MANAGING UNCERTAINTIES IN LOGISTICS PLANNING: THE ROLE OF SAFETY STOCK

Demand forecast errors, delays in material resupply, lower-than-expected production yield. These are common problems that are part of the logistics professional's daily life. To deal with these uncertainties, present in virtually all logistics processes, safety stocks can be used. However, its correct dimensioning still generates many doubts and divergences. Many companies improperly determine their safety stocks because they are not based on accurate measurements of process uncertainties. This can lead to unnecessary costs that often go unmeasured.

If, on the one hand, excess safety stock generates unnecessary inventory maintenance costs, related to financial costs (tied up capital) and storage, on the other hand, undersizing the same causes the company to incur sales losses or frequent backorders. (postponement of orders), generating an unsatisfactory level of customer service. Thus, the main question regarding the formation of safety stocks is: “what is the minimum stock that will guarantee the level of customer service desired by the company?”

The purpose of this article is, therefore, to analyze the formation of the safety stock based on quantitative techniques for measuring the level of uncertainty in the logistics process. First, the main problems identified in companies when trying to assess their uncertainties and form safety stocks will be presented. Afterwards, methods for measuring uncertainties and parameterization of indicators will be exemplified. Finally, means of dimensioning the safety stock will be analyzed considering the uncertainties of the process.
MAIN PROBLEMS IDENTIFIED IN THE TREATMENT OF UNCERTAINTIES AND SIZING SAFETY STOCKS

The costs of holding inventories and backorders and/or lost sales are often ignored because they are not recorded in the companies' accounting. Thus, it is frequent that even large companies do not have managerial information regarding the cost of excess or shortage of inventories in a given period of operation. It is important to emphasize that measuring these costs is the first step to assess the situation of the company's inventory policy and justify or not a revision work.

Due to lack of knowledge of the dimension of uncertainties inherent to the processes, mistakes can be made that translate into unnecessary costs. An example is the formation of safety stocks in the feeling, without any parameterization. It is common, for example, for the commercial sector of a company to place a safety margin in the demand forecast, in order not to lose sales, without relying on statistics or historical series of real demands and forecast errors. In turn, the PCP (production planning and control) and/or purchasing sectors, which are often unaware of this overestimated forecast, add their own safety margins for placing resupply orders. What you have in the end is an excessive cost of maintaining inventories, resulting from an oversizing of the safety stock.

Another common problem, similar to the previous one, is the use of the sales target as a demand forecast. If this target is frequently overestimated in relation to actual demand, that is, it includes a safety margin by itself, as a consequence stock levels must constantly remain above the necessary minimum.

It has also been common to apply simplified rules, not necessarily based on the specific characteristics of each company's process, which use a percentage of demand in lead time (expected demand during the resupply period), such as 50%, for training of safety stock. Thus, if the company expects to sell 100 units of a product during the lead time, 50 more units would be kept in stock to support any variability in this initial expectation. Similarly, some companies scale their safety stocks by number of demand periods, keeping for example “two weeks in stock” or “four days as safety stock”, generally empirically, without making a reasonable assessment of all the uncertainties.

There is also the problem of anticipating resupply requests without further care. There are cases in which the purchasing sector of a company, concerned about possible delays from the supplier, starts to order with a certain amount of time in advance, without relying on statistics of delays from that supplier. What happens in practice is an increase in the purchase lead time, which is often unnecessary, increasing the time in which capital is tied up in stock.

In order to know which uncertainties are relevant for defining inventory policies and what costs they are generating for the company, it is necessary to understand and model the entire logistical process, from opening an order request to customer service, passing through the production of finished products and procurement of raw materials. Thus, it is possible to define indicators referring to process uncertainties and quantify them. It is extremely important, therefore, to create a database containing historical series of these indicators that provide information on their behavior over time.
MAIN SOURCES OF UNCERTAINTIES IN THE LOGISTICS PROCESS AND FORMS OF MEASUREMENT

Uncertainty in demand and its forecast

Variations between actual demand and its forecast are unavoidable. There will almost always be a forecast error. However, depending on the size of this error, the impacts can be quite harmful for the planning process. From the point of view of inventory management, it is not enough to know if there are errors, but how many errors are made and how it varies. Efforts in an attempt to improve forecast accuracy, using quantitative techniques and analyzing possible scenarios, are essential to reduce the costs generated by excess or shortage of inventories.

To measure the uncertainty caused by variability in the forecast, an indicator can be used, which we call the forecast ratio (Rp), defined as:

Thus, an Rp less than 1 indicates that the demand was below the forecast and an Rp greater than 1 indicates a demand above the forecast.

