6. Since the CFP problem belongs to the class of NP- hard 7, heuristic and meta-heuristic approaches are mostly preferred to obtain optimal or near-optimal solution for this problem, especially for solving large-sized problems in reasonable computational time. The remainder of this paper is organized as follows:  Section 2 provides a brief literature review on CFPs and solution techniques. Sections 3 present brief description on CFPs, mathematical objectives and relevant performance measures. In section 4, a genetic algorithm heuristic is presented. The computational results as well as a comparison to the existing methods and the proposed method are presented in Section 5 and finally, Section 6 concludes the paper.2 Literature reviewFrom various literatures, CFP can be classified into three categories: (a) grouping machine cells 8 or part families 9 (b) formation of part families and machine cells separately 10, and (c) formation of machine cells and part families concurrently 11.Numerous studies based on heuristic methods have been carried out like production flow analysis 12, direct clustering algorithm 13, ZODIAC 14, GRAFICS 15, rank order clustering (ROC) 16, modified rank order clustering- MODROC 17, bond energy analysis (BEA) 18, Hamiltonian path heuristic 19, Mahalanobis distance based 20, principal component analysis (PCA) 21, single linkage clustering (SLC) 22-23, average linkage clustering algorithm (ALINK) 24, and complete linkage clustering algorithm (CLINK) 25. McAulay 22 first used Jaccard’s similarity co-efficient to find similarity coefficients of machines for cell formation in single linkage clustering.Since the CFP problem is seen to be a NP-hard grouping problem 26, there is a growing interest among researchers to implement metaheuristic algorithms due to its capability to search globally as well as locally to converge to the global optimality by exploring the search space more efficiently, whereby requiring reasonable computational time. During the last two decades, the application of soft computing techniques in MPCF problems has been utilized considerably. Various soft computing techniques found in the literature are fuzzy theory 27-28, artificial neural networks 29-30, simulated annealing (SA) 31, genetic algorithm (GA) 32-34, tabu search 33, and particle swarm optimization (PSO) 35. Zolfaghari and Liang (2002) 33 carried out a comparative study of effectiveness of GA, SA, and tabu search in cell formation problems and they found that SA is superior to other existing methods. Recently, hybrid heuristics and meta-heuristics are being applied in CFPs such as hybrid grouping GA (HGGA) 36, randomized greedy algorithm scratch by partially (GRASP) 37, hybrid GA (HGA) 38, correlation analysis and relevance index (CARI) 39, hybrid grouping based PSO (HGBPSO) 35. The methodology of GRASP was first introduced by Feo and Resende 40.To measure the quality of solutions in CFPs, Chandrasekharan and Rajagopalan (1987) 14 introduced grouping efficiency (GE). Afterwards Kumar and Chandrasekharan (1990) 41 introduced grouping efficacy (GC). The GC proposed by Kumar and Chandrasekharan (1990) 41 is based on a non-linear function of exceptional elements and void elements. Later, Banerjee and Das (2012) 42 proposed another model of GC where GC is linear function of exceptional elements and void elements. Also, Garbie, Parsaei and Leep (2005) 43 introduced “machine utilization” as another performance measuring parameter.