TEXTILE ITEMS CLASSIFICATION FOR SALES FORECASTING

Авторы: S. Thomassey, M. Happiette, J.M. Castelain

Источник: http://scs-europe.net/services/ess2002/PDF/tex-3.pdf

ABSTRACT

In order to reduce their stock, to avoid ruptures and to direct their marketing policies, textile companies must improve their supply chain management. This organization requires forecasting systems adapted to the uncertain environment of the textile field. Taking into account also delivery constraints, textile distribution need mean-term forecasting (one season) in order to launch new production. The proposed model, based on items classification, performs mean-term forecasting from forecast established on items families. To evaluate accuracy of our model, a simulation is realized on real sales data of an important ready to wear distributor.

INTRODUCTION

To schedule all steps require to produce and deal textile items, managers must rely on efficient and accurate forecasting systems. A sales forecast allowing to predict in a due time the right quantity to produce, is one of the most important factors for the success of a lean production (Kincade et al. 1993; Sboui et al. 2001).
Sales forecasting in textile domain is very complex. In deed, sales are disturbed by numerous factors. These ones can depend on item itself (color, price,...), on distributor (stores number, merchandizing,...), on customers (fashion,...) or on external factor (weather, economic conjuncture, ...).
These explanatory variables are not always available and their influences have various on sales (De Toni and Meneghetti 2000). Besides, sales historic are often short and noisy.
Figure 1 presents the creation, production and distribution planning of an autumn - winter item. It shows that purchasing managers need to know, at the end of the season, sales forecasting of the future season to anticipate the new production. To fit restocking predicted at mean-term, initial forecasting must be readjusted from the last sales. Thus, textile field requires mean term (1 season) and short term (1 to 6 weeks) forecasting. In this paper, we only present mean-term forecasting.

Figure1. Production planning of a autumn-winter textile item

The textile market also implies a number of items references growing, often renewed, with a life period increasingly short (maximum 6 weeks). In this context, forecast requires a data aggregation (Figure 2), which allows to obtain an exploitable history. In preceding works (Thomassey et al. 2001; Thomassey et al. 2002a), forecasts by items families have been resolved by soft computing based methods.
We propose to determine a distribution method of the textile items sales from precedent forecasts accomplished in the corresponding family. The suggested method is based on the achievement of a "life curve" performed by items clusters. The final forecast is carried out from the total items forecast of the family and all "life curves" of the items.

Figure 2. Different aggregation level of textile items

FORECASTING SYSTEM

General principle The proposed method, which carries out mean-term sales forecasting of new items, is composed of two stages : classification of historical items which allows to perform a "life curve" for each item of a family, distribution of the total forecast of the family on each item.
Hypotheses are the following : sales items until season A and mean term forecasting of season A+1 are known.

Items classification The most of items are renewed at each season and thus, no historical sales data are available. In this context, times series forecasting models become unsuitable. The proposed solution is based on the classification of items of each family according to different criteria. The effectiveness of classification for forecasting has been already validated (Daneshdoost et al. 1998; Fokianos and Kedem 1998) and particularly in textile sales (Boussu 1998; Happiette et al. 1996). The aim is to obtain clusters of items, which hold the same behavior in terms of sales. The main difficulty is the choice of significant and available criteria. According to experts, qualitative criteria like style, material,..., seem the most appropriate. However in our context, these data are rarely accessible (Vroman, 2000). The only knew criteria for new items are : period of sales, price, number of deal store and number of different color.
The classification procedure is based on hierarchical method (Bellman et al. 1996; Rham 1980) and composed of two phases : classification of historical items and attribution of new items to clusters.
The optimal cluster number is selected through the following validity criterion S (Xie et Beni 1995) :
with :
c = cluster number
n = item number

ak = center of cluster k
xi = item i
d min = minimum distance between cluster centers
µ ik = membership degree to cluster k of item i (µ ik = 0 or 1 with hierarchical classification).
The applied distance is the Euclidean distance.
A life curve of each cluster is performed from the life curve of all historical items included in the corresponding cluster.
Each new item is attributed to the cluster whose the center is the nearest in term of Euclidean distance. The estimate life curve of a new item is then the life curve of his attributed cluster, adjusted to his sales period.

Distribution model (IDAIC)
This model called IDAIC (Items forecasting model by Distribution of Aggregated forecast and Items Classification) performs mean-term forecasts from aggregated sales forecasting and items life curve. A historical items classification is performed upstream of the IDAIC model ; it allows to achieve a specific life curve for each new item. For each family, the predicted distribution of the total items sales is then given from the combination of the "life curves" of each item on their respective life period.

Figure 3. IDAIC principle

For example at period t, consider only two items i and j of a family (figure 3). Their respective life curve (lci and lcj) gives the life curve coefficient: ci and cj. Q is the predicted sales quantity [11] for the family at period t. Then, the sales forecasting of item i is traduced by the following relation:

EXPERIMENTATION

Forecasting evaluation
The applied criterion is the Median Absolute Percentage Error (MdAPE), which is recommended to compare forecasting models when numerous times series are available (Armstrong 2001). The APEn of the n-th series is defined as:

MdAPE is observation (S+1)/2, if S is odd, or the mean of observations (S/2 and S/2+1) if S is even, where the observations are rank-ordered APEn and S is the number of considered series. The lower this criterion is, the more accurate the model.

Sales data
Models are tested on historic of women T-shirt family composed of 143 items of an important ready to wear French distributor. These historic are composed of three years. The learning process is carried out on the two first seasons (108 items). The simulation is realized on the third season (35 items).
Comparison with classical models
Due to the specificity of the context, it is difficult to compare our models with classical ones. However, we propose and test the following solutions : a Basic Distribution (BD) of aggregated sales forecasting according to the number of items of the family , the IDA model (IDAIC without classification) (Thomassey et al. 2002b) with mean life curve and IDAIC model with life curve obtained by classification.
Results

Figure 4. Four obtained clusters and their center according to item price and stores number

Figure 5. Example of estimated profiles and forecasting sales

Models evaluations on 35 items of a same family are presented in table 1. The horizon applied is one season.
Selected criteria for classification are the item price and the number of stores, which deal the item.
Figure 4 shows the four obtained clusters and their center according to these two criteria.
Figure 5 relates an example of estimated profiles and sales forecasting of three tested systems. IDAIC and IDA models appear particularly more efficient than BF model in term of MdAPE criterion (table 1). Estimated profiles are more accurate with a classification procedure upstream the forecasting process (figure 5). Indeed, results obtained with IDAIC model are slightly better than IDA model (table 1). However, the quantities forecasts are sometimes imprecise, and thus decrease the final prediction accuracy (figure 5).
Table 1. MdAPE criterion of mean-term forecasting sales of 35 items

Model	BF	IDA	IDAIC
MdAPE	670	353	341

CONCLUSION

In order to answer to requirements of the textile field, the proposed system allows to obtain mean- term sales item forecasting. The use of classification procedure allows in the specific environment of the textile market, to increase the accuracy of sales forecasting for new items. The proposed mean-term forecasting model, distributes forecasts realized on aggregated sales according to life curve of each items belonging to considered family. However, if the classification increases the accuracy of the life curves, the estimated quantities still sometimes imprecise. These results must be generalized on larger number of items families and eventually with others pertinent classification criteria. The use of more pertinent criteria should add more efficiency to the classification procedure, but data obtaining are always problematic in textile context (Vroman 2000).

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