Integrated forecasting and inventory management in a wholesale company

Integrated Forecasting and Inventory Management in a Wholesale Company at Tescoma s.r.o Guilherme Guedes Lopes Dissertação de Mestrado Orientador na FEUP: Prof. Eduardo Gil da Costa Orientador na Tescoma s.r.o : Ivan Skalda Faculdade de Engenharia da Universidade do Porto Mestrado Integrado em Engenharia Industrial e Gestão 2012-01-25 Integrated Forecasting and Inventory Management in a Wholesale Company ii Ao meu avô, António Gouveia Lopes Integrated Forecasting and Inventory Management in a Wholesale Company iii Resumo Atualmente, em todas as áreas de negócio com qualquer grau de complexidade e de dimensão, as empresas são confrontadas com necessidades de planeamento e previsão. Em particular, estas necessidades prendem-se muitas vezes com a previsão de vendas e o planeamento, seja de produção, seja de ordem de produção, que no fundo e em perspectivas diferentes pretendem analisar a gestão de inventários. Neste trabalho foram exploradas estas necessidades, na dimensão de uma empresa multi nacional de artigos de kitchen and houseware, com um centro logístico de distribuição global. Numa primeira fase será abordada a temática dos métodos de previsão, onde serão propostos os diferentes modelos e processos, procurando assim os que melhor se adequem à realidade do projeto. Serão contrastados diferentes níveis de agregação dos dados, permitindo incluir uma avaliação mais pormenorizada de como tratar dados numa empresa de venda a grosso e as razões inerentes. Numa segunda fase, os métodos de previsão foram integrados com um sistema de reabastecimento de inventário, onde várias metodologias atuais de gestão de inventário serão alvo de estudo e debate. Surgirá uma revisão relativa ao stock de segurança, as suas diversas abordagens e limites, e onde a escolha residirá suportada por dados estatisticos. Esta integração será feita por meio de um algoritmo, testado sobre o ano de 2012 com os dados reais de vendas e stocks do período de Janeiro a Agosto. Integrated Forecasting and Inventory Management in a Wholesale Company iv Abstract Nowadays, in every business area with any degree of complexity and magnitude, companies face the need of planning and forecast. In particular, these needs often relate with sales forecasting and planning, either production planning, or production order, which at the end, and in different perpectives intend to analyse inventory management. In this work these needs are explored, in the dimension of a multi national company of kitchen and houseware articles, with a main logistics center of global distribution. In a first phase, an approach to the forecasting methods thematics will be made, where different models and processes will be proposed, in order to find the ones that better suit the project reality. Different levels of data agreggation will be compared, allowing a deeper analysis of how to process data in a wholesale company and the inherent reasons. In a second phase, the forecasting method will be integrated with the inventory replenishment policy, where different inventory management policies will be studied and debated. Naturaly in this context a review of safety stock is required, with its approches and constraints, and the choice suported by statistic data. This integration will be made by an algorithm, tested with 2012 data, with real sales and stocks data from January to August. Integrated Forecasting and Inventory Management in a Wholesale Company v Agradecimentos Gostaria de agradecer a todos aqueles que me acompanharam neste projecto, primeiramente ao meu orientador na FEUP, o Eng. Eduardo Gil da Costa, que apesar da distância mostrou-se sempre disponível no decorrer deste trabalho. De salientar também o meu orientador na empresa, Ivan Skalda não esquecendo todos os outros colegas de trabalho, em especial Libor Vecera e Jiri Vackulik. Um obrigado também a todos os meus amigos, que ainda que indirectamente, me ajudaram a concluir este projecto. Por fim, agradecer profundamente à minha família, pais, irmãos e avós, que foram sempre um exemplo na minha formação e fundamentais para todo o meu percurso pessoal e académico, e à Inês, que foi incansável e a base da estabilidade necessária para desenvolver este projecto. Integrated Forecasting and Inventory Management in a Wholesale Company vi Index 1 Introduction .......................................................................................................................................... 1 1.1 Tescoma Presentation ......................................................................................................................... 1 1.2 Tescoma Project Scope ....................................................................................................................... 3 1.3 Objectives ............................................................................................................................................ 5 1.4 Dissertation Structure ........................................................................................................................... 5 2 State of Art .......................................................................................................................................... 7 2.1 Forecasting .......................................................................................................................................... 7 2.2 Inventory Management....................................................................................................................... 12 2.3 Safety Stock and Safety Lead time .................................................................................................... 16 3 Structure and Competencies of Relevant Departments.................................................................... 20 3.1 Purchasing ......................................................................................................................................... 20 3.2 Logistics ............................................................................................................................................. 21 3.3 Trading ............................................................................................................................................... 23 4 Implementation .................................................................................................................................. 28 4.1 Products Selection ............................................................................................................................. 28 4.2 Forecasting methods .......................................................................................................................... 30 4.3 Safety Stock ....................................................................................................................................... 