CAIRO UNIVERSITY INSTITUTE OF STATISTICAL STUDIES & RESEARCH DEPARTMENT OF OPERATIONS RESEARCH An Intelligent Multi-Criteria Inventory Control System Presented by Eman Mostafa Own Supervised by Prof. Dr. Hegazy Zaher Professor of Mathematical Statistics Dr. Naglaa Ragaa Saeid Hassan Assistant Professor of Operations Research A Thesis Submitted To the Institute of Statistical Studies and Research Cairo University In partial fulfillment of the requirements for the degree of Master of Science In Operations Research 2012
ACKNOWLEDGMENT My Sincere gratitude to Prof. Dr. Hegazy Zaher for his suggestion this thesis, supervising, valuable help and guidance. Also, I would like to thank Dr. Naglaa Ragaa Saeid for her continuous support, fruitful help and guidance. I also have a special thanks to my family for their encouragement and help. Eman M. O.
List of Abbreviations SKUs MCIC MCDM AHP GAMIC FAHP MAIC PSO DIY FIFO ABC JIT BIRCH CF CURE DBSCAN OPTICS DENCLUE STING CLIQUE KNN DB-KNN SD DC VKNN W-KNN ID CB-KNN D-KNN NR GIS AI SMART DI Stock Keeping Units Multi-criteria Inventory Classification Multi-Criteria Decision-Making Analytic Hierarchy Process Genetic Algorithm for Multi-Criteria Inventory Classification Fuzzy Analytic Hierarchy Process Multi Attribute Inventory Classification Particle Swarm Optimization Do-It-Yourself First-In, First-Out Activity-Based Costing Just-In-Time Balanced Iterative Reducing and Clustering using Hierarchies Cluster Features Clustering Using Representatives Density-Based Spatial Clustering of Applications with Noise Ordering Points to Identify the Clustering Structure Density-based Clustering Statistical Information Grid Clustering in Quest K- Nearest Neighbor Density Based KNN Structural Density Degree of Certainty Variable KNN Weighted KNN Index of Discernibility Class Based KNN Discernibility KNN Net Reliability Geographical Information Systems Artificial Intelligence Simple Multi-Attribute Rating Dunn Index
List of Figures 1-1 Flowchart of ABC analysis 3 1-2 Joint Matrix of Two Criteria 8 2-1 The Basis of Inventory Control 16 2-2 Stock Gives a Buffer between Supply and Demand 18 2-3 Different Types of Stock 22 2-4 Three Types of Cost Allocations 28 2-5 Pareto Curve 31 2-6 ABC Classification 34 3-1 Examples of the Classic Clustering Algorithms, where K is the Number of Clusters 43 3-2 Augmented Cluster Ordering in OPTICS 44 3-3 Single Linkage 48 3-4 Complete Linkage 49 3-5 Average Linkage 49 3-6 Centroid 49 4-1 K- Nearest Neighbor 59 5-1 Steps of K-NN Technique Flowchart 68 5-2 Proposed Method Flowchart 75
List of Tables 2-1 ABC Inventory Control 35 5-1 Measures of Inventory Items of Ex1 77 5-2 Transformed Measures,Ex1 78 5-3 Attributes Weights,Ex1 78 5-4 Comparison between Proposed Technique, Simple Classifier and Traditional ABC Results 79 5-5 Measures of Inventory Items of Ex 2. 81 5-6 Transformed Measures, Ex2 82 5-7 Attributes Weights, Ex2 83 5-8 Comparison between Proposed Technique, Case Based Distance and Traditional ABC Results 83
Contents List of Abbreviations List of Figures List of Tables ii iii iv 1- Introduction and Literature Review 1 1-1 Introduction 2 1-2 Problem Definition 3 1-3Literature Review 4 1-3-1 Inventory Control Systems 4 1-3-2 Classification of Inventory Items 6 1-3-3 Data Mining (Classification) Techniques 11 2- Inventory 14 2-1 Introduction 15 2-2 The Role of Inventory Management 15 2-3 Objectives for Inventory Control 16 2-4 Reasons for the Current Stock 16 2-5 Types of Stocks 21 2-6 Measurement of Inventories 22 2-6-1 The Cost 22 2-6-2 Net Realizable Value 29 2-7 Inventory Control 30 2-7-1 Using Pareto Analysis for Control 30 2-7-2 Family Grouping 35 3- Clustering 39 3-1 Introduction 40
3-2 Unsupervised and Semi-Supervised Clustering 40 3-3 Data Mining Clustering Techniques 43 3-4 Cluster Validity Assessment 51 4- K-Nearest Neighborhood 54 4-1 Introduction 55 4-2 K-Nearest Neighborhood Algorithm 56 4-3 Quantifying Attribute Relevance 60 4-4 The Performance of the Classifiers 61 4-5 The application of K-NN 62 5- Proposed Method 66 5-1 Introduction 67 5-2 Methodology 67 5-2-1 K-Nearest Neighbour Clustering Model 67 5-2-2 K-Means Method 70 5-2-3 Simple Multi-Attribute Rating Technique 72 5-2-4 Clustering Validation 73 5-3 Proposed Algorithm 74 5-4 Illustrative Examples 76 5-4-1 Example 1 76 5-4-2 Example 2 80 5-5 Conclusion 85 5-6 Future Research 85
CHAPTER (1) Introduction and Literature Review
1-1 Introduction Inventory is one of the more visible and tangible aspects of doing business. Raw materials, goods in process and finished goods all represent various forms of inventory. Each type represents money tied up until the inventory leaves the company as purchased products. Likewise, merchandise stocks in a retail store contribute to profits only when their sale puts money into the cash register. In a literal sense, inventory refers to stocks of anything necessary to do business. Stock Keeping Units (SKUs) represent approximately 25% from the investment of any firm, so it should be well managed in order to maximize profit and minimize costs. In fact, many businesses cannot absorb the types of losses arising from poor inventory management. Unless inventories are controlled, they are unreliable, inefficient and costly (Wild T. et al, 2002). The cost of inventories should comprise all costs of purchase, costs of conversion and other costs incurred in bringing the inventories to their present location and condition. Many criteria of SKUs deserve management s attention, and hence affect the classification of SKUs. ABC inventory classification is a widely used for classification of inventory items. This technique allows organizations to separate SKUs into three classes: A: very important; B: moderately important; and C: least important. This traditional method is based on Group A inventory items are those making about 70% of company s business but only taking up 10% of inventory. They are critical to the functioning of the company. Group B inventory items are those representing about 20% of company s business and taking about 20% of inventory. Group C items are those representing only 10% of company business but taking up about 70% of inventory as shown in fig 1-1 (Tanwari A., 2000). ABC analysis is still widely used in practice. But this approach suffers from some drawbacks like the following (Tanwari A., 2000) : 1. Depending only on one or two criteria for grouping units to make clusters. 2. There is no objective method to determine the correct number of clusters to use.
3. Although a product may be classified as a C item, it may have a high profit margin. 4. Carrying C items may be necessary to maintain existing customers and attract new ones. 5. C items may complement A items. Fig 1-1 Chart of ABC analysis (Tanwari A., 2000). 1-2 Problem Definition Number of SKUs, which have different levels of importance, held by large firms can easily reach tens of thousands. This importance may be coming from multiple-criteria such as Annual dollar usage. Obsolescence. Order size of the item. Lead time. Substitutability. Repairability. Commonality. Criticality of a stock-out of the item. So it should be treated with (SKUs) in a specialized way to minimize cost and maximize profit. This study will use a new technique in classifying inventory items based on more than one criterion which allows us to classify inventory
items based on the similarity between items, importance of the item and criteria related per the items. 1-3 Literature Review 1-3-1 Inventory Control Systems Control of inventory is needed to ensure that the business has the right goods on hand to avoid stock-outs, to prevent shrinkage (spoilage/theft), and to provide proper accounting. Many businesses have too much of their limited resource, capital, tied up in their major asset, inventory. Worse, they may have their capital tied up in the wrong kind of inventory. Inventory may be old, worn out, shopworn, obsolete, or the wrong sizes or colors, or there may be an imbalance among different product lines that reduces the customer appeal of the total operation. Inventory control systems range from eyeball systems to reserve stock systems to perpetual computer-run systems. Valuation of inventory is normally stated at original cost, market value, or current replacement costs, whichever is lowest. This practice is used because it minimizes the possibility of over stating assets. The ideal inventory and proper merchandise turnover will vary from one market to another. Average industry figures serve as a guide for comparison. Too large an inventory may not be justified because the turnover does not warrant investment. On the other hand, because products are not available to meet demand, too small an inventory may minimize sales and profits as customers go somewhere else to buy what they want where it is immediately available. Minimum inventories based on reordering time need to become important aspects of buying activity. Carrying costs, material purchases, and storage costs are all expensive. However, stock-outs are expensive also. All of those costs can be minimized by efficient inventory policies. Three major approaches can be used for inventory control in any type and size of operation. The actual system selected will depend upon the type of operation, the amount of goods (Zhang J., 2006). The Eyeball System This is the standard inventory control system for the vast majority of small retail and many small manufacturing operations
and is very simple in application. The key manager stands in the middle of the store or manufacturing area and looks around. If he or she happens to notice that some items are out of stock, they are reordered. In retailing, the difficulty with the eyeball system is that a particularly good item may be out of stock for sometime before anyone notices. Throughout the time it is out of stock, sales are being lost on it. Similarly, in a small manufacturing operation, low stocks of some particularly critical item may not be noticed until there are none left. Then production suffers until the supply of that part can be replenished. Such unsystematic but simple retailers and manufacturers to their inherent disadvantage. Reverse Stock (or Brown Bag) Systems This approach is much more systematic than the eyeball system. It involves keeping a reserve stock of items aside, often literally in a brown bag placed at the rear of the stock bin or storage area. When the last unit of open inventory is used, the brown bag of reserve stock