STOCK MAPS APPLIED TO SPARE PARTS MANAGEMENT - PART 1

Strategic inventory management is gaining increasing importance in supply chain management.

With the increase in global competition and pressure on the market, companies are looking for competitive advantages, such as customization of services and products, improvement in the level of service and reduction of total costs. The biggest challenge is to ensure high levels of service at the lowest cost.

Research carried out by ILOS1 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.

Inventories appear in the supply chain in different formats, such as inputs, finished and semi-finished products. They can also be in the form of maintenance, repair and operation parts, known as MRO (Maintenance, Repair and Operation).

In addition to these, there are several other factors that contribute to a growing concern with the inventory management policy. Wanke (2003) cites some of them:

• The proliferation of SKUs, which makes determining lot sizes, reorder points, and safety stocks more complex;

• The high opportunity cost of capital – by maintaining inventories, the company immobilizes part of its working capital, which could be invested in the financial market;

• The reduction in Net Working Capital (difference between current assets and current liabilities), an important financial indicator for companies that wish to maximize their market value.

Considering all these factors, the main decisions to be made in inventory management are: how much to order, when to order, how much to keep in safety stock, where to locate inventories, and how to control the system. The structuring of these decisions by companies can be greatly aided by using a stock map.

Due to the length of the subject, this article will be divided into two parts. In the first, the concept of stock map will be approached, as well as ways of classifying demand, using this concept. In the second part, three tools developed to help control inventories will be analyzed. This will also have a case study, which will address the inventory management policies for a company that manufactures equipment for the agricultural sector.

STOCK MAPS

In the context of inventory management, one of the main difficulties is managing spare parts. These parts are essential in supporting maintenance operations and protecting against equipment failures (Silva, 2009). The greatest difficulties in managing these items are their high acquisition costs, long supply response times (lead-time), in addition to very low turnover (Wanke, 2003).

Large companies keep more than 500 different items in stock (Silver, Pyke and Peterson, 1998), increasing management complexity. Creating an inventory management model requires focusing on the most profitable items for companies. Through the Pareto Analysis methodology, the ABC classification of the products is carried out.

In general, 20% of items are responsible for 80% of profitability, justifying a more sophisticated control policy just for these items.

In addition to the ABC classification, stock items are classified according to their demand behavior:
high or low spin, regular, erratic, among others. This classification can be made from boundaries established for several variables, such as the average historical consumption and the variability in the size of the demand, in the average time between demands and in the lead-time. By establishing these boundaries, conceptual maps are created, which we will call stock maps.

The construction of a stock map is essential for companies, since, based on the classification of demands, the appropriate stock control policy can be established for each item. As the demands differ, it is possible to identify the probability distribution to which the demand adheres. Different ways of classifying these items are found in the literature.

Spare parts can be segmented, for example, according to average historical consumption:

• Parts for mass consumption: Consumption greater than 300 units per year.

• Low-turnover parts: Consumption between one and 300 units per year (average of approximately one unit per day).

• Very low turnover parts: Consumption of less than one part per year.

Bulk consumer parts

Mass consumption parts are those that are less complex to control. Because they have a high turnover and more regular demand, it becomes easier to make forecasts. They adhere to the Normal Probability Distribution.

This distribution, also known as the Gaussian distribution, plays a fundamental role in statistics.

Casella and Berger (2002) present reasons for this: (1) The normal distribution and distributions associated with it are analytically tractable. (2) The normal distribution has a familiar bell shape, whose symmetry is a choice for many populations. (3) The Central Limit Theorem, which under mild conditions shows that the normal distribution can be used to approximate a wide variety of distributions in large samples.
The distribution has two parameters μ and σ2, where:
E(X) = μ and Var(X) = σ2

The low turning parts

One of the difficulties in managing low-volume spare parts is the impossibility of demand adhering to the normal distribution curve, as with mass consumption parts. To overcome this issue, many authors assume that demand adheres to the Poisson distribution.

The Poisson Distribution is a discrete distribution, which allows us to calculate the probability of occurrence of a given event based on its historical average.
The probability of the Poisson distribution can be given by:

Where:
P(X=x) = Probability that the demand for parts is equal to x units;
λ = Average consumption rate per unit of time.

The main properties of the distribution are: E(X) = λ
and Var(X) = λ

Table 1 illustrates the example of a spare part with an average consumption rate (λ) of three units per year. The individual and cumulative probabilities of occurrence of demand were calculated, within a one-year horizon.

The probability of not having spare parts consumed is 4,98%. In turn, the probability that the demand is for at least one piece is 95,02%. The probability of there being no shortage if the stock is equal to historical consumption is 64,72%. Keeping five parts in stock, the probability of not having a shortage is 91,61%.