32 4.4 Inventory Management....................................................................................................................... 34 5 Results .............................................................................................................................................. 38 5.1 Safety Stock Reform .......................................................................................................................... 38 5.2 Multi-Criteria ABC products ................................................................................................................ 39 5.3 Management Products ....................................................................................................................... 42 6 Conclusions and future work perspectives ....................................................................................... 46 References ............................................................................................................................................. 48 ANNEX A: ............................................................................................................................................... 52 Integrated Forecasting and Inventory Management in a Wholesale Company vii Integrated Forecasting and Inventory Management in a Wholesale Company 1 1 Introduction The practical experience of Tescoma, associated with a perspective of the current methodologies used in the business will lead the way in the development of this work. Facing a continuous growth, and due to its national and subsequent international expansion, Tescoma recently felt the need to incorporate new models in distinct areas that could outperform the old ones, thus helping to boost this growth. Developments were made in the past few years in logistics, with a complete remodelling of the warehouse and distribution system, with the development of native software integrated with the ERP (Enterprise Resource Planning), (SAP). With this work we pursue to continue this evolution, emphasising efforts in performance improvements using several tools and techniques applied in inventory management. A selection of protocols and methods regarding forecasting, replenishment policies and safety stock literature will be reviewed, so a effective selection of the appropriate system can be achieved. Further, all these preceding ideas will be aggregated to obtain a robust algorithm that can retrieve an “Order planning” interface. 1.1 Tescoma Presentation Tescoma s.r.o is a company without foreign capital seat in Zlín, Czech Republic, focusing its main business in design, research and development of all kinds of kitchen and houseware. Tescoma is devoted to the following three principles: “1.Offer a wide range of products of excellent quality with favorable prices” “2.Apply and develop own original designs of Kitchen utensils” “3.Promote the brand and the reputation of the Czech Republic abroad” Tescoma Worldwide With a leading position on the global market of kitchenware, a range of over 2,000 SKU (Stock Keeping Unit), and average of 17 new utensils per month, Tescoma sells in over 100 countries worldwide. As a consequence of this worldwide growth Tescoma completed in 2008 his second stage of “Tescoma World Logistics Centre”, with an actual capacity of 30,000 pallets in Zlín headquarters. However, this reveals not to be enough in years to come, and so, a third stage is already in progress to rise the total capacity of the main warehouse in 16,000 pallets. Integrated Forecasting and Inventory Management in a Wholesale Company 8 At the same time, and working for the US Office of Naval Research, Holt developed exponential smoothing methods, quite different of Brown’s methodology concerning trend and seasonal components. Later on, his student Peter Winters (1960), made empirical tests achieving what is call Holt-Winter’s methods. In the following years extensions of the methods were made by other researchers such as Pegels (1969), Gardner and Mckenzie(1985) and Taylor(2003a). According with R. Hyndman et al. (2008) we can describe a time series as the combination of the following components: Trend (T): the long-term direction of the series; Seasonal (S): A pattern that repeats with a known periodicity; Cycle (C): A pattern that repeats with some regularity, but with unknown and changing periodicity; Error (E): The unpredictable component of the series. Table 1 presents the equations for the standard methods of exponential smoothing, all of which are extensions of the work of Brown (1959, 1963), Holt (1957), and Winters (1960)(E. Gardner, 2006). Two formulas are presented for each method, one refers to the recurrence forms, and the second is related with error-correction forms. Both can and are used till today, being the use of error-correction forms much more simple, and still they have proved to come up with similar forecast. The taxonomy is based on Hyndmans et al.’s (2002) with Taylor (2003) extension, where each method trend is described by one or two letters (row heading), and the seasonality of the methods is described by one letter (column heading); as an example, if we have A-N, it means additive trend with no seasonality. The following methods are in Table 1: N-N Simple exponential smoothing (Brown, 1959) A-N Additive trends (Holt, 1957) DA-N Damped additive trend (Gardner and Mckenzie, 1985) M-N Multiplicative trend (Pegel, 1969) DM-N Damped multiplicative trend (Taylor, 2003) Integrated Forecasting and Inventory Management in a Wholesale Company 9 Despite the lack of agreement on notation concerning exponential smoothing, Gardner (1985) notation will be followed, as it is the most used notation in the researched articles. Table 1Standard exponential smoothing methods (Source: Gardner, 2006) Integrated Forecasting and Inventory Management in a Wholesale Company 10 Regarding exponential smoothing study, some basic definitions to acknowledge the methods differences are presented. Additive and Multiplicative Seasonality Sales behavior during a year can be sometimes seasonal. As an example we may refer umbrellas sales where every year during winter sales will increase. Considering only one “raining month” the seasonality period will be 12 months. The seasonal length can be days, weeks, months etc., but they will always have the same general pattern (Kalekar, 2004). Seasonality can be for instance the increase of 10000 umbrellas sale in this seasonal months; so, every year we know there will be 10000 umbrella difference between the average sale and the seasonal period. This is additive seasonality (Kalekar, 2004). When the increase is a percentage of the average sale (50% as example), either has been the worst year of sale or the best one in the company history, we have a multiplicative seasonality (Kalekar, 2004). Additive, Multiplicative and Damped Trend As in seasonality, the same theory can be applied to trend. Table 2Notation for exponential smoothing (Source: Gardner, 2006) Integrated Forecasting and Inventory Management in a Wholesale