is opened and the new supplies it contains are placed in the bin as open stock. At this time, a reorder is immediately placed. If the reserve stock quantity has been calculated properly, the new shipment should arrive just as the last of the reserve stock is being used. In order to calculate the proper reserve stock quantity, it is necessary to know the rate of product usage and the order cycle delivery time. Thus, if the rate of product units sold is 100 units per week and the order cycle delivery time is two weeks, the appropriate reserve stock would consist of 200 units. This is fine as long as the two-week cycle holds. If the order cycle is extended, the reserve stock quantities must be increased. When the new order arrives, the reserve stock amount is packaged again and placed at the rear of the storage area. This is a very simple system to operate and one that is highly effective for virtually any type of organization. The variations on the reserve stock system merely involve the management of the reserve stock itself. Larger items may remain in inventory but be cordoned off in some way to indicate that it is the reserve stock and should trigger a reorder (Kwan S., 2009).
Perpetual Inventory Systems Various types of perpetual inventory systems include manual, card-oriented, and computer- operated systems. In computeroperated systems, a programmed instruction referred to commonly as a trigger, automatically transmits an order to the appropriate vendor once supplies fall below a prescribed level. The purpose of each of the three types of perpetual inventory approaches is totally either the unit use or the dollar use (or both) of different items and product lines. This information will serve to help avoid stock-outs and to maintain a constant evaluation of the sales of different product lines to see where the emphasis should be placed for both selling and buying (Kulish N., 2001). 1-3-2 Classification of Inventory Items The ABC inventory classification process is an analysis of a range of distinct items, referred to as Stock Keeping Units (SKUs), such as finished products into three categories: A - outstandingly important; B -of average importance; C -relatively unimportant as a basis for an inventory control scheme. Each category should be handled in a different way, with more attention being devoted to category A, less to B, and even lesser to C. The larger firms, with larger inventory investments, will often use much more class systems. The traditional ABC classification has generally been based on just one criterion the annual dollar usage of the items. However depending on what part of the organization is concerned; the criterion of what is most important with respect to inventory items can change. There are other criteria that represent important considerations for management such as lead time, obsolescence, availability, substitutability, criticality, repairability, commonality, certainty of supply, impact of stock out, inventory cost, number of requests for the item in a year, scarcity, durability, order size requirement, stock ability, and demand distribution. Multi-criteria Inventory Classification (MCIC) has been introduced by (Flores et al, 1986). Although they introduced several criteria such as obsolescence, lead times, substitutability, repairability, criticality and commonality, their concept of a joint criteria matrix was developed for two criteria as shown in fig 1-2 (Wan Lung Ng., 2007). This concept is not a
First Critical Criteria A B C Second Critical Criteria A B AA AB BA BB CA CB C AC BC CC Fig 1-2. Joint Matrix of Two Criteria. (Wan Lung Ng., 2007). suitable method for considering more than two criteria. They stated the greater the number of criteria that are viewed as important, the more complex the task of developing the classification becomes. If all criteria are important and need to be incorporated in the analysis, the task may be very hard. The joint criteria matrix, therefore, can be considered as a bi- criteria inventory classification (Wan Lung Ng., 2007). However based on the authors multi-criteria concept, several Multi-Criteria Decision-Making (MCDM) methods have been proposed to solve this problem used a statistical technique to group items across many dimensions. The main advantage of this approach is that it can accommodate large number of combination of attributes, which are significant for both strategic and operational reasons (Javar R.,2009). Partovi presented similar approaches to the ABC classification problem. The proposed methods based on Analytic Hierarchy Process (AHP), rated items on both qualitative and quantitative criteria. The main advantage of the AHP method is that it is able to consider several criteria. However, when the number of criteria is increased, the consistency rate will be very sensitive and reaching to a consistent rate will be very difficult (Partovi F. et al, 1993). Guvenir proposed a method to learn the weight vector along with the cut-off values for MCIC at 1998. The proposed method called Genetic Algorithm for Multi-Criteria Inventory Classification (GAMIC) used a genetic algorithm to learn the weights of criteria along with AB and BC cut-off points from pre classified items. Once the criteria weights are obtained, the weighted scores of the items in the inventory are computed similarly to the approach with AHP. Then the items with scores greater than AB cut-off value are classified as class A; those with scores between