Inventory control can be based on the supplier's response time or resupply cycle – the interval between placing an order and receiving it.

In this interval, the probability of a company's stock shortage is greater, since unforeseen resupply events may occur. Therefore, it is essential to calculate the reorder point properly. This can be found through the equation:

Where:
D = Demand per unit of time;
TR = Resupply cycle response time, in time units;
k = Safety factor;
σD = Standard deviation of demand per unit of time.
This formula can be adapted for adherent demands

to the Poisson distribution, since the demand per unit of time is equal to parameter λ and σD=

In this way, the order point can be calculated as illustrated:

Wanke (ANOX) describes a decision support system based on the probability of not having a stockout during the resupply period. Suppose that a certain spare part has a consumption rate (λ) of three parts per year, the lead-time is four months and the desired probability of not having a shortage is equal to 95%. The probabilities of not having a fault are shown in Table 2.

Gamma Distribution

The use of the Poisson distribution is restricted to situations where:
0,9 E(X) ≤ V(X) ≤ 1,1E(X)
If this restriction is not met and the period with zero demand is greater than 30% of the total, some authors suggest using the Gamma distribution. Bagchi et al, cited by Yeh, Chang and Chang (1997), consider that the quantity requested in a demand (A), the time interval between demand occurrences (T) and the resupply lead-time (Z) are adherent to the Gamma distribution, with parameters (μ,σ), (α,β) and (γ,δ), respectively. As with Poisson, the probability of stockouts during the lead-time (Os) can be calculated using the equation:

Where:
Ps = Probability of rupture during the leadtime (Z);
Ls = Level of Service (1- Ps);
Ti = Time interval between two demand occurrences
– parameters (α,β);
Ai = Quantity requested in a demand – parameters (μ,σ);
Z = Resupply lead-time – parameters (γ,δ);
W = Number of demand occurrences in the lead-time (Z);
S = Remaining stock quantity.

The low-turn parts
Inventory control of very low-turnover parts must be based on the analysis of total costs, deciding whether it is more appropriate to keep a unit in stock or not, triggering replacement on demand (Wanke, 2003).

Let the variables be:

CTR = Total cost associated with placing a supply order (R$);
Caq = Unit cost of acquisition of the part (R$);
LT = Request response lead time (months);
λ = Historical consumption rate per year (piece/year);
T = Annual capital opportunity rate (% per year);
Cip = Cost of Unavailability and Penalty, expressed as an absolute amount incurred every time a spare part is requested and it is not in stock (R$).

The cost of not keeping the item in stock is given by the calculation that can be seen:

And the cost of keeping a part in stock is given by:

Decision making from this calculation becomes simpler:
if CT(0) > CT(1), the item must be kept in stock.
If CT(1) > CT(0), the spare part must not be stored.

OTHER FORMS OF DEMAND CLASSIFICATION

We can classify demand in other ways, in addition to the one already described. Silva (2009) uses in his dissertation a classification based on the variability of the average time between demands, the size of the demand and the leadtime.

Other classifications arise, mainly, from the need to classify low-turnover items whose demand behavior is erratic – high variability in the size of the demand – and intermittent – ​​high variability in the average time between demands. A demand is classified as “lumpy” when it presents erratic and intermittent patterns.

The classification made by the author is based on the models proposed by Eaves and Kingman (2004) – variability of demand components during lead-time – and by Silver, Pyke and Peterson (1998) – expected value of demand.

Border values ​​were obtained experimentally, differentiating low-turning (slow-moving) or high-turning (fast-moving) items. This classification is shown in Table 3 and its respective stock map in Figure 1.

Silva (2009) developed in his study a model for controlling stocks of spare parts based on this classification. Control is based on the calculation of total inventory costs, fi ll rate and service level.

Conclusion

Inventory management grows in importance in the logistics of Brazilian companies. In addition to this, there is also a concern with reducing inventory costs, whether due to the high opportunity cost of capital immobilized in inventory or the reduction of net working capital.

However, finding a management policy is a delicate task for companies, but it can be simplified by using stock maps.

There are some suggested maps in the literature. However, the elaboration of new maps or the establishment of other frontiers is a great development opportunity for companies, since they will be adapting some patterns already studied to real needs. In the second part of this article, tools built based on the stock map concepts presented will be addressed, in addition to the presentation of a case study.

Bibliography

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1 – Research by the ILOS Institute – Logistics Costs in Brazil

Authors: Peter Wanke and Marina Andries Barbosa