Company 11 When we have a linear increase in sales every year, we have an additive trend. Multiplicative trend, just as multiplicative seasonality, is the increase of sales every year revealing a factor in this growth (Kalekar, 2004). Finally, damped trend has a different behavior, related with sales that increase with a decadent factor, i.e. sales growth in the second year will be 80% of the first year factor, in the third will be 80% of previous year factor, and so on (Kalekar, 2004) . Method Selection Many studies have been made in method selection. Meade (2000) proposed an experimental study where time series with known properties, and consequently, with the best suitable forecasting method identified, were analyzed. This analysis relates the data during the estimation period with its usability in predicting forecasting method. Meade’s study included, three naïve methods, 3 exponential smoothing methods, Robust trend, a non-parametric version of Holt’s linear trend method, and a third group, compromising ARMA (autoregressive moving average) based methods (Meade, 2000). The final conclusion revealed that summary statistics do contain sufficient information to select a method or a set of methods that will perform well (Meade, 2000). Concerning exponential smoothing methods, Tashman & Kruk, (1996) considered variance protocol, which was already considered by Gardner and McKenzie, (1988) Still according with Tashman & Kruk, (1996), the protocol consisted in the transformation of first and second differences of the series, identifying the minimum variance between these two and the original series; if the original series presents the least variance then a single exponential smoothing should be the chosen method, if the minimum was obtained with the first differenced series then Holt’s damped exponential smoothing should be applied, and finally, if second differencing had reached the minimum between the three, Holt’s linear or multiplicative trend is suggested. Gardner (2006) has applied these methodology with an extension to other exponential smoothing methods, (according with these notation) , which are presented in Table 3. Table 3Method Selection Rules (Source: Gardner, 2006) Integrated Forecasting and Inventory Management in a Wholesale Company 12 Variances and prediction intervals Prediction intervals for exponential smoothing were believed to be impossible to calculate in the past. The first analytical approach to this problem was to assume that the series were generated by deterministic function of time plus white noise (Brown, (1963); Gardner, 1985; McKenzie, (1986); Sweet, (1985)) (De Gooijer & Hyndman, 2006). Regression model would be more reliable if this was to be truth (De Gooijer & Hyndman, 2006). However, Johnston and Harrison (1986) calculated prediction intervals, by the equivalence of exponential smoothing methods and statistical models, finding forecast variances for the simple and Holt’s exponential smoothing for the state space models. Other authors later developed models to obtain prediction intervals for all the main exponential smoothing methods, having R. J. Hyndman, Koehler, Ord, & Snyder, (2005) accomplished to develop models for all the most common methods of the state space models. Fixed Parameters The use of arbitrary parameter in exponential smoothing has become worthless nowadays, once the existence of common search algorithms software (e.g. Microsoft Excel Solver may quickly calculate the parameters by minimizing the MSE (Mean square root). The use of adaptive parameters has been found to have no credible evidence of forecasting improvement Gardner (1985), so this section will not be reviewed. Initial values and parameters optimization The effect of initial values and loss function in the post-sample forecasting accuracy has been widely studied along the years. Makridakis and Hibon (1991) measured the effect of different initial values in N-N, A-N, and DA-N methods (E. Gardner, 2006). In this study, the most common initialization methods have been applied, such as Least Square Estimates, Backcasting, Training Set, Convenient Initial Values and Zero values. Various loss functions such as linear, quadratic and higher order functions have been used, penalizing bigger errors. The rationale behind such choice is that the negative consequence of forecasting error are not necessarily proportional (Makridakis & Hibon, 1991). To attain the purpose, MAD (Mean absolut error), MAPE (Mean absolut percentage error), Median and MSE were used as loss function in the study. Despite they are never utilized, cubic, 1.5, 2.5, and fourth power function were also included in these studies, so all theoretical and actually used alternatives could be compared. As a conclusion, it has been revealed that from a practical point of view the most used methodology (MSE) as a loss function and least square estimates to initialize the starting values are as good as all other alternatives as differences are statistically non-significant. 2.2 Inventory Management Inventory management seeks to answer three questions (Silver, 1981): 1) How often should we review our inventory? 2) When should a replenishment order be placed? 3) How large should the replenishment order be? Integrated Forecasting and Inventory Management in a Wholesale Company 13 The main objectives of a manager implementing inventory management are (Silver, 1981): 1) Maximize profit, rate of return on stock investment 2) Minimize total cost 3) Determine feasible solutions 4) Ensure flexibility of operation Developed by Ford Harris in 1915, Economical Order Quantity was the first theoretical approach to solve the problem of determining what quantity to buy or produce at a given time assuming constant rate demand with a single-item mode(Erlenkotter, 1990). Despite it has been published, Harris original EOQ paper was lost for many years, being rediscovered in 1988 (Erlenkotter, 1990). The simple square-root formula for the optimal order quantity for constant demand rate is now taken as common sense inside the scientific and practitioner’s community. Where: DAnnual Demand A-Fixed Cost per Order HHolding Cost per Unity Later models that could handle all kind of constraints and variables were developed. The most important and handled constraints are (Silver, 1981): -Supplier constraints: minimum order sizes, maximum order quantities -Marketing constraints: minimum service levels -Internal constraints: storage space limitations, maximum budget for purchases in each period As in terms of variable models reviewed, we can distinguish between: Single vs. Multi-item Deterministic vs. Probabilistic Demand Single Period vs. Multi period Stationary vs. Time-Varying Parameters (demand, costs..) Single vs. Multiple Stocking Points Costs have been considered in literature to decision-making purposes. This has led to the disaggregation of costs into categories that can be more easily measured. The relevant cost categories are (Silver, 