A global forecasting support system adapted to textile distribution

ARTICLE IN PRESS

Int. J. Production Economics 96 (2005) 81–95

A global forecasting support system adapted to textile distribution Se! bastien Thomassey*, Michel Happiette, Jean-Marie Castelain GEMTEX-ENSAIT, 9 rue de l’Ermitage, BP 30329, Roubaix cedex 1 F-59056, France Received 20 February 2003; accepted 8 March 2004

Abstract Competition and globalization imply a very accurate production and sourcing management of the Textile–Apparel– Distribution network actors. A sales forecasting system is required to respond to the versatile textile market and the needs of the distributor. Nowadays, the existing forecasting models are generally unsuitable to the textile industry. We propose a forecasting system, which is composed of several models and performs forecasts for various horizons and at different sales aggregation levels. This system is based on soft computing techniques such as fuzzy logic, neural networks and evolutionary procedures, permitting the processing of uncertain data. Performances of our models are then evaluated using the real data from an important French textile distributor. r 2004 Elsevier B.V. All rights reserved. Keywords: Sales forecasting; Textile distribution; Soft computing

1. Introduction As in other competitive industries, companies in the Textile–Apparel–Distribution network require the rigorous management of sourcing, production and distribution. Supply chain management (SCM) (Lee and Sasser, 1995), includes all these processes from the expression of the demand until delivery of the finished products. This SCM concept uses tools which intervene at various steps and places in the logistic chain (GPA, MRP, DRP, ERP, etc.) and include different functions, such as purchasing, sourcing, production planning, inventory control and exchanges of information. How*Corresponding author. E-mail address: [email protected] (S. Thomassey).

ever, even if existing methods improve the reactivity of Textile–Apparel–Distribution network, many transformations, which are required to produce textile item, always impose significant and not easily reducible manufacturing lead times. Globalization, which causes dispersion of network actors, also increases these lead times. Thus, in order to deal with the customer’s requests, companies often need to anticipate production and to produce items for stock. The main goal of the distributors is to offer the right product, at the right place and the right price, while maintaining the right stock. These constraints require an appropriate sales forecasting system. For the distributor, the correct anticipation of requests from the consumer allows the upstream companies to provision and adjust their production. Thus, the effectiveness of the supply

0925-5273/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2004.03.001

ARTICLE IN PRESS S. Thomassey et al. / Int. J. Production Economics 96 (2005) 81–95

82

chain optimization depends primarily on the precision of the sales forecasting (Graves et al., 1998). The features of the textile market activity also complicates the forecast procedure. Indeed, the proposed system must be able to: *

*

*

*

* *

*

deal with a large number of items (about 15 000 per year) and different aggregation levels of sales (Fig. 1), carry out mid-term forecasts (horizon of one season or year) to consider the quantities to produce and plan the sourcing, readjust the short-term (horizon from 1 to 3 weeks) from the mid-term forecasts in order to re-plan the sourcing, use short histories (very short lifespan of items: 1–2 months), treat new items (95% of a collection), take into account many factors, called explanatory variables (EVs), which influence sales (weather and calendar data, marketing action, promotions, fashion, economic environment, etc.), allow the easy intervention of decision makers.

Forecasting is common in many fields such as finance, economics, meteorology, energy production, sociology, etc. Amongst numerous existing models, we can group them into heuristic and statistical models (Armstrong, 2001). The first ones are based on exploitation of opinions or intentions of people or experts group; they are principally employed in the marketing field. Statistical models exploit historical data. In this category are: classical linear models (exponential smoothing, ARIMA model with EVs based on the Box and Jenkins method) (Franses, 1999;

MARKET

(man, woman, child,…)

STYLE

(urban, sport,…)

DEPARTMENT (trouser, T-shirt,) FAMILY

(short sleeves T-shirt)

ITEM

(H5490, G9135)

SIZE

(S, M, L, XL)

COLOR

(black, blue, red)

Fig. 1. Example of textile items aggregation.

Hamilton, 1994), and non-linear models (GARCH, SETAR, etc.) (De Gooijer and Kumar, 1992; Tong, 1990). Lots of software, which apply these models automatically, are available in the market (Bell and Kuster, . 1999). Lastly, it is possible to combine intuitive and quantitative methods, such as expert systems (Collopy et al., 2001) or Bayesian models (West and Harrisson, 1997). However, the performance of these traditional models depend strongly on the application field, the knowledge of the user and the forecast horizon (Dasgupta et al., 1994), which means that their effectiveness depends on the existence of reliable historical data to ensure correct identification of these model structure and an efficient tuning of parameters. Most items generally include short historical sales data, which are influenced by neither controllable nor identifiable factors (De Toni and Meneghetti, 2000). This suggests the need for new models to compensate for the limits of the traditional models. In fact, in recent years, methods based on ‘‘soft computing’’ have been largely developed for various forecasting problems. In particular, neural networks has been exploited by many forecasters (Wasserman, 1989; White, 1992; Yoo and Pimmel, 1999; Zhang and Hu, 1998). Although the contribution of these models compared to the traditional ones seems mitigated in particular contexts (Armstrong, 2001; Hill et al., 1994; Kuo, 2001), their capacity to model non-linear relations and their training and adaptation facility are potentially very attractive for forecasting issue. Fuzzy inference systems (FIS), which are able to model human knowledge and are tolerant of imprecise data (Shimojima et al., 1995; Van Lith et al., 2000; Zadeh, 1994), can easily be interpreted and applied in forecasting (Klir and Yuan, 1995; Mastorocostas et al., 2000): they are especially useful to quantify the influence of explanatory variables on the time series (Kuo and Xue, 1999). Lastly, the combination of several ‘‘soft computing’’ techniques (neural networks, fuzzy logic and evolutionary algorithms) allows adaptive systems to learn complex relationships in an uncertain environment (Kuo and Xue, 1998; Van Lith et al.,

