METHODOLOGICAL CONSIDERATIONS ON SPARE PARTS INVENTORY MANAGEMENT: A CASE STUDY

A typical consumer goods manufacturing company tends to keep between US$ 5 million and US$ 15 million in spare parts, at an annual opportunity cost that ranges from 20% to 40% of the value in stock (SANDVIG and ALLAIRE, 1998). In general, there is a consensus that spare parts inventories cannot be managed by traditional models or methods, since the conditions for their application are not met: sporadic consumption pattern (that is, it is irregular and small), long resupply response times and high acquisition costs (BOTTER and FORTUIN, 2000). Even so, the basic questions of inventory management still remain to be answered: which items should be stocked and how much of each item should be kept in stock.

Spare parts management can also be understood from the perspective of customer service, and not just from the financial and/or logistical aspect. For many companies facing a tougher competitive environment, customer satisfaction is crucial (FIGUEIREDO et al., 2003). A very common means of keeping customers satisfied is after-sales assistance, through the rapid repair of defective products and systems. To do this, a sufficient amount of spare parts must be kept in stock to meet certain levels of customer service. Customer service can normally be measured in terms of product availability, such as the probability indicators of not running out of stock and fill rate (SILVER and PETERSON, 1985 and WANKE, 2003), and in terms of delivery time.

Under the prism of materials management, spare parts can be divided into two main categories: repairable items or consumable or disposable items (BOTTER and FORTUIN, 2000). Repairable items include replacement parts that are technically and economically recoverable. In the event of failure, the old part is replaced with a new part and sent to a repair center, which is subsequently made available in stock. Consumable items correspond to parts that are not technically or economically recoverable. In case of failure, the old part is simply discarded. In the first case, the possibility of recovering an item has implications for inventory management, since, in general terms, quantities in the process of reconditioning must be deducted from future resupply (SHERBROOKE, 1967 and KIM et al., 1996) .

This article is based on a case study (YIN, 1994). It presents methodological considerations on how to determine inventory management for different spare parts in terms of their main characteristics (WILLIAMS, 1984): average consumption and coefficient of variation of consumption, that is, the ratio between its standard deviation and its average. Considerations are also made on how to operationalize the segmentation based on an inventory management model currently in progress and on how to estimate potential gains in terms of service level, inventory reduction and reduction in forecast errors. More specifically, the solution developed using the MS-EXCEL spreadsheet and the SPSS statistical package for consumable items of a company that manufactures agricultural equipment and implements located in Brazil is described. For obvious reasons, information sensitive to the company, its position in the industry and its operations will be withheld or disguised.

LITERATURE REVIEW

Inventory management has received substantial attention from academic and business circles in recent years. Most of the literature is focused on determining, establishing or applying methods to replenish inventories in production and distribution environments (BOTTER and FORTUIN, 2000). In these environments, demand and response time tend to be predicted with a greater degree of certainty, and the vast majority of models used allow adequate decisions to be made about how much to keep in stock for each item or product (see, for example, SILVER et al., 1998). In this article, the analyzed inventory management decision-making takes place in a totally different environment, that is, the resupply of spare parts. In this environment, companies and managers face a more complex problem: replacement parts are expensive, demand is erratic and difficult to predict, response times are long and stochastic, and customers want to receive replacement parts quickly.

In this way, the literature on the resupply of spare parts tends to be scarcer (BOTTER and FORTUIN, 2000) and the developments in the last ten years present several approaches to the problem, such as the determination of the last order (HILL et al., 1999), the determination of the optimal revision interval (SHIBUYA et al., 1998) and the determination of inventory policies based on the criticality of the items (DEKKER et al., 1998). More specifically, the development of the literature review was directed towards understanding realistic approaches, previously tested in companies, such as Yeh (1997), Robison (2001), Sandivg and Allaire (1998) and those of Botter and Fortuin themselves ( 2000); Purely theoretical and hypothetical approaches by nature were disregarded, with emphasis on their practical applicability.

