Li, Simon JrZhu, Yingyu Jr2017-09-292017-09-2920172017Zhu, Y. J. (2017). Hierarchical Clustering and Similarity Statistics for Solving and Investigating Cell Formation Problems (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/26356http://hdl.handle.net/11023/4171In cellular manufacturing, cell formation (CF) is to group similar machines into manufacturing cells and parts to product families. This research focuses on advancing hierarchical clustering to solve CF problems and analyzing similarity statistics to investigate CF problems. In the first aspect, the purpose is to find high-quality solutions for CF problems considering production information. Two-mode similarity coefficient is applied to simultaneously form machine groups and part families based on the classical framework of hierarchical clustering. The proposed simultaneous clustering algorithm has been tested through some literature examples. The results demonstrate that the proposed method can at least yield solutions comparable to the solutions obtained by metaheuristics. In the second aspect, the purpose is to distinguish whether a CF problem is difficult or not so that the users can decide whether using economical heuristics or relatively demanding metaheuristics for problem solving. Histograms are used to report the distribution of similarity values. The histogram of a not-difficult problem often presents a U-shape. To further quantify this observation, proxy measure from the Kolmogorov-Smirnov test is used to examine how well the distribution of similarity values fits the normal distribution which the similarity values of a difficult CF problem tend to show. By judging whether the proxy measure is high or low, the difficulty of a given CF problem can be determined. Sixty random matrices are used to examine the statistical approach, and the analysis results are verified by using simultaneous clustering method and genetic algorithm to solve these matrices. The results indicate that the proposed method can discern the difficulty of CF problems so that the users can select proper solutions approaches.engUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.Engineering--MechanicalCell formation problemsClustering algorithmStatistical analysisSimilarity valuemaster thesis10.11575/PRISM/26356