ABC inventory classifications are widely used in practice, where the items are classified based on one criteria, the annual use value, which is the product of an- nual demand and average unit price (Teunter et al., 2009) (Ramanathan, 2006). The framework of Perona et al. (2009), which is used as basis framework in this research, uses this traditional ABC inventory classification. However, for many items there may be other criteria that represent important considerations for man- agement (Flores & Whybark, 1987). The rate of obsolescence in food processing industry is an example of such considerations. Therefore, a literature review is conducted to find an ABC inventory classification model where the items are clas- sified based on multi-criteria. Note that we use an ABC inventory classification to be able to only rank the end products rather than classify them, since the limited inventory capacity will probably determine the classification.
In general, the ABC inventory classification method classifies items in a class (A, B or C) based on a criterion or criteria. Class A indicates to the most important items and need the most attention, where on the other hand class C indicates to the less important items (Teunter et al., 2009). The most common rule is that class A, class B, and class C consists of 20%, 30%, and 50% of the total items, respectively (Silver et al., 2017). Class A consists of 20%, since in many cases 20% of all items ensures for 80% of the total revenue. This is also called the 80/20 rule. The most important reason to classify items is that many companies have to deal with thousands of items, and therefore implementing a item-specific inventory control method is infeasible.
The literature consists of many papers about multi-criteria inventory classifica- tion. Many papers propose ABC inventory classification with multiple criteria methods where managers’ knowledge determines the ranking of the criteria. A
disadvantage of these methods is the subjectivity involved when making pair-wise comparisons. VED, AHP and distance modeling are examples of such methods (van Kampen et al., 2012). In contrast to many papers, Ramanathan (2006) provides an advanced statistical approach. Ramanathan (2006) proposes a simple classification scheme using weighted linear optimization, from now called R-model. The model is closely similar to the concept of data envelopment analysis. This model can automatically generate a set of criterion weights for each item and as- sign a normalized score to this item for further ABC analysis (Zhou & Fan, 2007). The model is simple and easy to understand for managers. Also, the model can easily integrate additional information. By solving the R-model repeatedly for each item, we obtain a set of aggregated performance scores, which can be used to classify the M inventory items. However, if an item has a value dominating other items in terms of a certain criterion, this item would always obtain an aggregated performance score of 1 even if it has added values with respect to other criteria (Zhou & Fan, 2007). Therefore, Zhou and Fan (2007) have made an extension to the model from now called ZF-model. Zhou and Fan (2007) propose an extended version of the model by incorporating some balancing features for multi-criteria ABC inventory classification. The extended version could be viewed as providing a more reasonable and encompassing index since it uses two sets of weights that are most favorable and less favorable for each item, while keeping the simplicity of the R-model (Zhou & Fan, 2007). The total aggregated performance score of an item is the combination of the normalized aggregated performance score of an item of the R-model and the ZF-model, which is expressed in equation 1.
nIi(λ) = λ× gIi−gI
−
gI∗−gI− + (1−λ)×
bIi−bI−
bI∗−bI−, (1)
where nIi(λ) denotes the total aggregated performance score of an item, gI∗
= max(gIi, i = 1,2, ..., M), gI−= min(gIi, i = 1,2, ..., M), bI∗ = max(bIi, i =
1,2, ..., M), bI− = min(bIi, i = 1,2, ..., M) and 0 ≤ λ ≤ 1 is a control parameter
which may reflect the preference of decision maker on the good and bad indexes. Despite the advantages of the R-model and the ZF-model, it should be noted that under these models each item uses a set of weights either most or least fa- vorable to itself for performance self-estimation. In other words, the weights for self-estimation may differ from one item to another. This actually implies that the resulting performance scores of all items obtained from either model are less com- parable (Chen, 2011). Therefore, Chen (2011) proposes an improved approach to the ZF-model by which all items are peer-estimated. Chen (2011) extended
the ZF-model by peer estimation and replaces the employed λ in equation (1)
by a maximizing deviation method due to the subjectivity of the λ. Hereby, the
performance index provided by the proposed approach could be viewed as more reasonable and comprehensive for multi-criteria inventory classification, which re- sult in a more appropriate ranking (Chen, 2011).