ARTICLE IN PRESS S. Thomassey et al. / Int. J. Production Economics 96 (2005) 81–95

2000). Taking into account the very strong and specific constraints relating to the industrial context in which we operate, we chose soft computing techniques to implement our sales forecasting models. In Section 2, we describe the general principle of our system, which consists of several models performing forecasts at various horizons (midand short-term) and at different sales aggregation levels (family, item, size and color). Section 3 describes and evaluates our models with real data (3 years including about 42 000 items organized in 322 families) supplied by an important French ready-to-wear distributor. Finally, Section 4 provides the conclusions.

2.1. Notation The main used notations are the following: p A XNF F XAþ1 ðtÞ

X# FAþ1 ## F ðt þ 1Þ X Aþ1 UNF

2. Proposed forecasting system xiN In this section, we describe a sales forecasting system, which has been adapted to the textile apparel distribution network. This system is composed of several models (Fig. 2) which meet the various requirements of distributors (mid- and short-term forecasts on aggregate data by family, item, size and color) according to features in the textile market (influence of explanatory variables, seasonality, reduced historical data) (Thomassey et al., 2002b).

xiAþ1 ðtÞ x# iAþ1 x## iAþ1 ðt þ 1Þ uiN

xNi uNi u iA+1

Xˆ AF+1

AHFCCX

period number (week) per season (or year) historical season number available historical sales data of season N for family F ; NpA sales at last known period t of season A þ 1; for family F mid-term sales forecast of season A þ 1 for family F short-term sales forecast at period t þ 1 of season A þ 1 for family F selected explanatory variables of season N for family F item historical sales data of season N for item i last known item sale of season A þ 1 for item i mid-term item sales forecast of season A þ 1 for item i short-term item sales forecast at period t þ 1 of season A þ 1 for item i descriptive criteria for items clustering of season N for item i

Short-term forecast

Mid-term forecast

X NF U NF U AF+1

83

Forecast by family

F (t) X A+ 1

SAMANFIS

ˆ Xˆ AF+1(t +1)

SAMANFIS

xˆˆ iA +1(t +1)

SAMANFIS

xˆˆi,C A +1(t +1)

Forecast by item

IDAC

xˆ iA+1 xiA+1(t) Forecast by size and color

xNi,T xˆi,C A+1

Distribution size - color

xˆ i,T A+1 xˆ CA+1 x i,C A+1(t)

Fig. 2. Global forecast system principle.

ARTICLE IN PRESS S. Thomassey et al. / Int. J. Production Economics 96 (2005) 81–95

84

xi;T N xi;C Aþ1 ðtÞ x# i;T Aþ1 x# i;C Aþ1 x## i;C Aþ1 ðt þ 1Þ

historical sales data by size T of season N for item i last known sale by color C of season A þ 1 for item i mid-term sales forecast by size T of season A þ 1 for item i mid-term sales forecast by color C of season A þ 1 for item i short-term sales forecast by color C at period t þ 1 of season A þ 1 for item i

*

*

The major difficulty is to quantify the influence of the explanatory variables. This problem can be solved by a fuzzy inference system (FIS) (see Appendix A on fuzzy theory) whose training procedure (founded on neuronal or genetic tools) exploits expert knowledge (Thomassey et al., 2001, 2002c). Indeed, the influence of some EVs on the sales, such as promotions, is a quite vague concept, which can be treated efficiently by a FIS (Kuo, 2001). However, taking into account of the numerous references number (322 families), reliance on expert intervention becomes unsuitable. The proposed AHFCCX model is based on an automatic learning of a Takagi–Sugeno FIS (Sugeno, 1985; Takagi and Sugeno, 1985) from historical data. The structural (choice of the inference rules) and parametric adjustments are established by a genetic algorithm and a gradientbased method, respectively (Thomassey et al., 2002a).

2.2. Family sales forecasting In order to treat the sales seasonal behavior and the influence of explanatory variables, forecasting models need complete historical data of several years. To obtain such as historical textile data, aggregation of each product is required. 2.2.1. Mid-term family sales forecasting: AHFCCX model In order to reduce the number of parameters to optimize, we have, when forecasting the mid-term horizon, chosen a family sales forecasting model based on separation of seasonality and the EVs. This automatic modeling principle, called Automatic Hybrid Forecasting model with Corrective Coefficient of eXplanatory variable influences (AHFCCX), mainly consists (Fig. 3) in: *

2.2.2. Short-term family sales forecasting: SAMANFIS model The purpose of the short-term forecasting model is not intended to model the influence of the explanatory variables and the seasonality of sales, but to readjust the mid-term forecasts X# FAþ1 of the last sales XAF ðtÞ: In this context, adaptation and

extracting the influence of EVs (price, data calendar) of the historical sales,

X

F N

Extraction of U NF influence

applying a simple forecasting model based on sales seasonality and not taking into account the influence of EVs, adding the influence of EVs of the future season to forecasts obtained from the past.

Application of

Seasonality based forecast

U AF+1 influence

corrective coefficients

U NF

Fuzzy inference system

corrective coefficients

Automatic learning procedure

X NF

U AF+1

U NF

Fig. 3. Principle of AHFCCX model.