AB and BC as class B; and the remaining items are classified as class C. This method had the advantages and disadvantages of AHP method. In addition, the classification results, to some extent, depended on the preclassified items (Guviner H., 1998) Puente et al. presented a fuzzy method of classifying different productive items of a company at 2002. This method allowed new fuzzy information about the future to be included, thus allowing stricter control of the fuzzy A-items that resulted from this classification. The authors, however, only considered two criteria of demand and cost in their study. The authors model was in fact a bi-criteria rather than a multi-criteria model (Javar R., 2009). Partovi et al presented an artificial neural network for ABC classification of inventory at 2002. They utilized two learning methods in their approach: back propagation and genetic algorithm. The reliability of their proposed methods was tested by comparing their classification ability with two data sets. The methods were compared with the multiple discriminate Analysis technique. Their results showed that both proposed methods had higher predictive accuracy than discriminate Analysis. There was no significant difference between the two learning methods used to develop the artificial neural network. However the application of these methods is difficult for an average inventory manager (Fariborz Y., 2002). Zhou et al presented an extended version of the Ramanathan s model. They incorporated some balancing features for MCIC using two sets of weights that are most favorable and least favorable for each item (Ramanatha R., 2006). Ramanathan proposed a weighted linear optimization method for classifying inventory items with multiple criteria. In the proposed approach, a weighted additive function was used to aggregate the performance of an inventory item in terms of different criteria to a single score, called the optimal inventory score of an item. The weights were chosen using optimization method subject to the constraints that the
weighted sum for all the items must be less than or equal to one. The weighted sum was computed using the same set of weights. This method used a maximization objective function. To obtain the optimal scores of all inventory items, proposed method should be solved repeatedly by changing the objective function. These scores can then be used to classify the inventory items (Ramantha R., 2006). Rezaei uses Fuzzy Analytic Hierarchy Process (FAHP), presented a MCIC method. The weights of the criteria were calculated by using FAHP; then a six-step algorithm was presented to calculate the final normalized weighted score of each item. Finally, using a principle of comparison for fuzzy numbers, the final scores were compared with one another and all items were classified into three classes according to their final scores (Javar R., 2009). Wan L. N. uses a simple model for inventory classification is proposed when multiple criteria are considered. A weighted linear model is first formulated. A transformation is then applied on and which induces a simple solution mechanism for calculating a unified measurement of overall score of an inventory item. The overall score can be easily obtained by some simple calculations on any commonly available spreadsheet package without any linear optimizer. One of the limitations of exogenous specification of ranking is the number of criteria. When the number of criteria under consideration is small, specification of ranking is not a hush requirement. However, when number of criteria is large, it is not an easy task for decision maker to rank all criteria (Wan Lung N., 2007). Cakir presented a methodology for MCIC by using FAHP as well. The difference of this method and Rezaei method was that this method was web-based and used a decision support system (Javar R., 2009). Bhattacharya et al uses the Technique for Order Preferences by Similarity to the Ideal Solution proposed a Multi Attribute Inventory Classification (MAIC) method. They illustrated this technique in a pharmaceutical company by considering these criteria unit cost, lead times, consumption rate, perish ability of items and cost of storing of raw
materials in a crisp format. They concluded that constructing fuzzy models such as fuzzy and neuro-fuzzy hybrid model would be suitable by taking the vagueness in attribute values into account (Javar R., 2009). Chu et al. proposed an inventory control approach combining ABC and fuzzy classification. They applied this method to an example with 159 SKUs and surprisingly classified 59 items in class A, 69 items in class B and 64 items in class C which is not consistent with the basic concept of ABC classification. However it does not seem logical to classify roughly the same number of SKUs at three classes A, B and C (wan L. N., 2007). Chen et al. introduced a case-based MCIC based on the right distance based preference expression. Using the decision-makers assessment of case sets as input, preferences over