Clustering | Ender Sari

Strategic Clustering with PCA and FCM

My primary goal of this project was to refine product classification strategies by leveraging Principal Component Analysis (PCA) and Fuzzy C-Means (FCM) clustering. This approach aimed to enhance data-driven decision making, improve visualization, and address multicollinearity among variables such as capacity insufficiency, annual sales, and seasonality.

Methodology:

Dimensionality Reduction: Utilized PCA to reduce the complexity of high-dimensional data, focusing on capturing the most significant information with minimal loss. The selection of principal components was guided by Kaiser's rule and visual inspection of a scree plot. The first two components, explaining over 82% of the variance, were identified as the most impactful, providing a clear and simplified representation of the data.
Clustering Analysis: Applied Fuzzy C-Means clustering to group products into meaningful categories based on their characteristics in the PCA-reduced space. The clustering process involved tuning parameters such as the number of clusters and the degree of fuzziness, with the goal of achieving optimal separation and compactness as indicated by the Fuzzy Hypervolume (FHV).
Strategic Insights: Developed a strategic 2x2 matrix to categorize products based on their scores along the two principal components. This matrix serves as a decision-making tool, offering tailored strategies for each product category to enhance operational and marketing effectiveness.

You can access the sample Python notebook code.

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Results:

Cluster Visualization: Produced scatter plots to visually assess the clustering of products, with clusters clearly differentiated by color and their centroids marked for reference.
Product Cluster Analysis: Detailed analysis of each product cluster was provided, highlighting central tendencies and variabilities, which informed specific strategic recommendations for each cluster.

Strategic Recommendations:

Outlined actionable strategies for inventory management, demand forecasting, and marketing, tailored to the characteristics of each product cluster. These strategies are designed to leverage seasonal trends, manage capacity effectively, and optimize product availability.

Conclusion:

This project successfully demonstrated how statistical techniques like PCA and FCM can be applied to real-world business challenges, leading to more informed strategic decisions and efficient resource management. The findings have significant implications for improving inventory turnover, customer satisfaction, and overall profitability.

insights

I present a comprehensive analysis of the product clusters, showing the central tendencies and variabilities across the dimensions. This analytical insight has led to the development of a strategic 2x2 matrix. This matrix classifies products based on the difference of high and low scores along the two principal components, PC1 and PC2. Each quadrant of this matrix provides a strategic overview that can guide decision-making.

strategic 2x2 matrix

Characteristics: Products have seasonal demand with lower annual sales volume but are still at risk for backorders.

Actions:

Demand Forecasting: Improve forecasting to better anticipate seasonal spikes in demand.

Marketing Activities: Implement promotions outside of peak seasons to smooth demand.

Inventory Preparation: Pre-build inventory ahead of high-demand seasons to meet potential peaks.

HIGH PC2

LOW PC2

Characteristics: Seasonal products with generally adequate capacity and a low risk of backorders.

Actions:

Market Analysis: Investigate new markets or alternative uses for products to increase off-season sales.

Operational Review: Evaluate and adjust production schedules to align with demand without overproducing.

Customer Loyalty: Develop loyalty programs or incentives to retain customers and encourage off-peak purchases.

LOW PC1

Characteristics: Products with high sales volume, but there is a risk of capacity insufficiency and a high tendency for backorders.

Actions:

Capacity Planning: Invest in increasing production capacity or improving supply chain efficiency to meet high demand.

Inventory Management: Maintain higher inventory levels, especially before peak seasons, to avoid stockouts.

Order Fulfillment: Implement advanced order fulfillment strategies, such as backorder management systems, to handle excess demand.

Characteristics: Products with strong sales and potential capacity issues, but with a lower tendency for backorders.

Efficiency Optimization: Streamline operations to improve production cycle times.

Sales Distribution: Diversify sales channels to manage demand effectively.

Customer Engagement: Enhance customer communication to manage expectations and smooth out demand curves.

HIGH PC1

inspiration # 1- multi-criteria inventory classification

If you are interested in how cutting-edge research and multi-criteria classification techniques are transforming inventory management, please continue reading to discover the studies and methodologies that have inspired my innovative project.

The article introduces a new hybrid method for Multi-Criteria Inventory Classification (MCIC) in inventory management, integrating Analytical Hierarchy Process (AHP) and K-means clustering, termed AHP-K. This method is designed to enhance the classification of inventory items by considering multiple criteria, offering a more objective and precise classification than traditional methods. The AHP-K method, however, is fully compensatory, meaning that poor scores in key criteria can be offset by high scores in others, potentially leading to misclassification.