Fuzzy inference system

Xˆ AF+1

ARTICLE IN PRESS S. Thomassey et al. / Int. J. Production Economics 96 (2005) 81–95

training capacities of neural techniques thus appear very useful. The main constraint is to model complex relationships with limited historical data. Earlier work has showed the limitations of neural networks, which require too many parameters to optimize for such strategy (Thomassey et al., 2002d). We developed the model short-term forecasting model by adjustment of mid-term forecast adaptive neural fuzzy inference system (SAMANFIS) (Fig. 4) based on a neuro-fuzzy system ANFIS (Jang, 1993) which translates a FIS into a neural network. The application of a neurofuzzy system is justified as a better model for interpretation (Kuo and Xue, 1999) which allows some adjustments of parameters by the operator, such as the input membership functions classical parameters (Jang, 1993; Klir and Yuan, 1995). Thus, this procedure reduces the data requirements training. The input’s space (Fig. 4) is composed of real F sale ðXAþ1 ðtÞÞ and the mid-term sale forecast (AHFCCX model) ðX# FAþ1 ðtÞÞ of the last week, and mid-term sale forecasting of the future week ðX# FAþ1 ðt þ 1ÞÞ: The model output is the short-term forecast ðX## FAþ1 ðt þ 1ÞÞ: In order to limit the number of parameters, only two fuzzy sets (‘‘low’’/‘‘high’’), are defined for each input. Thus, the number of rules, derived from three previous inputs, is equal to r ¼ 2  2  2 ¼ 8: Each rule, which is associated with a constant output membership function (Cj where 1pjpr), is given by the following relationship: F IF XAþ1 ðtÞ is low AND X# FAþ1 ðtÞ is high AND X# FAþ1 ðt þ 1Þ is high THEN X## FAþ1 ðt þ 1Þ is Cj : The neural network is composed of three hidden layers which translate respectively the input membership function, the inference rules

system and the output membership functions of the FIS. 2.3. Item sales forecasting The approach is different compared to the family sales forecasting model. Items references (i) are generally not renewed and have a very short lifetime (6–12 weeks) compared with the families sales periodicity (52 weeks). Correspondence between items, codified in alpha-numeric characters, is also often lost from one season to another. Generally, historical sales of new items data are not available. The only accessible historical data are the last seasons items sales of the respective item family ðF Þ: However, the distributor can provide various criteria concerning future items such as life time, price, number of stores distributing the item, different number of colors, etc., which will permit a new item to be classified into an appropriated family. 2.3.1. Mid-term items sales forecasting: IDAC model Generally, the items of a new collection do not have a historical data (95% of items are not renewed). The use of the mid-term forecasting AHFCCX model is unsuitable. The proposed model, called IDAC (Items forecasting model based on Distribution of Aggregated forecast and Classification) (Thomassey et al., 2002e) estimates the item ðiÞ sales of the same family ðF Þ without requiring historical data. This model is based on the family sales forecasts distribution (computed by model AHFCCX) from the life curves achieved by a classification procedure. This last method integrates the descriptive criteria of

Xˆ AF+1(t +1)

Inference system

Artificial neural network

Output membership functions

Xˆ AF+1(t)

input membership functions

Fuzzy inference system (Sugeno)

F (t) X A+ 1

85

Fig. 4. Principle of SAMANFIS model.

ˆ Xˆ AF+1 (t+1)

ARTICLE IN PRESS S. Thomassey et al. / Int. J. Production Economics 96 (2005) 81–95

86

xNi

uNi

Classification

Xˆ AF+1

u iA+1 Cluster life curve computation

Future items sales profile estimation

Family sales forecasting distribution

xˆ iA+1

Fig. 5. Principle of IDAC model.

items which are available in the distributor database such as average prices, number of stores distributing the item or variety colors. The principle of model IDAC is as follows (Fig. 5):

quantity sales estimated for the family F at period t

Xˆ AF+1(t)

"sale profile" coefficient at period t : ck (t)

"sale profile" coefficient at period t :ci (t) item i profile

*

*

*

*

*

a partition PðcÞ; composed of c classes, is carried out from historical items sales data of the same family, similar according to the descriptive criteria quoted previously, historical sales data belonging to the same cluster allow computation of a specific life curve, new items are associated with the cluster, defined by the appropriate descriptive criteria, whose centro.ıd is the closest, the estimated sale profiles of the future items are characterized by the life curve of their associated cluster and adapted to their lifespan, finally, from these specific profiles, the sales forecast of each future item i ðx# iAþ1 Þ is defined by distributing the corresponding family forecasts ðX# FAþ1 Þ according to the life curves (Fig. 6), and translated by the following relationship: ci ðtÞX# F ðtÞ x# iAþ1 ðtÞ ¼ PNI Aþ1 ; j¼1 cj ðtÞ

item k profile

weeks

t life time of item i life time of item k

Fig. 6. Example of family forecast distribution on two items.

the difficulties of training become acute. Thus, contrary to the family forecast where system training is carried out for each family reference, the parameters are estimated using the overall historical items sales data belonging to the same family. The short-term sales forecasting of each new item in the same family, is computed from the SAMANFIS model identically to the family forecast. 2.4. Sales forecasting by color and size

where NI is the number of items (NI ¼ 2 in example of Fig. 6) and cj ðtÞ is the life curve coefficient of item j at period t:

The finer the data aggregation level is, the more difficult the forecast is. Difficulties encountered in the preceding section (limited historical data and references not renewed) are thus amplified, especially for forecasts by color.