Yeh (1997) adopted the premise of the Gamma distribution of demand to determine the resupply points in a medium-sized company, manufacturer of electronic products, located in Taiwan. Because more than half of the 10.000 items are consumed less than 10 times a year, the Normal distribution assumption was initially discarded. The Poisson distribution, also widely used in practice (cf. SHERBROOKE, 1967 and WANKE, 2003) and proposed as an alternative to the Normal distribution for low consumption items, was also discarded. According to Yeh (1997), the applicability of the Poisson distribution premise depends on the ratio between the variance and the average demand, which must be between the limits of 0,9 and 1,1.

Robison (2001) developed a technique to analyze, considering 15.000 items simultaneously, stock levels and predict the level of customer service. Conversely, given a given level of service, the technique allows calculating the necessary stock levels in an environment where items are kept in stock. More specifically, through methods such as Linear Regression Analysis, Robison (2001) determined equations that relate inventory levels and service levels with coefficients of determination (R2) around 0,70.

Sandvig and Allaire (1998) developed a MS-Excel spreadsheet model to show how inventory management responded, in terms of service level, under different demand scenarios. Based on actual consumption data for thousands of spare parts in a US company, the authors determined that lower service levels resulted from the interaction of high demand variability with long response times. Actions were taken to reduce stock levels based on changes in the systematic ordering by customers.

Botter and Fortuin (2000) segmented 50.000 spare parts into levels of decreasing importance for consumption, response time, price and criticality of each item, with the subsequent determination of these average parameters for each group. Service levels were calculated for segments based on these average parameters, considering alternative resupply situations from a regional distribution center or a local warehouse. Gains in terms of reducing inventory levels and increasing service levels were estimated for each segment.

The brief description of these four practical approaches applied to spare parts management allows inferring some methodological aspects about how companies and managers are directing the determination of stock levels:

• The approximation of consumption data by Gamma distribution to calculate points or levels of replacement of stocks (YEH, 1997);

• The use of multivariate statistical analysis techniques to relate stock levels to service level measures, such as, for example, the Fill Rate (ROBISON, 2001);

• The use of real consumption data to test the proposed inventory policies (SANDVIG and ALLAIRE, 1998) in terms of service level;

• The segmentation of spare parts based on different criteria and the use of their average values ​​to represent the segments in the calculation of estimates on service level gains and reductions in stock levels (BOTTER and FORTUIN, 2000).

THE COMPANY AND THE CURRENT POLICY INVENTORY MANAGEMENT

The company is one of the largest multinational manufacturers of agricultural equipment and implements installed in Brazil. To support technical assistance and after-sales service for its equipment, the company maintains 20.833 different types of items centralized in its factory warehouse, totaling an amount of capital tied up in stock in the order of 20 million dollars. There are approximately 1.000.000 units in stock, which makes an average unit value of $20.

Currently, the company decides to replenish stocks based on consumption forecasts for the coming months. All spare parts are produced in-house and spare parts production scheduling cycles follow a one-month horizon. In general terms, it can be said that the response time for making an order for spare parts available has an average of one month and a standard deviation of zero.

According to Table 1, the average annualized consumption per item (D_YR) is almost 63 units and its standard deviation is 422 units. Annualized consumption per item (based on the last 36 months) ranges from a minimum of 0,30 to a maximum of 29.756 units, denoting great dispersion and asymmetry of the data for values ​​below the average. The average coefficient of variation of monthly consumption (CV) is approximately 2,8 and the average monthly forecast error in absolute values ​​(MAD) per item is 4,1. The standard deviation of the mean absolute forecast error is 24 units per month.

According to Table 2, half of the items (median) present annualized consumption (D_YR) less than or equal to 5,70 units. Regarding the average coefficient of variation of monthly consumption (CV), half of the items (median) have a ratio between standard deviation and average monthly consumption greater than 2,4. These data denote the basic characteristics involved in the management of spare parts inventories: small and irregular consumption, with a high standard deviation of forecast errors, implying high inventory levels in relation to average consumption.

The company measures the level of service offered to its customers through Fill Rate indicators for each ordered item. For example, for a certain item, if the initially requested quantity was 100 units and there were only 80 units available in stock, the Fill Rate is calculated as 80%. As indicated in Table 3, in the last 36 months, the average Fill Rate for all the company's items was 80,28%, with 50% of the items having a Fill Rate lower than 83,30%. A quarter of the items had a Fill Rate greater than 91,70%, probably denoting an excess of items in stock.