1981): Equation 1EOQ Formula Integrated Forecasting and Inventory Management in a Wholesale Company 14 Replenishment Costs: The costs incurred when a replenishment action is taken. They can be divided into fixed part of the cost, due to the order itself, such as setup costs or transportation costs, and a variable part that can include cost of materials or products. Carrying Costs: These are the in stock products multiple costs, as the cost of borrowing capital invested, warehouse costs, insurance, taxes, and obsolescence. Insufficient Inventory Costs: When customers demand is not satisfied, due to stock out, backordering or lost sales are costs incurred by the company, as well as company image, that can affect future sales. The evolution of Harris method was a natural path, for practical industrial environment deals with variable demand along the time, finite capacity along with many other variables and constraints cited before. Harris method takes assumptions that would mislead our decisions by not considering serious and significant information (Okhrin & Richter, 2011). Most recent works deal with the dynamic version of the economic lot size model. In Wagner & Whitin, 2004 work, single item replenishment is studied handling inventory holding changes and variable setup costs over time, thus minimizing the total cost and satisfying the time-varying demand in every period. P.Dixon (1981) considers a multi-item replenishment model for a single work centre, considering setup cost at each time, production costs, and finite capacity. Single item with stationary, probabilistic demand and known distribution is a common inventory management variant, which uses different control procedures. The four most well known replenishment systems schemes for single item are the time based (R,S), the quantity time based (s,Q) and (s,S) , and a hybrid approach, that is the time-andquantity based (R,s,S). Figure 1, 2 and 3 (Esteves, 2011) will support each model understanding. L= Delivery time R= Review interval (R,S) Control System This policy is a time-based policy with a predetermined R period review. The procedure in this scheme is: in each R period inventory level is compared with the predetermined S level, the difference between the current stock, and S is calculated, obtaining the replenishment quantity to order. This is a common method for multi-item with single supplier cases, for it's a simple and static solution for replenishment planning. However it is characterized by having big holding costs (Smits, 2003). Integrated Forecasting and Inventory Management in a Wholesale Company 15 (s,Q) Control System Continuous review is the primary positioning of this scheme. A minimum quantity level is designated as s and every time the on-hand inventory falls below this s level it triggers the process indicating the need of re-supply. The replenishment order is then placed to the supplier with Q quantity size. The risk of this scheme is to potentially run out of stock, in the short term, if the s quantity is not enough to cover the lead-time of the new order, and also in the long term, with the continuous decrease of the inventory level (Smits, 2003). Figure 2- (s,Q) Graphic Model (Source: Esteves, 2011) Figure 1- (R,S) Graphic Model (Source: Esteves, 2011) Integrated Forecasting and Inventory Management in a Wholesale Company 16 (s,S) Control System Similar to the s,Q policy, this policy is a small variant, where the order quantity after process triggering will not be a Q fixed quantity. Instead, this lot size will be the difference between the current stock at triggering time and an S level (Smits, 2003). Usually this method outperforms the previous one, as it prevents stock run out in the longterm. (R,s,S) Control System With an R periodic review, this hybrid approach combines advantages of both continuous and periodic policies. In every cycle the current stock level is compared with a predetermined s quantity. If this level is above s, the order doesn’t take place. However, if this level is below s an order is placed. The batch size is equal to the quantity needed to refill the inventory to the predetermined S level (Smits, 2003). 2.3 Safety Stock and Safety Lead time In order to deal with the uncertainties in demand and supply, companies usually keep a buffer to prevent stock-out. This buffer is usually called safety stock when it means extra inventory kept, or safety lead-time when “extra time” is used. “Safety stock is defined as the average amount of inventory kept in hand to accommodate short-term uncertainty in demand and variability in supply, and safety lead-time as the difference between release time and the due date, minus the supply lead-time of the product” (Van Kampen, Van Donk, & Van der Zee, 2010). The comparisons between both approaches were made by Kampen et.al (2009) considering different combinations of lead-time variability, demand variability, product type changes among with others. Concerning both lead-time variability and stochastic demand, (where this is the relevant case in this study), some conclusions have been acknowledge: Figure 3- (s,S) Graphic Model (Source: Esteves, 2011) Integrated Forecasting and Inventory Management in a Wholesale Company 17  In case of demand uncertainties, safety lead-time results in lower average inventory levels at low levels of uncertainty, but when in the presence of high uncertainty level, the required inventory level increases drastically (Kampen et.al, 2009).  Kampen explains this rapid increase by the fact that in the presence of excess inventory using safety stock, the next supplying order is made later, while using safety lead time the order has already been made, resulting in even more stock (Kampen et.al, 2009).  The results also showed that as the number of SKU increased the inventory levels of safety lead-time time also reveal worst results than safety stock (Kampen et.al ,2009). Because demand variability is a high and real fact in the current project, and because all suppliers and orders by the company effectively present more than one SKU, the rest of the analysis deeps in the safety stock approach. Talluri, Cetin, & Gardner (2004) described the four well-established models of safety stock and applied both demand and lead-time variability model on a made-to-stock pharmaceutical company thus comparing it with the current model. Plus they have done a sensitivity analysis using demand and lead-time variability. The conclusion of this paper provided the idea that an extra effort in the accuracy of forecasting models, along with the lead-time variability estimation, should be done as they have a significant impact on stock levels (Talluri, Cetin, & Gardner, 2004). Figure 4 presents the four models: Eppen & Martin, (1988) considered a problem of setting safety stock in the presence of both lead-time and demand variability. They developed two procedures, one considering the knowledge of demand lead-time distributions, and a second where they were