2.3.2. Short-term item sales forecasting: SAMANFIS model The principles of the short-term family and item forecast are identical. Thus, the same SAMANFIS forecasting model can be applied. However, taking into account the reduced number of data per item (short items lifetime),

2.4.1. Sales forecasting by color Generally, the various colors of a collection are selected according to the fashion evolution and are not renewed from one season to another, except for the basic colors (white, black, etc.). Sometimes, they are also added or withdrawn during the item life time. Due to these constraints, experts must

ARTICLE IN PRESS S. Thomassey et al. / Int. J. Production Economics 96 (2005) 81–95 Experts knowledge

xˆ Ai +1

Sales distribution by color

xˆ CA+1

SAMANFIS

xˆˆ CA+1(t +1)

xCA+1(t)

Fig. 7. Forecasting model by color principle.

intuitively estimate forecasts by color from their market knowledge. In this context, automation appears difficult. The system under consideration (Fig. 7) relies on the forecast distribution already established by item. The initial distribution is carried out by the expert (or if possible by the history), and the on going sales allow adjustment of forecasts using SAMANFIS model. 2.4.2. Sales forecasting by size Contrary to forecasting difficulties associated with color, the forecasts by size can be estimated relatively easily by the distributor. The distribution of sizes remains steady from season to season; therefore, historical data can constitute a reliable information source. Thus, the proposed sales forecasting method is based on the corresponding items sales distribution, computed according to the historical data. The mid-term forecasts being generally reliable, the short-term readjustment according to the last sales is not necessary for the sizes.

3. Experimentation In this section, we validate the performance of our models with a real database from the past three years (1998, 1999 and 2000), which is composed of 322 families and 42000 items from a large French textile distributor. The first 2 years are employed for the training of the models’ parameters and the third year evaluates the forecasts’ accuracy. 3.1. Traditional models for comparison These traditional models, tested on the mid- and short-term families and items sales forecasting, are:

87

Basic model with seasonality (BMS): Basic model BMS, applied for the mid-term families sales forecasting, is founded on the average seasonality of historical data. Holt winter model with seasonality (HWS): This model, tested on the families’ sales at mid- and short-term, is based on the multiplicative seasonality principle and takes into account of the mean and the trend of the series. The optimization of parameters is carried out by least squares. Automatic model selection by the Forecast Pro software (AS-FP): These models do not take into account the available explanatory variables and are applied for comparative families’ sales forecasting at mid and short-term. The Forecast Pro software selects one of the three models (moving average, exponential smoothing, Box & Jenkin’s), most adapted to the series and then optimizes its parameters. Various statistical tests are also carried out automatically to detect series stationary and the seasonality. ARMAX model (Franses, 1999): In order to include an additional model with explanatory variables in the comparisons, we also tested an ARMAX model for mid- and short-term family sales forecasts. The parameters are optimized by a Gauss iterative Newton algorithm (Ljung, 1987). The explanatory variables used (Section 3.3) are the same as in our proposed models (AHFCCX and SAMANFIS), i.e. UNF for mid-term family sales forecasting and X# FAþ1 for short-term family sales forecasting. IDA model: This model (Thomassey et al., 2002e) relies on the same sales forecasting distribution principle as IDAC model. The estimation of the sales profiles of new items results from the sales profile average of all historical items belonging to each family. Basic distribution model (RB): The model RB, which is used for new items without proper history, uniformly distributes the family forecasts by the following relationship: x# iAþ1 ðtÞ ¼

X# FAþ1 ðtÞ ; NIðtÞ

ARTICLE IN PRESS S. Thomassey et al. / Int. J. Production Economics 96 (2005) 81–95

88

where NIðtÞ is the number of items which sold at period t:

models on numerous series (Armstrong and Collopy, 1992).1992).

3.2. Accuracy criteria

3.3. Family sales forecasting

In order to quantify the errors of tested models, we selected the following two criteria:

The performances of mid-term forecasting models BMS, AS-FP, HWS, ARMAX and AHFCCX are evaluated for 322 families (composed of 41 966 items). The explanatory variables by the AHFCCX mid-term automatic forecasting model were selected by textile market experts in accordance to their perceived significance but also for their availability in the database. The only EVs included are: the selling price per week and holiday periods.

*

Root Mean Square Error sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Xp ðRMSEÞ ¼ e2 ðtÞ: t¼1 p This criterion strongly penalizes large forecasts errors. It is expressed in the same unit as the studied series. RMSE criterion or its alternative MSE ¼ RMSE2 ; is frequently applied. However, its strong penalization of large errors and its poor reliability for comparing models on several series are particularly criticized (Armstrong and Collopy, 1992; Armstrong and Fildes, 1995; Fildes et al., 1998; Thompson, 1990). Nevertheless, the RMSE which describes the magnitude of the errors, is relatively more useful to decision makers (Armstrong and Collopy, 1992) because they could, for example, interpret this criterion as stock holding costs. Thus, practitioners generally prefer the RMSE to all other error measures (Carbon and Armstrong, 1982).

*

3.3.1. Mid-term family sales forecasting The AHFCCX model, which separately integrates sales seasonality and the influence of EVs, permits training of parameters on relatively limited historical data. The procedure is suitable to process many products automatically. Thus, the AHFCCX model, tested for 322 families on a 52week horizon, significantly improves the accuracy criteria RMSE and MdAPE compared to traditional models (Fig. 8). We can also see that the ARMAX model is less efficient than AS-FP and HWS models in our simulation. Despite this model taking into account the EVs, its linear structure is unable to map series with short historical data. 3.3.2. Short-term family sales forecasting Three models, HWS, ARMAX and SAMANFIS tested for 322 families on a one-week horizon, ensure a reduction of the mid-term forecasting model (AHFCCX) error (Figs. 9 and 10). The SAMANFIS model gives the best performance

Median absolute percentage error ðMdAPEÞ ¼ median value of APEt ¼ jeM;t =xt j classified by ascending order of the considered series.

improvement in %

The MdAPE criterion, only slightly sensitive to aberrant points, is recommended to compare

40

35.8

RMSE

29.6 30 20

15.7

MdAPE

21 9.1

10

9.7

0 AS-FP

ARMAX

HWS

Fig. 8. Average improvements achieved by AHFCCX model (RMSE ¼ 885; MdAPE ¼ 47:2) on 322 families.

