STOCK MAPS APPLIED TO SPARE PARTS MANAGEMENT - PART 2

As pointed out in the first part of this article1, strategic inventory management is gaining increasing importance in supply chain management. Research carried out by ILOS2 reveals the importance of inventory costs for Brazilian companies. Out of total logistics costs, inventories account for 26%, a percentage that is only smaller than transportation costs.
The same survey also reveals that logistics costs represent 11,6% of the national Gross Domestic Product, of which 3,5% are related to inventories.
Specifically, key decisions to be made in inventory management – ​​how much to order, when to order, how much to keep in safety stock, where to locate inventories, and how to control the system – can be aided by applying inventory mapping concepts.
Based on these concepts, simple-to-use tools were developed, in Ms Excel/VBA, to assist the decision maker. These tools will be discussed in this part of the article. In addition, a case study was carried out for a company in the agribusiness sector.

DECISION SUPPORT SYSTEMS

Seeking greater ease in inventory management, three simple-to-use tools were developed, in Ms Excel, to support decision-making.

The first one, the Stock Planning tool, aims to plan the amount of stock of spare parts needed to meet a level of service desired by the decision maker. After entering the data in the worksheet, the spare parts are classified into very low-speed, low-speed and high-speed parts, as explained in section 2. The tool inputs are shown in Table 4.

The tool presents as outputs the stock level and the investment required to maintain this quantity in stock, as well as the associated opportunity cost. This is done for three levels of service: 90%, 95% and 98% in the case of mass consumption and low-turnover parts.

It should be noted that, for very low turnover items, the mentioned outputs are calculated only when the option is made to keep the items in stock. This decision is taken from the comparison between the CT(0) and CT(1) costs, also calculated by the spreadsheet.

the second tool
– Lumpy Demand – is an alternative to the Stock Planning tool for managing slow-moving parts with fluctuating demand, whose main objective is to calculate the reorder point.

The inputs are: item code, demand history and lead-time. As outputs, the stock level (Q batch), the shortage fraction and the reorder point are provided, in addition to the parameters of the Stuttering Poisson3 distribution.

Using the Stuttering Poisson distribution is an alternative for erratic items. It is the result of combining the geometric and Poisson distributions. This happens when order arrival is represented by λ (Poisson parameter) and the order lot size is represented by ρ
(geometric parameter).

Through the use of this distribution, tabulated probabilities allow the determination of the order point through linear regression.
It is important to emphasize that the use of Lumpy Demand can only be done when the main constraint is met – the average quantity ordered must be positive and less than one (0≤ρ≤1). Otherwise, the Stock Planning tool must be used. The classification of items, as well as the stock map, were presented in section 2.4.

The third tool was developed based on Silva's master's thesis (2009). Like Lumpy Demand, this tool is an alternative for slow-moving items, which show great variability in demand patterns. It is based on demand during the lead-time.

The author assumes adherence of demand during lead-time (DLT) to the La Place and Gama distributions. The first is not only indicated for slow-moving items, but an alternative to Normal for fast-moving items when there is more propagation in the tails, moving away from the Normal distribution profile (Silva, 2009). The use of the Gamma distribution is suggested by Silver, Pyke and Peterson (1998) in situations in which the demand distribution is inclined to the right or when the coefficient of variation (σL/DL) is greater than 0,5.

The differential of this tool lies in the methodology used to estimate demand during lead-time (LTD). Data are generated by the modified bootstrap method, presented by Willemain, Smart and Schwarz (2004), as cited by Silva (2009). In this method, a sequence of null and non-null values ​​is generated for the entire forecast horizon.

The inputs of the third tool are the same used by Stock Planning and presented in Table 5, with the exception of the annual interest rate. As outputs, the reorder point, the Q lot and the fi ll-rate, in addition to the total cost of inventory, are provided.

APPLICATION OF TOOLS

Motivated by the strategic importance of inventory management, a case study was carried out for a manufacturer of equipment for the agricultural sector that has more than 20 parts in stock.

To illustrate the use of the tools described in the previous section, we used series of six items with different characteristics. First, the Stock Planning tool was used, which provided a first classification of the items, as can be seen in Table 5. It should be noted that item 2, low turnover, was considered to have demand adhering to the Gamma distribution, and not Poisson.