According to Table 3, regarding spare parts stock levels, there are on average 52,4 units for each item in stock. 25% of items have more than 27 units in stock, with a maximum inventory of 9.810 units. Another 25% of items have less than two units in stock, with a minimum stock of zero. These data, when compared to Table 1, denote an average coverage of almost 10 months of consumption in stock.

The company is currently restructuring its spare parts inventory management. Its main objective is to determine more accurate consumption forecasts for each item as a means of simultaneously reducing inventory levels, as well as balancing the average Fill Rate levels for different items, reducing their dispersion.

Methodology Used

Based on the literature review, the methodology used to redefine spare parts inventory management consisted of the steps described below. Initially, inventory replacement levels were determined based on the Gamma distribution of monthly demand. The Gamma distribution is defined by two parameters (YEH, 1997), the first being the ratio between average consumption and the consumption variation coefficient and the second parameter, the consumption variation coefficient itself.

For each item, these replenishment levels were first determined for different levels of probability of not running out of stock (10%, 20%, 30%, 40%, 50%, 60%, 70%, 75%, 80%, 85%, 90%, 95% and 99%) and secondarily used as probabilistic consumption forecasts. These probabilistic forecasts of consumption were compared with the actual data for each item for the last 36 months, calculating item by item the mean absolute forecast error (MAD), the Fill Rate and the stock level.

Through multivariate analysis techniques, it was possible to relate the annual consumption and the coefficient of variation of the monthly consumption of each item to the variations in MAD, Fill Rate and stock level, resulting from the comparison between the model currently adopted by the company and the proposed models . It was also possible to relate, for each item, the consumption forecast model with the lowest error to annual consumption and the coefficient of variation of monthly consumption.

Results Analysis

The probabilistic consumption forecasts generated from the Gamma distribution resulted in the reduction of the mean absolute forecast error (MAD) to 8.893 items. The model used by the company (MCOMPANY) showed the lowest forecast error for 11.940 analyzed items (57,3% of the total). Table 4 presents the frequency distribution of the consumption forecast models that presented the lowest MAD for the considered horizon of 36 months. The medians of the annual consumption (D_YR) and the coefficient of variation of the monthly consumption (CV) of each model are also presented.

 

 

A Multinomial Logistic Regression Analysis was conducted with the 8.893 items, for which there was a reduction in the forecast error, with the objective of simultaneously quantifying and relating the values ​​of annual consumption (D_YR) and the coefficient of variation of monthly consumption (CV) for each model. Although the medians shown in Table 4 provide a measure of central tendency for D_YR and CV, their joint use may not be representative of most items in each model. The regression results are presented in Table 5, with the Gamma 99% model constituting the reference category. The regression is significant at the 0,001 level and explains almost 32% of the variation in the association of a given model with a given pair of D_YR and CV values. The coefficient of variation does not discriminate all models simultaneously, being significant at 0,05 for the Gamma 10%, Gamma 85%, Gamma 90% and Gamma 95% models. Annual consumption also does not discriminate all models simultaneously, being significant at 0,01 for all models except for the 95% range.

 

Based on the results in Table 5, an analysis with a cutoff point equal to 50% was conducted to determine some points of indifference (pairs of D_YR and CV values) between each of the analyzed models and the reference category. These results are shown in Table 6 and illustrate the relationship between annual consumption and the monthly coefficient of variation for different probabilistic forecasting models. Through the order of magnitude of their values, it is possible to assess the impact of any distortions compared to the medians shown in Table 4.

 

According to Table 6, it is possible to infer some conclusions:

• The 10% Range model is associated with items with the highest consumption scale, with a direct relationship between consumption and coefficient of variation.
• The models from Range 20% to Range 70% are associated with items with annual consumption below 200 and monthly coefficient of variation below 2, with an inverse relationship between consumption and coefficient of variation.
• The Gamma 75% to 95% models are associated with items with annual consumption greater than 100 units and a monthly coefficient of variation greater than 3, with a direct relationship between consumption and coefficient of variation.