ARTICLE IN PRESS

improvement in %

S. Thomassey et al. / Int. J. Production Economics 96 (2005) 81–95

40

RMSE

33

MdAPE

30

89

27

23 16.7

20 10

5.2

2

0 HWS

ARMAX

SAMANFIS

Fig. 9. Average improvements achieved by short-term forecasting models, comparing to the AHFCCX mid-term forecasting model ðRMSE ¼ 885; MdAPE ¼ 47:2Þ on 322 families.

14000

real sales AHFCCX

sales

SAMANFIS

9 -4

5 00 20

-4

1 -4

00 20

7 20

00

-3

3 20

00

-3

9 20

00

-2

5 -2

00 20

1 20

00

-2

7 -1

00 20

3 -1

00 20

00

-0

9 20

5 -0

00 20

00 20

20

0-

10

0

weeks

Fig. 10. Example of AHFCCX (mid-term) and SAMANFIS (short-term) forecasting models on a women’s sweater family.

with the MdAPE criterion. However, the ARMAX model proves more precise according to the RMSE criterion.

100 90 80

The three mid-term items sales forecasting models RB, IDA and IDAC, and short-term SAMANFIS model are tested on the 4070 items sales from families with the highest sales turnover.

Stores number

70

3.4. Items sales forecasting

60 50 40 30

center of clusters

20

item

10

3.4.1. Mid-term item sales forecasting The criteria used for items classification of IDAC model are average price and number of stores distributing the item. The choice of criteria is justified by their influence on the sales and their availability. The envisaged classification procedure is a hierarchical type, which joins individual items or clusters together sequentially. The IDAC model classification procedure generates, for the same family, clusters quite distinctive according to item price and number of stores

0 0

10

20

30

40

50 60 Price

70

80

90

100

Fig. 11. Eleven clusters resulting from women T-shirt classification.

distributing the item (Fig. 11). Thus, we can hope that the estimated sale profile of each cluster is more accurate than the average profile computed (IDA model) for all items included in the same family (Fig. 12).

ARTICLE IN PRESS S. Thomassey et al. / Int. J. Production Economics 96 (2005) 81–95 cluster 2 cluster 5

0.1

average profile 0.05

52

49

46

43

40

37

34

31

28

25

22

19

16

13

10

7

4

0 1

sales profile adapted to 52 weeks

90

weeks

Fig. 12. Example of cluster center life curve and average profile.

real sales RB IDA IDAC

real sales RB IDA IDAC

1200

sales

sales

2500

0

00 20 -32 00 20 -34 00 20 -36 00 20 -38 00 20 -40 00 20 -42 00 20 -44 00 20 -46 00 20 -48 00 20 -50 00 -5 2

0 -3

20

00 20

20 00 20 01 00 20 04 00 20 07 00 20 10 00 20 13 00 20 16 00 20 19 00 20 22 00 20 25 00 20 28 00 -3 1

0

weeks

weeks

Fig. 13. Examples of RB, IDA and IDAC models forecasts.

3.4.2. Short-term item sales forecasting The last sales of the season allows an important readjustment of the IDAC model forecasts on a 1week horizon, in particular the quantity (mid-term

30 improvement in %

However on a 52-week horizon, the results are sometimes ambiguous. In fact, the IDAC forecasting model is often more accurate than either the RB or the IDA models (Fig. 13), in particular the estimation of the item sale profiles; nevertheless, an inadequate sales quantity forecast of some items is strongly penalized by the RMSE criterion because of its scale dependence. Thus, the RB model delivers the best average performance in terms of RMSE, compared with the IDAC model (Fig. 14), whilst the IDAC model is substantially better as measured by MdAPE. This difference arises because the RMSE error measure weights the larger volume items.

RMSE MdAPE

25

21

20 10 1.2 0 -10

-4.6

RB

IDA

Fig. 14. Average improvements achieved by IDAC model ðRMSE ¼ 8906; MdAPE ¼ 128Þ on 4070 items.

sale profile estimation are generally relatively correct). Thus, the short-term SAMANFIS forecasting model permits a significant improvement of the mid-term IDAC forecasting model: RMSE and MdAPE criteria decrease of 55% and 36%, respectively. These results indicate the benefit to re-estimating the forecasts each week, especially on the item aggregation level where the mid-term forecast accuracy is sometimes uncertain.

ARTICLE IN PRESS S. Thomassey et al. / Int. J. Production Economics 96 (2005) 81–95

3.5.1. Sales forecasting by size The analysis of Fig. 15 reveals, over 3 years, a relatively stable sales distribution on the four traditional sizes of the 2520 items belonging to a T-shirt short sleeves woman family. In general, the sales forecast by size appears to be highly reliable and easy to evaluate.