To guarantee a service level of 90%, 303 units of item 3 and 432 of item 4 must be kept, totaling 735 units in stock. To raise the service level to 95%, 1.598 units must be stocked, increasing inventory investment and opportunity cost by 57%. If the desired service level is 98%, the quantity of items in stock jumps to 2.946 units, increasing the opportunity cost and investment in inventory by 77%, in relation to a 90% service level.

Inventory for the slow-moving item (item 2) must be equal to 490 units for the lowest service level considered. Increasing this by 5 pp, the increase in stock should be 26%, while investment grows by 59%.
The use of the first tool also allows us to conclude that the very low turnover items (1, 5 and 6) should be stocked, since, in the three situations, we obtained CT(0) > CT(1).

The Lumpy Demand tool provides the batch size, which in the case of these three pieces must be equal to one for the different levels of service analyzed. Table 3 compares order points for items 1, 5, and 6, as well as showing average annual demand and replenishment lead-time.

We can see that the order point ranges from zero, at the lowest level of service, to one, at the highest level for all items. Only at the 95% service level do the order points differ. Note that, although the items have the same average annual demand and, consequently, the same parameters for the Stuttering Poisson distribution, the order points differ. This difference is given by the variation in lead-time.

The use of the third tool leads us to another classification of items, as shown in Table 4.
Considering a desired probability of a 10% shortage, the tool indicates that, for the economic lot Q(LEC), the average inventory is equal to 103 units, guaranteeing a fill-rate equal to 96,18% and 2,08 .214% of days with stockout, when using the La Place distribution. The Gamma distribution indicates that the economic lot is 97,93 units, with a fill-rate of 0,92% and the percentage of days with stockout of 2%. For this item, therefore, it can be said that the Gamma distribution is a better approximation for item XNUMX.

As a differential of this tool, it is also possible to calculate the Q lot of the demand during the lead-time.
The La Place distribution indicates an average stock of 69 units, with a fill-rate of 90,19%, while the Gama distribution provides us with a fill-rate of 90,86% and a batch of 73 units.

Conclusion

This article highlights the importance of implementing stock control policies in companies, which manage an increasing number of SKUs. If, on the one hand, this variety makes inventory management more complex, on the other hand, it emerges as a competitive differential, fundamental nowadays.
The use of tools developed in Excel/VBA can be a simple alternative for managers, as it allows simulating total inventory costs for different levels of service – the great trade-off present in management. This trade-off has become more and more significant, as inventory costs become more and more representative in the Brazilian scenario, as revealed by the Logistics Costs Survey.
In 2002, grade 3,6 was assigned in prioritizing inventory cost reduction – where 5 represents the highest value. In 2009, this value approaches 4,3, revealing the importance of inventory management.

REFERENCES

CASELLA, G.; BERGER, RL Statistical Inference.
2nd ed. Pacific Grove. Duxbury, 2002. 660 p.
DA SILVA, GLC Stock Model for Spare Parts Subject to Intermittent Demand and Stochastic Lead Time. 2009. 75 f. Dissertation (Master in Production Engineering) – School of Engineering, Federal University of Minas Gerais, Belo Horizonte.
SILVER, EA; PYKR, DF; PETERSON, R. Inventory Management and Production Planning and Scheduling.
3rd ed. John Wiley & Sons, 1998. 754 p.
WANKE, P. Inventory Management in the Supply Chain.1st ed. São Paulo. Atlas Publisher. 2003. 176 p.
WARD, JB Determining Reorder Points When Demand is Lumpy. Management Science, v. 24, n.6, pp.
623-632, 1978.
WANKE, P. Management of Very Low Turnover Spare Parts. 2002. Available at: http://www.ilos.com.
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WANKE, P. Low Turnover Spare Parts Management. 2003. Available at: https://ilos.com.br/site/index.php?option=com_content&task=view&id=767
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YEH, QJ; CHANG, TP; CHANG, HC An Inventory Control Model With Gamma Distribution. Microelectron.
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1 – The first part of the article was published in the November edition (nº 180) of Tecnologística 2 – Research from the ILOS Institute – Logistical Costs in Brazil 2010 3 – For more information on the use of the Stuttering Poisson distribution, see Ward, JB
Determining Reorder Points When Demand is Lumpy.
Management Science, v.24, n.6, p. 623-632, 1978

Authors: Peter Wanke and Marina Andries Barbosa