unknown and had to be estimated. Again the analysis will be focused on the second procedure because that is the project scope. Figure 4Safety Stock Models (Source: Talluri, 2004) Integrated Forecasting and Inventory Management in a Wholesale Company 24 With a young and dynamic team in the design and development departments, Tescoma launches an average of 17 new products per month. Whether completing already existing product families or building up new ones, the range of products is getting wider to fulfill all costumers needs. Suppliers Tescoma does not produce its own products, the key and core business is their development and design. Outsourcing the production allows Tescoma to focus all efforts and human resources in what they know to do best. Because of its wide range of products, so are the raw materials required and the production techniques needed. This means the need of different factories, which may fit every product need. Factories specialized in each kind of product, each kind of material, and each kind of technique so that Tescoma quality standards are achieved. A team of workers has the skills to fulfill this objective at the company. Ther task is to search and target all factories that can better suit Tescoma products previously developed in headquarters. Product prices and specialized tooling, along with all other variables in the contract are negotiated directly by the department with the potential suppliers. Nowadays Tescoma works with over 150 suppliers, 70%, which are based in Asia, and 30% in Europe. As a direct consequence of their location, European suppliers are only a few hours away from Tescoma headquarters, providing a better control of all stages of the process, whether considering the initial negotiation process, as the re-negotiation of raw material prices and production info. Uncertainty and average lead-time are lower among European suppliers than Asian suppliers. Also breakdowns vulnerability is decreased by the quicker response available. The shorter lead-time of European suppliers has another planning advantage, as it provides the company to save investment and volume in the warehouse by the reduction of cycle and safety stock required. Asian suppliers on the other hand are far away and for many years when something went wrong there was no way to catch up the delivery date or to pressure the suppliers to solve problems on time. To fix these kinds of problems, or to at least decrease its occurrence and effect in the business, Tescoma has created a team of native people divided in two offices in Asia. Their only concern is, beyond cooperating in the search of new suppliers, to monitor every factory, check every single stage and process of production and push the factories so they are not late in their deliveries. This strategy and investment has become of major importance for Tescoma as monitoring and checking all the processes increases the probability of quality to be according with standards, decreasing the probability of the lot to be turn down by the quality department in Europe headquarters. The relationships with factories also turn to be closer, prioritizing Tescoma orders, performing a greater capability to deliver goods on time and with quality to costumers. Integrated Forecasting and Inventory Management in a Wholesale Company 25 Customers Tescoma costumers may be divided in three categories: -National -Stores -Market -Branch -International National National customers are Czech customers, divided in two subcategories: -Stores Despite not being the biggest customer group, stores are a key and strategic customer, as they can give direct feedback to the company, in term of sales as well as customers feeling about Tescoma products and needs. Stores may be owned by Tescoma or franchised. Stores are important under Tescoma strategy as the full range of products can be presented to customers and chain is shortened one step, profit margin gets higher and retail price is lower and more competitive. At the moment Tescoma has 80 stores all over Czech Republic, and strategically plans to reach 100 stores in 2014. -Market “Market” customers are national customers with whom Tescoma built a relation over the years. Convenience stores, big-chains and supermarkets as Tesco, Globus are examples. Branch Selling for more than 100 countries gave more visibility to Tescoma and with internationalization came the necessity to expand and build some infrastructure to support the business in some of those markets. Tescoma has branches in, Slovakia, Italy, Russia, Poland, Spain, Portugal and Ukraine. Tescoma headquarters manages branches. However branches have their own strategy and a low rate of integration, in order to be better suit each market. Branches buy from Tescoma headquarters like common costumers, placing orders and receiving information without integrated software. This has some disadvantages in terms of information to headquarters and even to branches, resulting in a lack of knowledge of branches detailed selling, stock, and updated abroad market behavior. To minimize this lack of information several meetings are held during the year to discuss new products, market analysis and strategy, and gathering of information. Integrated Forecasting and Inventory Management in a Wholesale Company 26 International “International” costumers are all costumers outside Czech Republic that are not branches. Despite headquarters is based in Czech Republic, international sales is responsibility of Tescoma Spa (Italy), on account of their better geographic positioning and infrastructures for export. Integrated Forecasting and Inventory Management in a Wholesale Company 27 Integrated Forecasting and Inventory Management in a Wholesale Company 28 4 Implementation 4.1 Products Selection The product selection began with a statistical analysis, based on the development of an algorithm which could apply a multi criteria ABC classification (Chen et al., 2008). This multi criteria ABC analysis has considered three factors: underlying sales volume, average investment and average volume occupied. Table 4 presents a matrix representation of this approach obtained by a sales-investment relation, and the same philosophy was conducted for a sales-volume relation (Table 5). A last category was created by the integration of both schemes, thereby showing a CACA category. This CACA group possesses the most economically unfeasible products, which were considered to be the most important and where greater improvements are expected in all KPIs (Key performance indicator). Table 4Multi Criteria Sales/Investment ABC Analysis ABC Sales-Investment Investment A B C Sales A AA AB AC B BA BB BC C CA CB CC Table 5Multi Criteria Sales/Volume ABC Analysis ABC Sales-Volume Volume A B C Sales A AA AB AC B BA BB BC C CA CB CC In order to corroborate this classification, a further ABC analysis has been made upon a sales per investment factor and sales per volume factor (Table 6). An integration algorithm was