To measure it systematically, it is necessary to create a database containing a historical series of this indicator, for each product. From this base, Rp statistics must be calculated, such as its mean and its standard deviation. These, in turn, must be used in the calculation of the safety stock. The average, in this case, is a measure of centralization of the Rp indicator, that is, it indicates whether there is any bias, or systematic error, in the forecast. An average of less than 1 shows that the forecast is systematically above the actual demand, perhaps characterizing one of the problems already mentioned, such as the use of the sales target instead of the forecast. The standard deviation is a measure of dispersion, quantifying the variability of the indicator around its mean.

Of course, it is possible, and more commonly used, to measure demand variability for parameterizing inventory models rather than forecasting errors. However, what we need to assess is actually our uncertainty about demand, and forecast errors give us valuable information about this. In this way, if we are analyzing a system that presents a very variable demand behavior, but also predictable, we will be able to use smaller safety stocks. For example, in the case where there are known seasonal variations, if we scale inventories directly relating them to demand variability, we will tend to use safety stocks that are larger than necessary.

Uncertainty in lead time

Delays in the resupply of products and raw materials are caused by a wide range of factors, such as machine breakdowns, strikes in the transport sectors and lack of supplier inventories. Thus, it is fundamental to evaluate the magnitude and frequency of these delays in order to parameterize the inventory management system.

Here it is also necessary to build a database to systematically measure lead time uncertainty. This base can be built from orders to suppliers or production sectors, measuring the interval between placing the order and its availability, that is, the actual lead time for resupply. This, in general, can be decomposed into sublevels, such as requisition lead time, supplier lead time and analysis lead time, which would be defined as follows:

• Requisition Lead Time = Order Placement Date – Requisition Opening Date;
• Supplier lead time = Order Receipt Date – Order Placement Date;
• Analysis lead time = Order Release Date – Order Receipt Date;

The total resupply lead time is the sum of all sub-levels. It is desirable that this be decomposed so that it is possible to identify bottlenecks and critical points in the process, with a view to reducing the average lead time and its variability (standard deviation). The smaller the lead time variability, the smaller the required safety stocks.

Thus, the database must contain historical series of these lead times, segmented by products, raw material items, suppliers or transporters. From there, the aforementioned statistics can be calculated, also serving as a basis for dimensioning the safety stock.
The uncertainty in the quantity received

Often, the quantity actually received is less than the quantity requested. In the case of a factory, when the order is placed to the production sector, this fact may be a consequence of the yields of the production processes being below the expected levels. As for orders placed with suppliers, batch disapproval due to quality problems can be the main cause of the problem of having less available than ordered.

However, when the quantity received is sufficient to meet demand for a period longer than the lead time, eventual shortages may not represent major problems, as there would be time to receive another order. For example, assuming that the lead time for resupply is one week and that the demand expectation is 100 units of product per week, if you order a quantity of 300 units from the supplier, you would expect to meet the demand for three weeks. But if, for some reason, only 200 units were available, there would be no major problems, as this quantity would be enough to meet the expectation of two weeks of demand, with enough time to place a new order with the supplier without increasing the risk of having Lack of stock.

But, in many cases, the order covers an expectation of demand during a shorter period of time or close to the lead time, making uncertainties related to shortages in the supplied quantity relevant for inventory management. Thus, it is convenient to create an indicator of the supplied quantity, here called Qf, expressed as follows:

As in the previous cases, a database containing, for each product, a historical series of that indicator is necessary. Once again, its mean and standard deviation must be calculated, in order to have all the parameters for sizing the safety stock.

Sizing of safety stocks

Having the correct information on the past behavior of the uncertainties, it is possible to use quantitative techniques to dimension the minimum stock corresponding to the desired customer service level.

Sizing is based on calculating the probability that the need for a given inventory item in a given period will take on values ​​within a certain range. Thus, the need we want to estimate revolves around an average or expected level, which can vary both upwards and downwards, following a certain distribution of probabilities. The normal curve, exemplified in Figure 2, is one of the most used to model this probability distribution, making it possible to define, as a function of the standard deviation, the probability of a value occurring within certain ranges, called confidence intervals.

As can be seen in Figure 1, the need is symmetrically distributed around its mean, that is, there are equal probabilities of a value lower or higher than the expected need.

The standard deviation of this need, as already mentioned, provides the dispersion around the mean. Thus, for variables that behave according to the normal curve, there is a 68% probability of occurring a value within the interval bounded below by the mean minus 1 deviation and above by the mean plus 1 deviation. Likewise, there is a 97,5% probability that the same variable will take on a value less than the mean plus 2 standard deviations. Therefore, knowing the mean and standard deviation, it is possible to build intervals with the desired confidence.