Comparing the results of Tables 4 and 6, the risks of distortions are illustrated when measures of central tendency are considered to represent the items associated with each inventory management model. These distortions become more evident in the discussion that follows, with the determination of estimates to evaluate the reduction in absolute forecast errors, the increase in Fill Rate levels and the reduction in inventory levels.

In order to determine the simultaneous relationship between the reduction of absolute forecast errors, annual consumption and the coefficient of variation of monthly consumption, a Multiple Linear Regression Analysis was conducted with these 8.893 items. The D_YR and CV variables were standardized with the aim of mitigating possible multicollinearity effects and allowing quantification of their relative impact on MAD reduction. The regression results are shown in Table 7. The analysis is significant at the 0,0001 level and explains almost 50% of the variance in forecast error reduction from D_YR_STD and CV_STD (standardized). The coefficient of variation is not significant at the 0,10 level. Consumption is significant at a level of less than 0,001 and has a relative impact almost 70 times greater than the coefficient of variation in reducing the MAD. The greater the annual consumption, the greater the reduction in absolute forecast error.

 

Table 8 presents the expected reductions in the absolute forecast errors from the application of the results presented in Table 7 to the data in Table 6. It is possible to infer some conclusions about the behavior of the reduction of the absolute forecast error for the analyzed models. First, substantial reductions in forecast errors are concentrated in the Gamma 10%, Gamma 85%, Gamma 90% and Gamma 95% models, mainly because these models concentrate a greater number of items with higher annual consumption. Secondly, an eventual strategy for implementing the new consumption forecasts should take into account their sequence, aiming at greater efficiency in production scheduling due to greater precision in the estimates for each item.

Also for these 8.893 items, a Multiple Linear Regression Analysis was conducted with the objective of determining the simultaneous relationship between the Fill Rate variation and the annual consumption and the coefficient of variation of the monthly consumption, both standardized. The regression results are presented in Table 9. The analysis is significant at the 0,001 level and explains almost 14% of the variation in Fill Rate from D_YR_STD and CV_STD (standardized). Both the coefficient of variation and the annual consumption are significant at 0,001, with the former having a relative impact almost 5 times greater than the latter. The signs of the coefficients denote that the greater the coefficient of variation, the smaller the positive impact on the Fill Rate resulting from forecasts with less error and the greater the consumption, the greater the positive impact on the Fill Rate. In other words, in the 8.893 items for which the probabilistic forecast implied a reduction in the MAD, increases in the Fill Rate tend to be verified the higher the annual consumption and the lower the coefficient of variation of the monthly consumption. On the other hand, reductions in the Fill Rate can be attributed to higher coefficients of variation and lower levels of annual consumption.

Table 10 presents the expected variations in the Fill Rate, in percentage points, based on the application of the results presented in Table 9 to the data in Table 6. It can be seen that the main opportunities for obtaining substantial increases in the Fill Rate are concentrated in the Gamma 10% and Gamma 95% models, especially in the items with the highest coefficient of variation and consumption. It should be remembered that in these models the items present a direct relationship between these two variables. More modest increases in the Fill Rate are concentrated in the models from Range 20% to Range 70%, for which the items have an inverse relationship between consumption and coefficient of variation. Finally, reductions in Fill Rate are concentrated in models from Gamma 75% to Gamma 90%. Items under these models present a direct relationship between consumption and coefficient of variation, however, the coefficient of variation presents a greater marginal contribution to the reduction of the Fill Rate than the consumption to increase it.

In order to determine the simultaneous relationship between the reduction of stock levels, annual consumption and the coefficient of variation of monthly consumption, a Multiple Linear Regression Analysis was also conducted for these 8.893 items. The regression results are presented in Table 11. The analysis is significant at the 0,001 level and explains almost 10% of the variation in the reduction of inventory levels, when a model other than the company's is adopted. Both the coefficient of variation of monthly consumption and annual consumption were standardized and are significant at the 0,001 level. Consumption has a relative impact almost six times greater than the coefficient of variation in reducing inventory levels. The signs of the coefficients denote that the higher the consumption and the coefficient of variation, the greater the positive impact on the reduction of stock levels resulting from forecasts with lesser error. In other words, reductions in inventory levels tend to be verified the greater the annual consumption and the coefficient of variation of monthly consumption. On the other hand, lower reductions in stock levels can be attributed to lower coefficients of variation and low levels of annual consumption.