To address this issue, the authors propose an enhanced version called AHP-K-Veto. This variant includes a veto rule in the sorting process, preventing an item with a low score in any key criterion from being classified in the highest category, despite high scores in other areas. This addition aims to prevent the oversight of significant weaknesses in individual items. While the AHP-K-Veto method slightly reduces the clustering validity index, it provides a safeguard against hidden problems in classification.

The case study presented in the paper involves an engineering firm manufacturing electrical resistors, using the AHP-K-Veto method to classify 95 Stock Keeping Units (SKUs) for inventory management. The SKUs are categorized into three classes based on Annual Dollar Usage (ADU), Critical Factor (CF), and Replenishment Lead Time (LT), with each class corresponding to a specific target service level for safety stock calculations.

The implementation of AHP-K-Veto in the case study demonstrates several benefits. It allows for more objective determination of cluster sizes without subjective judgment, modifies classifications to account for individual criterion scores, and is user-friendly, requiring no specific technical knowledge. The method's application on each criterion separately improves the understanding of SKU characteristics.

Finally, the paper compares AHP-K and AHP-K-Veto with other classification methods using a benchmark dataset. It concludes that AHP-K has a higher clustering validity index than other methods, including its variant AHP-K-Veto, which, despite a slight decrease in this index, offers a valuable check against potential misclassifications due to compensatory scoring.

Lolli, F., Ishizaka, A., & Gamberini, R. (2014). New AHP-based approaches for multi-criteria inventory classification. International Journal of Production Economics, 156, 62–74.

inspiration # 2

The article presents DEASort, a novel method in inventory management. It combines Data Envelopment Analysis (DEA) with the Analytic Hierarchy Process (AHP) for a more effective and realistic classification of inventory items. Traditional DEA methods are limited by their reliance on arbitrary class constructions and lack of a sorting mechanism. DEASort overcomes these limitations by integrating expert opinion through AHP, resulting in classifications that are more aligned with real-world scenarios.

DEASort operates in several steps. Firstly, item scores are normalized, and criteria weights are evaluated using AHP, considering the judgments of decision-makers. This process includes bounding the weights to a realistic range based on expert inputs. The method then calculates item priorities and defines classes, where each item is sorted into these predefined classes.

A case study in a company managing warehouses for spare parts demonstrates the practical application of DEASort. Criteria considered in the study include Annual Usage Value, Frequency of Issue, and Current Stock Value. The study shows DEASort's robustness and its superiority in safety stock holding cost reduction when compared to traditional ABC classification and Ramanathan's DEA method.

In conclusion, DEASort proves to be an effective tool for complex MCIC problems, addressing the limitations of traditional DEA by considering multiple criteria and incorporating expert judgment. The method avoids fixed class percentages, leading to more accurate and realistic classifications, and demonstrates significant cost savings in inventory management. DEASort's flexibility also makes it suitable for various sorting problems beyond inventory classification.

Ishizaka, A., Lolli, F., Balugani, E., Cavallieri, R., & Gamberini, R. (2018). DEASort: Assigning items with data envelopment analysis in ABC classes. International Journal of Production Economics, 199, 7–15.

inspiration # 3

The article presents an optimization model aimed at improving ABC inventory classification. This model simultaneously determines the number of inventory groups, their corresponding service levels, the assignment of SKUs to these groups, and the allocation of a limited inventory budget. The objective is to optimize the trade-off among service level, inventory cost, and net profit, thereby providing a decision-support tool for inventory and purchasing managers.

The authors propose a mixed-integer linear programming (MILP) model to enhance ABC inventory grouping and control decisions. This model integrates the determination of inventory group numbers, SKU assignments to these groups, target service levels for each group, and the optimal allocation of inventory budget. Unlike traditional methods focusing on minimizing inventory costs, this model aims to maximize total net profit, balancing profit with inventory investment and customer satisfaction through service levels. The model is applied to a real-life case of an industrial products’ distributor.

The case study demonstrates the model's effectiveness in improving total net profit compared to traditional ABC methods. Computational experiments show the model's behavior under varying conditions, particularly the impact of management cost per group and available inventory budget on optimal inventory grouping solutions. The model's performance over time is also evaluated, showing consistent outperformance over traditional ABC methods in terms of profitability and inventory spending efficiency.

The model provides insights into the optimal number of inventory groups based on management costs and budget constraints and illustrates the diminishing return on profitability with increased inventory budget. The paper acknowledges limitations such as the static nature of the model and the focus on single-objective optimization. Future research directions include developing a multi-period dynamic model, integrating simulation-optimization approaches for uncertainty, and considering multiple criteria in optimization.

Millstein, M. A., Yang, L., & Li, H. (2014). Optimizing ABC inventory grouping decisions. International Journal of Production Economics, 148, 71–80.