*2.1. Inventory Case Study: Spare Parts for Fluid Conduction Systems*

In a first exploratory analysis of the data obtained from enterprise resources planning software (ERP) utilized by the company. There are 9072 references which can be object of study, and that can be categorized as follows:


From this product aggregation, the category of 'Plastics' account for 2735 product references, that represent a 30.3% of the total number of articles considered. These are the specific targeted parts

focused in the present study, as most of them could in fact be manufactured by plastic AM technologies, despite being originally designed to be manufactured by other means.

In these selected plastic product references, the next step in the methodology consists on evaluating the relative demand and rotation of each product reference. Therefore, the study analyses both the distribution of the orders and the average lot size of each of them.

Firstly, it has been studied the number of orders received for each of the references. For this reason, a Pareto-type analysis has been made showing the distribution of the number of orders of each product or reference within the category 'Plastics' (see Figure 2). During the study year, the 2735 product references were called in a total of 99,009 independent orders.

**Figure 2.** Pareto distribution A-B-C of the orders received for all references within the category 'Plastics'. Elaborated by the authors from *Unistral Recambios* data.

The Pareto analysis divides the orders received in the category 'Plastics' within three population levels 'A', 'B' and 'C'. The 'A' sector comprises the products that represent the 80% of orders expressed in number of units. The 'B' sector comprises the products that represent a supplementary 15% of the orders and, finally, the 'C' sector includes the products that represent the 5% of the remaining orders. The specific data for this analysis is shown in Table 1. In this table it is also shown the maximum, average and minimum numbers of orders for the references classified in each sector. As a preliminary conclusion, the 166 references categorized in Sector A have continuous levels of demand, which can continue to be produced by conventional manufacturing means that lead to economies of scale. On the contrary, the references in the sectors B and C are potentially good candidates to be analyzed in the present study as they add up total of 2569 part references (93.9% of the products in the 'Plastics' category) with discontinuous levels of demand (29.9 orders/year in average for Sector B and 2.4 orders/year in average for sector C).


**Table 1.** Pareto distribution A-B-C of all references. Elaborated by the authors from thanks to the data facilitated by *Unistral Recambios* data.

Secondly, it is important to quantify the real rotation of the products; i.e., how many of each of the parts are ordered in their (possible) different orders. As stated earlier, these figures can be obtained by analyzing the average number of parts served in each of the orders for every part. Concerning to this, Figure 3 depicts the actual rotation of the products.

Figure 3 shows a very clear distribution for a company dedicated to the spare parts supply. In effect, the quantity of parts ordered in average in an independent order is relatively small. This fact, combined with what was demonstrated in Figure 2, shows how most of the parts receive relatively low numbers of orders containing relatively low numbers of units of products in each order. Only few products receive recurrent large orders. In fact, the plastic parts that do have large recurring orders are commonly small plastic bags and small foam spacers with manufacturing costs that normally fall below 0.0002 €/unit, having a limited impact in the inventory costs. Furthermore, some 142 product references accounted for zero orders in the study year.

**Figure 3.** 3D quantification of the rotation of the products. For each part, a plot in X and Y is configured with the number of orders received and the average number of units sold in each order within the categories 'Plastics'. Elaborated by the authors from *Unistral Recambios* data.

More specific information on the distribution of the number of units in an independent order can be found in Table 2. In particular, having an average number of units in an order of 78.9 parts, in fact 75% of the orders are of 15 parts or less. Therefore, in this sector, the real industrial interest for manufacturing solutions is to respond to the orders of small batches of products.

**Table 2.** Distribution of the number of units demanded in each independent order.


From the mass distribution perspective of the analyzed parts, it can be produced an analogous study which is shown in Table 3. For the 2735 references analyzed in the 'Plastics' category, some weighty parts increase the overall average weight of a part to 2.179 kg. However, 75% of the references weight are of 1.005 kg or less. Clearly, the majority of the parts within the category have small masses.

**Table 3.** Distribution of the mass in the product references.


As a summary, the taxonomy analysis undertaken in the present exploration yields that the prototype part in the 'Plastics' category, for this company in this sector:


Therefore, the case study will focus on the parts that fulfil these conditions and will be referred as the fraction 'α' of the inventory.

#### *2.2. Total Inventory Manufacturing Costs*

In order to quantify the costs in its context, it can be formalized the total inventory manufacturing cost (TIMC), which can be calculated by making the addition for all parts in the inventory of its number and manufacturing cost, as formalized in Equation (1):

$$TIM\mathbb{C} = \sum\_{i=1}^{i=n} \sum\_{j=1}^{j=m} \left( Q\_i^j \cdot \mathbb{C}\_{MANi}^j \right),\tag{1}$$

where:


In particular, *TIMC<sup>α</sup>* can be used to refer the Total Inventory Manufacturing Cost (TIMC) of a subset of products 'α', in particular those belonging to the filtering undertaken with the 'Plastics' category.