Table 12 shows the expected reductions in stock levels based on applying the results shown in Table 11 to the data in Table 6. Substantial reductions in stock levels are mainly concentrated in items associated with the 10% Range model, but are also verified with less intensity in the items associated with the Range 80% to Range 95% models. In these models, the items present a direct relationship between annual consumption and coefficient of variation of consumption. In the 20% Range to 75% Range models, the items have an inverse relationship between consumption and coefficient of variation, and reductions in stock levels are not verified for low consumption items with a high coefficient of variation. Overall, there is potential to reduce inventory levels across all models.

 

Finally, Table 13 compares, for each of the models (Gamma 10%, Gamma 20%, etc.), the actual and predicted values ​​for the reduction in the absolute forecast error, the variation in the Fill Rate and the reduction in the stock level . In general, the regression analyzes presented in Tables 7, 9 and 11 have good aggregate predictive capacity on the expected behavior of these indicators when probabilistic forecast models are adopted instead of the forecast model used by the company. It should be noted that for more than 2/3 of two items (Gamma 10% model) conservative estimates are made for the reduction in stock levels, the error and the increase in the Fill Rate. These results are complementary to the analyzes presented in Table 5, which probabilistically indicates the level of association of a given spare part (represented by the annual consumption and the coefficient of variation of the monthly consumption) to a given model.

 

 

Discussion of Results

The presented results represent advances in the theoretical and practical aspects of spare parts inventory management. The theoretical implications are related to the joint application, in a manufacturer of Brazilian agricultural equipment and implements, of four practical approaches recently reported in the literature: (1) approximation of consumption data by the Gamma distribution, (2) use of multivariate statistical techniques for estimating of variations in key inventory management indicators, (3) use of real consumption data to test proposed alternative models and (4) segmentation of inventory policies based on the main characteristics of spare parts. In turn, the practical implications are related to the estimated earnings for the analyzed company and the ease of replicating the analyzes presented in the management environment.

Specifically with regard to theoretical progress, the good explanatory and predictive capacity of the analyzes developed to segment inventory management models and estimate variations in indicators such as MAD, Fill Rate and inventory levels, based on annual consumption and the coefficient of variation of monthly consumption, allows to formalize a methodology for the management of stocks of spare parts, consisting of 10 steps, as described in Table 14.

With regard to earnings for the analyzed company, the results point to a potential reduction of 14 million dollars (approximately 70%) in the amount of capital tied up in stock. This sum was obtained considering the product of the average value of each item in stock (20 dollars) with the verified average reduction of 79,46 units for each of the 8.893 items considered in the analysis (cf. Table 13). Considering the average coverage of inventories (cf. Tables 1 and 3), it is expected that 50% of this potential will be converted into working capital at the end of 10 months.

Finally, with regard to the managerial means, the described methodology can be easily implemented and operated in MS-Excel spreadsheet and SPSS statistical software, specifically necessary for the execution of Step 8. Based on the average annual consumption and the coefficient of variation of monthly consumption For a given item, this methodology allows you to answer the following questions: (1) “Which model is more likely to present a lower forecast error?”, (2) “What are the expected variations in terms of the mean absolute forecast error, from Fill Rate and inventory level when adopting this model?”.

CONCLUSION

This article reports a case study developed in a Brazilian manufacturer of agricultural equipment and implements, in which recent approaches to spare parts management are used together. The good predictive and explanatory capacity of the developed multivariate analyzes allowed the proposition of a new methodology to determine more accurate inventory management models and quantify variations in forecast errors, service levels and inventory levels. Among other elements, the methodology is based on the premise of the Gamma distribution of spare parts consumption and on the segmentation of the models by their main characteristics: average consumption and consumption variation coefficient.

Future studies should consider in multivariate analyzes the interaction of average annual consumption with the coefficient of variation of monthly consumption. The joint effect of these two variables can increase the predictive and explanatory capacity of the analyzes carried out, given that items with higher consumption tend to have lower coefficients of variation and vice versa.

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