And it is in this way, according to a certain level of confidence, that the safety stock is calculated. For example, considering that the only existing uncertainty is that of demand, if 100 units of a product are expected to be sold in the next week and it is known, from historical data, that the standard deviation is 20 units, it can be say with 97,5% confidence that demand will not exceed 140 units. The safety stock, for a customer service level of 97,5%, would then be 40 pieces.

The question, therefore, is to determine, based on the statistics of the indicators, how much the uncertainties will cause this demand to deviate from its expected value.

The formation of safety stock in the classic reorder point model

Most of the inventory management texts present the classic reorder point model, in which safety stock sizing is based on the combination of demand variability and lead time. The order point model starts from the logic that as soon as the stock level reaches or falls below a certain level, called the resupply point, an order request is opened. The demand during the lead time thus has an expected value that is equal to the average lead time multiplied by the average demand per unit of time, with the safety stock formed exactly to support the variability that this demand in the lead time may present. Figure 3 illustrates the separate effect of each uncertainty: 

In the graphs in figure 3, known as sawtooth, the upper level represents the maximum stock, which occurs exactly at the moment when the order arrives. This level decreases over time, due to the demand per unit of time, until it reaches the resupply point, when another order is requested.

With the two uncertainties present in the process, the safety stock is dimensioned as a function of the level of customer service and the averages and standard deviations of the demand per unit of time and the lead time for resupply, calculated based on the historical series of data.

The formation of safety stock in planning environments

Planning environments, whose basis for calculating needs is associated with demand forecasting, have the advantage of being able to incorporate explained variations in demand over time, such as seasonality and growth trends, however requiring more complex analysis methods for sizing stocks.

MRP, for example, the most used system for material planning, presents a logic based on the net need for a certain product in a certain period. Thus, the system always “looks” ahead, according to the parameterized lead time, identifying whether the demand forecast, plus the safety stock, plus the quantity already ordered, minus the initial stock, give a positive or negative value . In case the value is negative, an order requisition is immediately opened.

The safety stock can then be dimensioned in two ways, which will depend on the company's process. If orders always have a coverage greater than the lead time or failures in the supplied quantity are not relevant, the ideal is to parameterize the safety stock to supply variability in demand during the lead time in an analogous way to the classic model, but combining the error of forecasting with variability in lead time. Safety stock would thus be a function of the desired service level, demand forecast, Rp statistics, and resupply lead time statistics.

If failures in the supplied quantity play a relevant role, the best way to size the safety stock is based on the variability that the net requirement may present. This would then be calculated as a function of the customer service level, the Rp, Qf and resupply lead time statistics, the demand forecast and the initial stock of the product in question.

In both forms of sizing, both based on demand variability in lead time and based on variability in net demand, the safety stock is a dynamic parameter, sensitive to forecast variations over time. This represents major advantages over a fixed safety stock, as illustrated in figure 4:

The calculation techniques containing all uncertainty parameters are generally very complex, making use of a mathematical tool that is sometimes difficult to implement.

Thus, simpler formulas, containing a smaller number of parameters, can be combined with other techniques. An example is dimensioning the safety stock according to the uncertainties in the demand forecast and in the supplied quantity, parameterizing in the system a lead time greater than the average lead time, according to the desired level of confidence. For example, a supplier might deliver an order with a mean of 15 days and a standard deviation of 3 days. Approximating the lead time by a normal distribution, it would be possible to guarantee that 97,5% of orders would be delivered within 21 days. Therefore, for a lead time confidence level of 97,5%, it would be enough to parameterize 21 days of resupply time in the system instead of 15.

CONCLUSION

Knowing and measuring the uncertainties present in logistics processes is the first step towards a good inventory management policy. Creating indicators of these uncertainties is essential for the correct dimensioning of safety stocks, guaranteeing the desired service level at the lowest total cost of operation.

In addition, with these indicators it is possible to quantify costs associated with certain activities. The safety stock parameterized according to demand forecast error indicators, for example, allows quantifying the cost that larger or smaller forecast errors generate for the company. Likewise, it is possible to evaluate suppliers and the company's own production processes with regard to the reliability of their services and their impact on inventory levels.

Therefore, in addition to reducing inventory levels and improving the level of customer service, an inventory management policy with a more formal and scientific basis can help in measuring the impact of certain activities on the company's logistics processes, identifying critical points and pointing to opportunities for improvement.

BIBLIOGRAPHY

Bowersox, DJ, Closs, DJ, 1996, Logistical Management – ​​The Integrated Supply Chain Process, 1st ed., New York, McGraw-Hill.

Fleury, PF, Wanke, P., Figueiredo, K., 2000, Business Logistics – The Brazilian Perspective, 1 ed., São Paulo, Atlas.

Authors: Rodrigo Arozo, Eduardo Saggioro Garcia and Leonardo Lacerda