26%

9%

9%

2000

23%

23%

35%

1999 11%

34%

33%

31%

33%

sales distribution in %

1998

33%

3.5.2. Sales forecasting by color The forecasts by color is more complex to evaluate, in particular by the need to rely on estimates from the experts. It is generally very difficult to obtain these data within textile distribution. The tests are carried out on two women T-shirt items available in three basic colors (black, gray, white) and ten fashion colors (red/ kaki, rust/red, etc.). The initial sales distribution on the item basic colors is relatively easy for an expert to determine and the SAMANFIS model ensures a precise distribution readjustment according to the latest sales. The accuracy improvement of the RMSE criterion is, respectively of, 29%, 28% and 6%, for white, gray and black colors. However, the sales distribution for fashion colors fluctuates much more. The expert estimates of the quantities distributed between the various colors is more difficult (Fig. 16). The SAMANFIS model also gives results which are more difficult to interpret and does not systematically improve the

0% S

L

M

XL

sizes

Fig. 15. Size distribution for a T-shirt short sleeves woman family.

19

-4

GREENNAVY BLUE

RUST/RED

RED/KHAKI

NAVY BLUE/GREEN

5 YELLOWHAKI

-9

10 GREY/WHITE

WHITE/GREY

-20

BLUE/WHITE

7

7 0

32 18

20

BEIGE/WHITE

improvement in %

Due to the numerous item/size/color references, our study of sales by size and color is restricted to the 2520 items of the same T-shirt short sleeves woman family, for the years 1998, 1999 and 2000.

40%

36

40

KHAKI/RED

3.5. Sales forecasting by size and color

91

Fig. 16. RMSE Average improvement achieved by SAMANFIS short-term model comparing to expert distribution on fashion colors.

initial expert distribution when incorporating the sales (Fig. 16, color white/gray and rust/red).

4. Conclusion and prospects From real data provided by a major textile distributor, we have applied our global system which is composed of various forecasting models. These deal with sales forecast aggregated at different levels, for mid- and short-term horizons. The use of real data forces the proposed models to take into account the strong constraints of the textile industry. The mid-term family sales forecasting performed by a model, based on a FIS (AHFCCX model), integrates separately and automatically the sales seasonality and the influence of EVs. The short-term family sales forecasting is completed by the SAMANFIS model, founded on a neuro-fuzzy procedure. This principle of the model is to readjust, from the latest observed sales, the midterm forecasts of the AHFCCX model. The principle of the IDAC model, which forecasts the mid-term sales items, relies on the family forecast distributions of the corresponding items and on the life curve estimation from a classification procedure. As the items are generally not renewed from one season to another, the principal problem for this model remains the difficulty in exploiting the historical sales of new items. The short-term items sales forecasting is computed by a neuro-fuzzy SAMANFIS model, which is also used at the family level. This model readjusts the IDAC model mid-term forecasts. Taking into account the uncertainty of the

ARTICLE IN PRESS 92

S. Thomassey et al. / Int. J. Production Economics 96 (2005) 81–95

mid-term forecasts, the improvement carried out by SAMANFIS model is very important. The textile items sales distribution by size is relatively stable. Thus, the forecast by size is computed using a basic historical distribution. The sales distribution on colors, which is very sensitive to fashion phenomena, requires expert intervention. This intuitive method, supplemented by the short-term SAMANFIS model readjustment, gives acceptable results for basic colors (white, gray, black) but is inadequate for fashion colors. Improvements in forecasting by color requires the integration of qualitative data on fashion tendencies. However, our experimental results have the potential to be refined and lead us to consider future developments in to the following thematic areas: *

*

*

*

*

to take into account more effectively the influence of EVs on family sales, to improve the AHFCCX model training procedure by clustering the families, to implement the short-term SAMANFIS forecasting model for a longer horizon (2–3 weeks) sometimes required for the stores sourcing, to more accurately determine item sales, by using a classification procedure which includes qualitative parameters characterizing the products (style, raw material, etc.), to develop more effective methods for the sales by color, by integrating the fashion phenomena.

This sales forecasting system can be associated with a simulation and provisioning optimization tool (Sboui, 2003) in order to produce a complete decision-making aid. Currently this tool, developed by the ‘‘Institut Fran@ais du Textile et de l’Habillement’’ (IFTH), appears as a service accessible from the Internet to each actor from the textile network.

Appendix A. Fuzzy theory and fuzzy inference system for AHFCCX model Fuzzy set theory was introduced by Zadeh (1965). Major fields of applications include analysis and classification, statistics and data analysis,

image processing, speech recognition, decision making and finance (Klir and Yuan, 1995). A.1. Basic concepts All the classical set-theoretic operations can be extended to the fuzzy theory. Suppose A and B are fuzzy sets with membership functions mA and mB : The union A,B; intersection A-B and complement Ac are also fuzzy sets with, respectively, the following membership functions: mA,B ðxÞ ¼ maxðmA ðxÞ; mB ðxÞÞ; mA-B ðxÞ ¼ minðmA ðxÞ; mB ðxÞÞ and mAc ðxÞ ¼ 1  mA ðxÞ: Other operators, using an axiomatic basis have been introduced to extend the classical settheoretic operations (Fodor and Roubens, 1994). These operators referred to as t-norms for the intersection, t-conorms for union, and negations for the complement, extend the classical logic settheoretic operations since they reduce to their binary logic counterparts when the valuation set is restricted to f0; 1g: The fuzzy extension of the classical modus ponens principle allows the construction of fuzzy inference systems (Dubois and Prade, 1991). These systems encode fuzzy statements with the following form: IF X is A THEN Y is B where A and B are fuzzy sets. A.2. Takagi–Sugeno fuzzy systems Usually, rules are processed and combined in systems called FIS. Takagi–Sugeno fuzzy systems (Sugeno, 1985; Takagi and Sugeno, 1985) are a very special class of fuzzy systems because the consequence of each rule is a scalar. A typical single antecedent fuzzy rule in a zero order Takagi–Sugeno model (TS0) has following the form: IF X is A THEN Z ¼ C where A is a fuzzy set with membership function mA and C is a constant. The output Z of a TS0 system processing the r rules (IF X is Ak THEN Z ¼ Ck ) can be then written: Pr m ðX ÞCk Pr Ak z ¼ k¼1 : k¼1 mAk Fig. 17 represents the inference process with r ¼ 2:

ARTICLE IN PRESS S. Thomassey et al. / Int. J. Production Economics 96 (2005) 81–95

93

mA1(X1) A1

R1

a1 mA2(X1)

x1

X1

Z

z1 = c1

F

UN

Rj

Rr

C1 Cj

C NF

A2

Cr

a2

X1 x1

z2 = c2

Z

Fig. 18. The FIS of the AHFCCX model. z = a1z1+a2z2

IF ‘‘selling price’’ is SPi AND ‘‘holidays’’ is Hj AND ‘‘holidays-1’’ is Hk AND

Z z

Fig. 17. Inference process of a zero-order Takagi–Sugeno fuzzy system (1 input, 2 fuzzy sets).

A.3. Implementation In order to treat the influence of EVs, the AHFCCX model is composed of a FIS (Fig. 18). The input space is built with the EVs fUNF g series that influence the sales predictions. The selected EVs should be the most important ones, but they must be also available. According to the experience of marketing managers in the industry, the chosen variables (Thomassey et al., 2002a) are: selling price, holiday periods and year sequences. In order to locate the beginning and end of holiday periods, a fourth input variable is chosen: holidays with a lag of one week. The selling price and holiday variables are associated to two fuzzy sets: ‘‘promotion’’/‘‘no promotion’’ and ‘‘holidays’’/‘‘school’’, respectively. The year sequence variable is associated to five fuzzy sets: ‘‘All’s Saint Days’’/‘‘Christmas’’/ ‘‘Winter’’/‘‘Eastern’’/‘‘Summer’’. The output of the FIS is the Corrective Coefficient fCNF g of the influence of EVs. Output membership functions are singletons (TS0). Each rule is associated with an output membership function. The rules (Rj where 1pjpr) are of the form:

‘‘period sequence’’ is PSn THEN ‘‘Corrective Coefficient’’ is Cm ; where SPi ; Hj ; PSn and Cm are the fuzzy sets described previously. Thus, before the selection of rules, the inference system is composed of: 2  2  2  5 ¼ 40 rules. We apply the generalized Gaussian-type membership functions for the coding of the inputs: mAk ðX Þ ¼ GðX Þ where G is defined by GðxÞ ¼ 2 eðxmÞ =2s : Using Gaussian membership functions ensures our fuzzy system is complete, i.e. for every input, at least one of the fuzzy rules is activated. The FIS learning process is composed of two stages: *

*

output membership functions are tuned with a least-square optimization: the Levenberg–Marquardt method (More! , 1977), rules are selected by genetic algorithms.

References Armstrong, J.S., 2001. Principles of Forecasting—A Handbook for Researchers and Practitioners. Kluwer Academic Press, Norwell, MA. Armstrong, J.S., Collopy, F., 1992. Error measures for generalizing about forecasting methods: empirical comparisons. International Journal of Forecasting 8, 69–80. Armstrong, J.S., Fildes, R., 1995. Correspondence on the selection of error measures for comparisons among forecasting methods. Journal of Forecasting 14, 67–71.

ARTICLE IN PRESS 94

S. Thomassey et al. / Int. J. Production Economics 96 (2005) 81–95

Bell, M., Kuster, . U., 1999. The Forecasting Report—A Comparative Survey of Commercial Forecasting Systems. IT Research, Germany. Carbon, R., Armstrong, J.S., 1982. Evaluation of extrapolative forecasting methods: Results of a survey of academicians and practitioners. Journal of Forecasting 1, 215–217. Collopy, F., Adya, M., Armstrong, J.S., 2001. Expert systems for forecasting. In: Armstrong, J.S. (Ed.), Principles of Forecasting—A Handbook for Researchers and Practitioners. Kluwer Academic Press, Norwell, MA, pp. 283–300. Dasgupta, C.G., Dispensa, G.S, Ghose, S., 1994. Comparative the predictive performance of a neural network model with some traditional market response models. International Journal of Forecasting 10, 235–244. De Gooijer, J.G., Kumar, K., 1992. Some recent development in non linear time series modeling, testing, and forecasting. International Journal of Forecasting 8, 135–156. De Toni, A., Meneghetti, A., 2000. The production planning process for a network of firms in the textile-apparel industry. International Journal of Production Economics 65, 17–32. Dubois, D., Prade, H., 1991. Fuzzy sets in approximate reasoning, Part 1: Inference with possibility distributions. Fuzzy Sets and Systems 40, 143–202. Fildes, R., Hibon, M., Makridakis, S., Meade, N., 1998. Generalizing about univariate forecasting methods: Further empirical evidence. International Journal of Forecasting 14, 339–358. Fodor, J., Roubens, M., 1994. Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer Academic Publishers, Boston, USA. Franses, P.H., 1999. Time Series Models for Business and Economic Forecasting. Cambridge University Press, Cambridge, UK. Graves, S.C., Kletter, D.B., Hetzel, W.B., 1998. A dynamic model for requirements planning with application to supply chain optimization. Operations Research 46, 35–49. Hamilton, J.D., 1994. Time Series Analysis. Princeton University Press, NJ, USA. Hill, T., Marquez, L., O’Connor, M., Remus, W., 1994. Artificial neural network models for forecasting and decision making. International Journal of Forecasting 10, 1–15. Jang, J.S.R., 1993. ANFIS: Adaptive network based fuzzy inference system. IEEE Transactions on Systems, Man and Cybernetics 23 (3), 665–681. Klir, G.J., Yuan, B., 1995. Fuzzy Sets and Systems, Theory and Applications. Prentice-Hall, Englewood Cliffs, NJ. Kuo, R.J., 2001. A sales forecasting system based on fuzzy neural network with initial weights generated by genetic algorithm. European Journal of Operational Research 129, 496–517. Kuo, R.J., Xue, K.C., 1998. A decision support system for sales forecasting through fuzzy neural network with asymmetric fuzzy weights. Decision Support Systems 24, 105–126.