applied, thereby determining AA as the critical criterion (Factor sorted from lowest to highest value). It must be noted that there would be cases of wrongly assigned A products due to the existence of articles at the end of their life-cycle, or with very low sales, thus revealing high factors that clearly mislead this classification. To prevent such cases a filter with a minimum sales volume was proposed, which should remove the occurrence of this situation. Integrated Forecasting and Inventory Management in a Wholesale Company 29 Table 6Multi Criteria (Sales/Volume)/(Sales/investment) Factor ABC Analysis ABC Sales/Volume-Sales/Investment Sales/Investment A B C Sales/Volume A AA AB AC B BA BB BC C CA CB CC Results turn to be significantly satisfying, confirming that these different approaches produced overall similar classification, with an 87% correspondence. The 13% of non correspondence articles may be explained by C sales products that have been removed by the filter and in some other cases attributed to the B or even A sales products in some of the criterias that have high factors but that were not considered by the first approach. From the aforementioned list a random selection of 3 products was made, considering products from the same supplier. In other words a random selection was made in the universe of products which the supplier had at least 3 articles in the “critical list”. Justification for this approach will be discussed later on. A second analysis was performed after the presentation of the first results to the top management. Acknowledging the potential of the method equivalent study was assigned by management to 18 other products, replacing the previous selection for an ABC analysis using sales as main criteria, thereby considering and characterizing products in a financial importance distribution. The sample of series examined should then include all kind of behaviors, in order to project the benefits in a wider range of products. Combinations of 6 products was made for each category, namely A, B and C. In each level two sub-groups were decomposed into “stable” and “unstable” sales for A and B products, and “parasite” and “slow movers” to C products. It is quite intuitive to understand that “sales stability” in C products does not affect inventory planning. On the other hand it is quite important to correctly understand parasite products behavior. Parasite products are defined as products that are not economically interesting to the company but play a high role in marketing and products benchmarking, by completing ranges. Data Collection Data was gathered and provided by the company, in a weekly basis, for every product life. Such a disaggregated data gave the possibility to make considerable analysis, successfully evaluating the best aggregation level, according with the most accurate forecast model, thereby, weekly, monthly and tertile aggregated data were submitted to the forecasting model. Numerous variations of the original data have been proposed. However tertile aggregation was recommended as an alternative for the quarterly evaluation, as products clearly denote 3 different seasons along the year and also due to the considerable amount of suppliers with 4 months lead time. Integrated Forecasting and Inventory Management in a Wholesale Company 30 Commonly used in retail, a 4-5-4 Calendar was used to aggregate the monthly data, allowing a more consistent month flow, providing the same number of weekends for each month. Tertile aggregation on the other hand was divided in a 17-17-18 weeks respectively, essentially owing to the (statistical non-important) last week sale of the year. Looking back this could sound odd but observations presented average sales of 9% compared with the weekly sales in the same month, in other words, an expected 2.25% increase on overall tertile sale. Further research involving management suggests that this can be supported by the existence of national holidays and Christmas time, decreasing labor days and general work in the warehouse. 4.2 Forecasting methods Although there are several models underlying exponential smoothing, we proposed the ones that could eventually achieve better results according to the following studies. Gardner & Anderson, (1997) and E. Gardner, (2001) bend their study in a cookware company manufacturer, comparing focus forecasting to damped-trend, seasonal exponential smoothing, and conclude that exponential smoothing proved to be more accurate, thereby, relating the equivalent situation, is worth emphasizing our study in the DA-M method. A standard autocorrelation test was programmed, conducting to non-seasonal times series identification. This procedure ensured the correct use of the non-seasonal version of the damped-trend model for time-series that showed to be non-seasonal. Equation 2DA-M Exponential Smoothing Method (Source: Gardner, 2006) Equation 3DA-N Exponential Smoothing Model (Source: Gardner, 2006) Integrated Forecasting and Inventory Management in a Wholesale Company 31 To avoid fitting a model that handles trend and/or seasonality, and yet increasing variance, the N-N method was suggested for reasons of robustness as a naïve method. Initial values and loss functions Within each time series one of several alternatives for initial values and loss functions mentioned in the state of art chapter was used. Although it seems an unreasonable alternative “Zero Values” was chosen as it provides an advantage in terms of large initial error which force the estimated values to approach the actual ones much faster than alternative initialization procedures (Makridakis & Hibon, 1991). S1=Least Square estimate T1=0 The error using the two-step-ahead forecast was measured, and smoothing parameters alpha, beta, gamma and theta were chosen as to minimize the Mean Square Error (MSE): Further along, forecast comparisons for the time series are summarized. Performance evaluation began with each level of time series aggregation comparisons divided in three groups (weekly, monthly an tertile aggregation), selecting the procedure with the lowest value. Following the same reasoning, the selected methods were compared, and the one revealing the best accuracy was chosen. Equation 4N-N Exponential Smoothing (Source: Gardner, 2006) Equation 5Zero Values Formula (Source: Makridakis & Hibon, 2006) Equation 6MSE Formula Integrated Forecasting and Inventory Management in a Wholesale Company 32 The measure of equivalent levels of aggregation accuracy was defined by the MSE, therefore penalizing the errors with bigger magnitude. On the other hand, and due to the inappropriate application of the MSE in values with different degrees, the MAPE was chosen as reference for different level of aggregation comparisons. 