Between theory and practice of inventory management – part 2

These are the starting point for the topics discussed in the subsequent parts of the series:

• examples of errors in assumptions and calculations, resulting in service level indicators or costs that are far from expected values, as well as
• situations where simple and convenient theoretical solutions require adjustments when confronted with real-world conditions to avoid such deviations.

For simplicity, these examples are presented for a classic inventory replenishment system based on the reorder point. The first article discussed the impact of errors in determining the actual replenishment cycle time (underestimating its duration) on the execution of inventory replenishment, and especially on reducing the actual service level. This article will present the problem of errors consisting of incorrectly estimating the standard deviation of demand during the replenishment cycle due to incorrect determination of demand variability or replenishment cycle time. Two situations, often observed in practice, will be presented, consisting of:

• not taking into account the standard deviation of the replenishment cycle time when it is in fact subject to random changes
• overestimating the standard deviation of random demand changes by incorrectly treating certain demand quantities as random, when in reality they are predictable (for example, additional orders placed with more lead time).

The errors discussed below occur particularly often when auxiliary calculations of the reorder point (often also referred to as the reorder level) are carried out using simple spreadsheet-based applications with a large amount of data.

Ignoring random changes in the inventory replenishment cycle time
Random delivery delays, or more precisely, random changes in the duration of the replenishment cycle, can have various sources:

• variability (most often) in the extension of production or picking time
• delays in transport and/or unloading caused, for example, by weather conditions, traffic-related problems, etc. Such a situation can apply to both sea shipments, for example from China, where delays will be measured in weeks, and Just-in-Time deliveries, where unforeseen delays of around 30 minutes will be significant.

Random changes in the replenishment cycle time can be described by a frequency distribution, similar to how it is done for random demand changes, creating something like a “replenishment cycle time profile”. It should be noted, however, that the frequency distribution will rarely match a normal distribution. These will rather be asymmetrical distributions, in which the so-called mode of the distribution (the most frequently occurring value) will be consistent with, for example, agreements with the supplier, while with a certain probability, larger values will occur, posing a threat to the proper execution of the inventory replenishment process. Figure 1 shows an example of such a distribution. However, regardless of the shape of the profile, just as in the case of demand distributions, the key parameters calculated here will be: the mean value and the standard deviation of the replenishment cycle time. Knowing them, alongside the mean value and standard deviation of demand (referred to an accepted unit of time), is necessary to calculate the mean value and standard deviation of demand during the replenishment cycle, which is crucial for correctly determining safety stock, and further, the reorder point or maximum stock, which are the control parameters of the two basic inventory replenishment systems: the reorder point system and the periodic review system.

The article comes from the magazine “Logistyka” 6/2008.