Kuo, R.J., Xue, K.C., 1999. Fuzzy neural networks with application to sales forecasting. Fuzzy Sets and Systems 108, 123–143. Lee, H.L., Sasser, M.M., 1995. Product universality and design for supply chain management. Production Planning and Control 6 (3), 270–277. Ljung, L., 1987. System Identification—Theory for the User. Prentice-Hall, Englewood Cliffs, NJ. Mastorocostas, P., Theocharis, J., Kiartzis, S.J., Bakirtzis, A.G., 2000. A hybrid fuzzy modeling method for short-term load forecasting. Mathematics and Computers in Simulation 51, 221–232. Mor!e, J.J., 1977. The Levenberg Marquardt Algorithm: Implementation and Theory, Numerical Analysis. In: Watson, G.A. (Ed.),, Lecture Notes in Mathematics, Vol. 630. Springer, New York, USA, pp. 105–116. Sboui, S., 2003. Mod!elisation, e! valuation des performances et optimisation des flux logistiques d’un r!eseau d’entreprises partenaires dans la fili"ere THD. Th"ese de l’Universit!e des Sciences et Technologies de Lille I, France. Shimojima, K., Fukuda, T., Hasegawa, Y., 1995. Self-tuning fuzzy modeling with adaptative membership function, rules, and hierarchical structure based on genetic algorithm. Fuzzy Sets and Systems 71, 295–309. Sugeno, M., 1985. Industrial Applications of Fuzzy Control. Elsevier Science Publishers, Amsterdam. Takagi, T., Sugeno, M., 1985. Fuzzy identification of systems and its applications. IEEE Transactions on Systems, Man and Cybernetics 15 (1), 116–132. Thomassey, S., Vroman, P., Happiette, M., Castelain, J.M., 2001. A comparative test of new mid-term forecasting models adapted to textile items sales. Studies in Informatics and Control 10 (3), 209–225 http://www.ici.ro/ici/revista/ sic.html. Thomassey, S., Happiette, M., Castelain, J.M., 2002a. An automatic textile sales forecast using fuzzy treatment of explanatory variables. Journal of Textile and Apparel, Technology and Management 3(1); http://www.tx.ncsu. edu/jtatm/. Thomassey, S., Happiette, M., Castelain, J.M., 2002b. Three complementary sales forecasting models for textile distributors, IEEE SMC’02, International Conference on Systems, Man and Cybernetics, Hammamet, Tunisia, October 6–9. Thomassey, S., Happiette, M., Castelain, J.M., 2002c. Mod"ele de pr!evision des ventes a" moyen terme avec traitement flou des variables explicatives—Application a" la logistique textile, Journal Europ!een des Syst"emes Automatis!es JESA, 36(8). Thomassey, S., Happiette, M., Castelain, J.M., 2002d. A short-term forecasting system adapted to textile distribution. IPMU 2002, Annecy, France, July 8–9, pp. 1889–1893. Thomassey, S., Happiette, M., Castelain, J.M., 2002e. Textile items classification for sales forecasting. ESS 2002. Fourth European Simulation Symposium and Exhibition Simulation in Industry, Dresde, Germany, October 23–26.

ARTICLE IN PRESS S. Thomassey et al. / Int. J. Production Economics 96 (2005) 81–95 Thompson, P.A., 1990. An MSE statistic for comparing forecast accuracy across series. International Journal of Forecasting 6, 219–227. Tong, H., 1990. Non-linear Time Series: A Dynamical System Approach. Oxford University Press, Oxford, UK. Van Lith, P.F., Betlem, B.H.L., Roffel, B., 2000. Fuzzy clustering, genetic algorithms and neuro-fuzzy methods compared for hybrid fuzzy-first principles modeling. ISIAC 2000, June 11–16. Wasserman, P.D., 1989. Neural Computing: Theory and Practice. Van Nostrand Reinhold, New York, USA. West, M., Harrisson, P.J., 1997. Bayesian Forecasting and Dynamic Models, 2nd Edition. Springer, New York, USA.

95

White, H., 1992. Artificial Neural Networks: Approximations and Learning Theory. Blackwell, Oxford, UK. Yoo, H., Pimmel, R.L., 1999. Short-term load forecasting using a self-supervised adaptive neural network. IEEE transactions on Power Systems 14 (2), 779–784. Zadeh, L.A., 1965. Fuzzy sets. Information and Control 8 (3), 338–353. Zadeh, L.A., 1994. Fuzzy Sets, Fuzzy Logic and Fuzzy Systems: Selected Papers by Lotfi A. Zadeh. River Edge, Singapore. Zhang, G.B.E.P., Hu, M.Y., 1998. Forecasting with artificial neural networks: The state of the art. International Journal of Forecasting 14, 35–62.