4.3 Safety Stock The proposed safety stock policy is based in the concept that the business runs with a stochastic demand and lead-time, thus a model that allows the incorporation of demand and lead time variability as follows is indicated. As abovementioned, Zinn & Marmorstein (1990) applied the same formula but, unlike the standard approach, they recommended the use of forecasted error in variance calculation. This procedure will be applied, and further along, the improvements with such a technique will be presented. This approach is easily generalized and simplified by assuming the normal distribution of the errors and, in fact, such assumption is reasonable to be taken once the required tests to the expected value and the correlation between errors procedures were both consistent (Almada Lobo, 2011b). Equation 7Safety Stock Formula (Source: Talluri, 2004) Equation 8Test to the Expected Value (Source: Lobo, 2011) Integrated Forecasting and Inventory Management in a Wholesale Company 33 Despite this normal distribution assumption, further research showed that we are still in the presence of bias, and that this forecasting bias directly affects safety stock level. In fact, forecasts revealing an over forecasting tendency required a SS level superior than the maximum under forecast value that SKU had ever experienced. The following picture helps understanding this case scenario, where a Normal (0,1,000) and a Normal (1,000, 1,000) distribution are set to a service level of 95%.(Manary & Willems, 2008) The picture clearly validates our theory, reinforcing the need to statistically eliminate the bias; for a 95% service level, a Normal (0, 1,000) cumulative distribution function corresponds to - 1,645 factor, while for a Normal (1,000, 1,000) this value is found to be -.645. Therefore, and to eliminate the bias with a feasible process, a new and modified estimate of the standard deviation of the forecast error was calculated according to Manary (2008). Figure 5Normal(0, 1,000) and Normal(1,000 , 1,000) Distribution Graphic (Source: Manary & Willems, 2008) Equation 9Autocorrelation Coefficient of The Error (Source: Lobo, 2011) Equation 10Modified Standard Deviation Formula (Source: Manary, 2008) Integrated Forecasting and Inventory Management in a Wholesale Company 40 Table 9Multi-Criteria ABC Products Resume Sales Deviation Product 1º Tertile 2ºTertile Average ABS Average EPAM F/Model Stock Variation Abs Err Service Level A -34% 8% -13% 21% 24% 4% 13% 100% B -104% -1% -52% 52% 14% -2% 52% 100% C -40% 5% -18% 23% 17% -25% 18% 100% Average -8% 28% 100% Figure 8Product A Chart Figure 9Product B Chart Integrated Forecasting and Inventory Management in a Wholesale Company 41 Despite the more or less close values of sales deviation and the model sample EPAM, the stock variation does not attain great results, with a overall 8% decrease and an increase of 4% in the average stock of product A, suggesting that the model improvements were not so obvious and worth of implementation. However, a deeper analysis and detailed review of stock behavior, SS, s and demand values shown in figures 8, 9 and 10 can contribute to a very consistent explanation of this low improvement. In fact, Figure 8 shows that product A requires a safety stock clearly higher than the demand for both periods. This will naturally result in very high average stock. But why is this SS level higher than the demand for the period, if the average deviation of forecast vs. demand is 24%? The explanation relies on the standard deviation value, which is the only that varies between articles. This could be quite confusing, since if we had a low EPAM, this would theoretically drive us to the idea that the errors were low, and thereby, the standard deviation and the SS (Safety stock) would be also low. However, when presenting a product that is in the descendent part of his life cycle, considering all the time series for standard deviation calculation will significantly increase the SS required. Though the percentage error is the same, the order of magnitude is quite superior. This is the case of products A and B and it has been possible to marginally decrease the average stock of product B and as abovementioned, increase in only 4% product A average stock, what gives us good perspectives if we consider to correct the calculation of the standard deviation. A second implication undermining the model is the fact that low rotation products require only 1 or maximum 2 replenishment orders a year, very much conditioned by the MOQ, therefore decreasing the potential improvement. Although we have reasons to believe that in high rotation products, our improvement will be higher than 8%. Figure 10Product C Chart Integrated Forecasting and Inventory Management in a Wholesale Company 42 5.3 Management Products Following the same reasoning as for the Multi-Criteria ABC products, the 18 management products were submitted to test. As these products come from random suppliers, adjustments had to be made. In order to estimate the order planning, for all given SKU it has been assumed that the placed order can full a container, therefore, for a major or small supplier, the combination of products can always meet a feasible order. Table 10 presents the results for management chosen products (where the red rows are not considered to stock variation improvements due to article sold out, and yellow rows are also not considered due to data unavailability by the company). Table 10Management Products Resume The forecasting potential, as opposed to the previous test, produced great impact in average stock level. The comparison between the “order planning” and actual data results from January 2012 to August 2012, confirmed our previous correlation between high rotation products and the potential of the program. Sales Deviation Art 1º Tertile 2º Tertile Average ABS Aver. EPAM F/ Model Stock Variation Abs Err Aver. Error Servic e Level A Stable 1 9% -29% -10% 19% 24% -55% 10% 18% 100% 2 36% 17% 27% 27% 14% - 27% 92% 3 34% 4% 19% 19% 17% - 19% 87% A Unstable 4 43% 51% 47% 47% 10% - 47% 33% 62% 5 -121% 41% -40% 81% 16% - 40% 100% 6 -26% 3% -12% 14% 46% - 12% 100% B Stable 7 -22% 4% -9% 13% 9% -36% 9% 15% 100% 8 -2% 24% 11% 13% 13% -32% 11% 100% 9 14% 33% 24% 24% 20% -39% 24% 100% B Unstable 10 30% 53% 41% 41% 27% -64% 41% 27% 100% 11 -17% -13% -15% 15% 20% -59% 15% 100% 12 17% 32% 24% 24% 31% -43% 24% 100% C Parasite 13 -29% 49% 10% 39% 28% -55% 10% 62% 100% 14 -38% -87% -62% 62% 34% -94% 62% 100% 15 -255% 28% -113% 142% 14% 56% 113% 100% C Slow 16 -27% -2% -14% 14% 26% 15% 14% 45% 100% 17 -90% -71% -80% 80% 44% -72% 80% 100% 18 6% -85% -40% 46% 26% -84% 40% 100% Average -43% 33% 97% Integrated Forecasting and Inventory Management in a Wholesale Company 43 The overall data contributed for a 43% average decrease in the average stock, along with a 97% of service level. Compelling evidence led us to recommend this model as it outperforms the current one. However, some inefficiencies must be considered as subject of deeper study. Considerable inefficiency was observed in articles 2, 3 and 4, underlying service level, and articles 15 and 16 regarding stock variation, therefore a review can conveniently