Although the models are simple and easy to use, the processing time can be very long when the number of inventory items is large in scale of thousands of items in
inventory (Ng, 2007). Therefore, Ng (2007) proposes an alternative weight linear optimization model (model (2)). Ng (2007) makes some adjustments to the R- model. Namely, Ng (2007) transforms all measures to comparable base and the decision maker has to rank the importance of the criteria. Although this involves certain degree of subjectivity, this is a far weaker requirement than that in AHP (Ng, 2007), where only ranking is required.
maxSi = N X n=1 winyin (2) s.t. N X n=1 win = 1, win−wi(n+1) ≥0, n = 1,2, ...,(N −1), win≥0, n= 1,2, ..., N,
where maxSi, yin and win denote the aggregated performance score of an item,
the performance score of theith item in terms of thenth criterion, and the weight
of the ith item terms of thenth criterion, respectively. The model automatically
calculates the weights of each criterion with such each item can achieve the max- imal score (Ng, 2007). However, the processing time can be very long as well. Therefore, Ng (2007) adopts a transformation to simplify the model (model (3)). This model can be easily solved without a linear optimizer.
maxSi = N X n=1 uinxin (3) s.t. N X n=1 juin = 1, uin≥0, n= 1,2, ..., N, where uin = win−wi(n+1), and uiN = wiJ, and xin = win
Although this model can be easily solved without a linear optimizer, the model has some limitations. One of the limitations is the number of criteria. When the number of criteria is large, it is not an easy task for decision makers to rank all criteria (Ng, 2007). Moreover, the model can handle only continuous measures and the normalization scaling requires the extreme values of measures. And thus, all normalized measures will be affected if the extreme changes. Hadi presented an extended version of the Ng-model. Hadi (2010) provides a model for ABC classification that not only incorporates multiple criteria, but also maintains the effects of weights in the final solution (Hadi-Vencheh, 2010).
Finally, Douissa and Jabeur (2016) tackle the ABC inventory classification prob- lem as an assignment problem and not as a ranking problem, which is the case of
the most existing ABC classification models. The PROAFTN method is used to classify inventory items into ABC categories and the Chebyshevs theorem is used to estimate the PROAFTN parameters (Douissa & Jabeur, 2016). A comparative study is conducted to test the performance of PROAFTIN with respect to some other existing classification. The performance is defined as the inventory costs and the service level. This comparative study is represented in table 3.2. The NG model provides the highest fill rate, while the PROAFTN model provides the lowest inventory cost.
Classification model Total inventory cost Fill rate
NG model 1011.007 0.991 Hadi model 999.892 0.990 Peer model 958.14 0.988 ZF model 945.357 0.984 R model 927.517 0.986 PROAFTN 897.31 0.983
Table 3.2: Comparative study from Douissa and Jabeur (2016)
There are many SKU classification models available in the literature, which have
their own advantages and disadvantages. In food processing industry, multi-
criteria ABC inventory classification is useful, since food processing companies have to deal with perishability of products while in need to meet a relative high service level. However, in many multi-criteria ABC classification methods is ei- ther subjectivity involved or the method can not be easily implemented due to the complexity of the company. In contrast to these models, the six models described above can be easily implemented and subjectivity is limited. Since we prefer a model with limited subjectivity that provides a high service level, we will use the peer model. However, due to the peer estimation involved, the processing time will be very long. The difference between the ZF model and the peer model is the peer estimation and the maximization deviation method used in the peer model. That is why the peer model gives a small improvement in the ABC classification over the ZF model. Since we classify products in two classes, namely make-to-stock and make-to-order, rather than three classes, the peer estimation will add even less value. Therefore, due to the trade-off that we have made we will use the peer model, by removing the peer estimation and retaining the maximization deviation method, to rank the end products.