alternatives were represented intuitively by using weighted euclidean distances. Then a quadratic optimization program finds optimal classification thresholds. Although this method is robust one, this method requires some complicated implementation steps which may confuse the decisionmaker. This method classified items to just three classes and for the cases requiring more than three classes the complication of the method will be dramatically increased (Kevin W. et al,2008). Chi-Yang T. introduced an inventory classification algorithm by applying the Particle Swarm Optimization (PSO) technique. Other classification schemes require the number of item groups to be specified before classification. In addition, they are designed for particular objectives (e.g. cost minimization specific costs) or they classify items based on certain criteria (e.g. demand rate, item values). In contrast, the PSO algorithm can be utilized to incorporate with various objectives. It simplifies the decision process of having to decide how many item groups there should be before item classification. Experimental design was employed for PSO parameter selection. Four objectives, cost minimization, demand correlation maximization, inventory turnover ratio maximization, and a combination of the above three, were discussed (Chi- Yang T. et al., 2008).
Jaehun P. et al introduced the cross-efficiency method in data envelopment analysis. It claims that the proposed model can provide a more reasonable and accurate classification of inventory items by mitigating the adverse effect of flexibility in the choice of weights and yielding a unique ordering of inventory items (Jaehun P. et al, 2010). Golam K., introduced Fuzzy analytic hierarchy method. Fuzzy Analytic Hierarchy process is used to determine the relative weights of the attributes or criteria, and to classify inventories into different categories (Golam K., 2011). 1-3-3 Data Mining (Classification) Techniques Data mining is a process that uses a variety of data analysis tools to discover patterns and relationships in data that may be used to make classification. It does not tell you the value of the patterns to the organization. Furthermore, the patterns uncovered by data mining must be verified in the real world (Danial T.,2005). There are two keys to success in data mining: First is coming up with a precise formulation of the problem you are trying to solve. A focused statement usually results in the best payoff. The second key is using the right data. After choosing from the data available to you, or perhaps buying external data, you may need to transform and combine it in significant ways. Unlike classification you don t know what the clusters will be when you start, or by which attributes the data will be clustered. Consequently, someone who is knowledgeable in the business must interpret the clusters. Often it is necessary to modify the clustering by excluding variables that have been employed to group instances, because upon examination the user identifies them as irrelevant or not meaningful. After the clusters are found that reasonably segment your database, these clusters may then be used to classify new data (Danial T.,2005).
Some of data mining techniques used in classification are listed as follow: Neural networks are of particular interest because they offer a means of efficiently modeling large and complex problems in which there may be hundreds of variables that have many interactions (Guoqiang P., 2000). Decision trees are a way of representing a series of rules that lead to a class or value (Rasoul S., 1991). Rule induction is a method for deriving a set of rules to classify cases. Although decision trees can produce a set of rules, rule induction methods generate a set of independent rules which do not necessarily (and are unlikely to) form a tree. Because the rule inducer is not forcing splits at each level, and can look ahead, it may be able to find different and sometimes better patterns for classification. Unlike trees, the rules generated may not cover all possible situations. Also unlike trees, rules may sometimes conflict in which case it is necessary to choose which rule to follow. One common method to resolve conflicts is to assign a confidence to rules and use the one in which you are most confident. Alternatively, if more than two rules conflict, you may let them vote, perhaps weighting their votes by the confidence you have in each rule (Bramer M., 2000). K-nearest neighbor is a classification technique. It decides in which class to place a new case by examining some number k in k-nearest neighbor of the most similar cases or neighbors. It counts the number of cases for each class, and assigns the new case to the same class to which most of its neighbors belong (Khan M.,2002). Genetic algorithms are not used to find patterns, but rather to guide the learning process of data mining algorithms such as neural nets. Essentially, genetic algorithms act as a method for performing a guided search for good models in the solution space. They are called genetic algorithms because they loosely follow the pattern of biological evolution in which the members of one generation (of models) compete to pass on their characteristics to the next