evidence any problems arising from this model. The development of the model was adjusted and there was no considerable suspicious that this inefficiency could come from some error of the process, even though a complete review of all processes was made and proved there was no evidence of such a hypothesis. The link between some of these errors was discovered after a meeting with the management, and each case was properly investigated. The most alarming article is no. 4, an A sales article, with a availability of only 67% during the first 2 tertile. The first impression was that the accuracy of the method performed badly. The truth, however, was far from any statistical method. Management examination indicated that for the first two years this article was produced by an Asian supplier, which together with business relation problems had successive delays in deliveries and quality problems. In 2012, a new supplier was assigned to this article boosting the sales of the product. This fact explains the inaccurate forecasting. The service level of Article 2, is not as severe as article’s 4, and presents no evidence of abnormal situation during the year, therefore was considered part of the variability of the series and the statistical hypothesis of missing the forecast. Article 3 is an article with an exponential sales growth, which caused some out of stock problems in the past 2 years. In the beginning of 2012 a bigger order has arrived, for it was perceived by the company that more quantity was needed to fulfill the market need. The stored data however only relates to actual sales, and this practice misleads the general model. Nevertheless, the model uses actual sales rather then “actual sales + missed sales due to out of stock”, which caused the model to under forecast. Article 16, follows the same reasoning as multi-criteria ABC products, as the accuracy of the forecasting is according to the model, which leaves us with the supposition that the safety stock is higher than expected due to the life-cycle of the product. Further observations confirmed this theory. Despite the generalized 100% service level, each product could incur in delays in the leadtime, which are not taken into account in this study. It is advisable to evaluate the model robustness to handle these possible delays and quantify these delays feasible range in order to keep such a service level. Table 11 shows us the remaining weeks of stock for each product, (assuming a constant demand in each tertile calculated by actual sales in the tertile divided by the number of weeks). Beyond the already mentioned articles 2, 3 and 4, which in fact sold out during the periods, we should be award that articles 8 and 9 appear to be in a particularly fragile situation that can quickly fall into a default situation at the end of the second tertile. Integrated Forecasting and Inventory Management in a Wholesale Company 44 It must be noted that it was already expected that the average stock in the second tertile would be smaller than in the first one, due to the fact that SS is made as a provision for a 2 period lead time. Therefore, the consumption is theoretically made gradually along the 2 periods. The display of every product evolution in terms of stock, replenishments, s, SS, and demand values along the first two tertile of 2012 is showed in ANEXO A. Table 11Management Products Stock Left Product Service Level Stock Left (Weeks) 1ºTertile Stock Left (Weeks) 2ºTertile A Stable 1 100% 8.0 23.3 2 92% 0.0 0.0 3 87% 0.0 0.0 A Unstable 4 62% 0.0 0.0 5 100% 32.2 15.1 6 100% 20.9 23.0 B Stable 7 100% 8.6 9.0 8 100% 8.0 2.3 9 100% 6.7 0.8 B Unstable 10 100% 12.9 2.9 11 100% 12.2 16.6 12 100% 5.5 8.5 C Parasite 13 100% 103.0 14.4 14 100% 59.7 42.4 15 100% 67.3 15.7 C Slow 16 100% 26.4 18.4 17 100% 77.8 32.6 18 100% 14.1 26.8 Average 97% 25.7 14.0 Integrated Forecasting and Inventory Management in a Wholesale Company 45 Integrated Forecasting and Inventory Management in a Wholesale Company 46 6 Conclusions and future work perspectives This study corroborates empirical studies conclusions, providing opportunities of improvement by the use of exponential smoothing forecasting methods and inventory management policies. The first test points out the need of continuously reviewing the time series and suggests a future discussion to conclude about the extension of data to use in the analysis in order to reduce the SS level. It is important to understand the consequences of the life cycle of the product and the effect that it can produce in the method. It is believed that a 3-year database is wide enough to avoid this effect and to still have a trustful method. All the calculations were conservative, according to a 95% service level, whether for A, B or C products. The stock level could decrease even more, if a service level of 95% for A, 85% for B and 75% for C products was considered (by standards). Despite the robustness of the procedure the human factor was found to be important to prevent cases such as article 4, therefore correcting information’s that the system cannot handle. On the same basis, the implementation of a “expected sales” data is recommended, to complement “actual sales” database and ticking the point in the period where the sales started to be restricted due to low stock. This will perform a more reliable and accurate forecasting. For each supplier, the method follows fixed points of review. In particular, the system considers the ordering in 3 production seasons. A more conservative approach should be considered in future works, projecting different review points with the same interval and avoiding peaks in the factories. Comparisons were made using different suppliers, but never regarding all the products. It is reasonable to accept the fact that big suppliers demand can require more than one container in each order. Therefore, a future analysis should consider planning rules where the total order should be divided in two or more sub orders along the period, according with the total volume and MOQ constraints. A significant improvement can be attained in the average stock by this approach, while giving the opportunity to correct under or over forecasting. The collection and storage of lead-time data for each supplier is also a suggestion for a more reliable safety stock level. Finally, it would be interesting, in products with clear and deep seasonality, to explore the possibility of 2 or 3 different safety stock levels along the year. Integrated Forecasting and Inventory Management in a Wholesale Company 47 Integrated Forecasting and Inventory Management in a Wholesale Company 48 References Almada Lobo, B. (2011a). Apresentação MQAD. Diapositivos da disciplina MQAD, FEUP Almada Lobo, B. (2011b). Análise de Erros, (2011), 1–19. Diapositivos da disciplina MQAD, FEUP Brown, R. (1963). Smoothing, forecasting and prediction of discrete time series. Englewood Cliffs N.J.: Prentice-Hall. 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