A Fuzzy-Control-Based Quick Response Reorder Scheme for Retailing of Seasonal Apparel. Ta-Wei Hung, S.-C. Fang, H.L.W. Nuttle, R.E. King. Operations ...
A Fuzzy-Control-Based Quick Response Reorder Scheme for Retailing of Seasonal Apparel Ta-Wei Hung, S.-C. Fang, H.L.W. Nuttle, R.E. King Operations Research and Industrial Engineering North Carolina State University, Raleigh, N.C., U.S.A.
more traditional procedures for seasonal apparel to investigate of the underlying performance differences between the two operating paradigms, as well as to explore the limitations on QR effectiveness imposed by season length and the number of items offered per SKU4-6.
Abstract A fuzzy-control-based Quick Response (QR) reorder scheme for seasonal apparel is being developed. The fuzzy-control scheme uses Mamdani inference logic. A stochastic computer simulation model of the apparel-retailing process is employed to evaluate the performance of the proposed scheme vis-a-vis that of existing approaches.
In this paper we develop a fuzzy-controlbased alternative to the QR reorder schemes that have been examined in the previous studies.
Background
Simulation Model of QR Retailing Process for Seasonal Apparel7
“Quick Response” (QR) for apparel retailing refers to the application of well-defined quality-management and industrial engineering practices, together with the use of available hard and soft technologies, to reduce significantly the length of the apparel pipeline and thus opening the door to a different supply procedure1. Research has shown that the successful implementation of QR for apparel retail involves: a collapsed and responsive supply system; smaller initial store inventories of garments; Point-of-Sale (POS) tracking; bar-coding of merchandise and Electronic Data Interchange (EDI); continual reestimation of a season's customer demand; and frequent reorders on the vendor that allow matching of the stock-keeping-unit (SKU) assortment being offered to what the customer wants1-3.
Initial Supply
Reorders
Retail SKU Inventory
Consumer Purchases
Fig. 1 Simplified view of the model
As shown in simplified form in Fig. 1, the model tracks the inventory by SKU at the retail store week by week. This inventory is affected by the initial supply, any reorders that arrive during the season, and consumer purchases. There is an underlying consumer demand expressed in terms of customer volume, SKU mix, and seasonality of demand (i.e. percentage of customer volume in each week). The volume, mix, and seasonality of demand are unknown and must be estimated by the retail buyer. The buyer's plan (preseason) also determines the initial supply. Within the season, the buyer may employ one of several alternative techniques for re-estimating the season's demand and incorporate the re-estimate in a scheme for issuing reorders to the apparel manufacturer. The buyer may also employ price reductions (markdowns) in order to stimulate sales.
Nuttle et al. (1991) developed a stochastic simulation model of the apparel-retailing process for a retail store selling seasonal apparel, i.e., merchandise with a shelf life of 4-6 months. The model was designed to explore the applicability and benefits of QR vis-a-vis traditional retailing procedures and, in particular, to aid in the development of demand re-estimation and reorder algorithms capable of adjusting the SKU mix on the shelves to reflect true, as opposed to buyer forecast, consumer desires. The model has been used to quantify the retail performance characteristics (service and economic) of QR and
A major requirement of the simulation model is that it should capture the random nature of consumer behavior at the retail store within a
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robust framework which allows investigation of alternative buyer strategies. Consumer arrivals at the retail store are modeled as a Poisson process, i.e., the time between arrivals is exponentially distributed with a given rate. This rate is determined for each week in the retail season from the specified customer volume for the season and the seasonal demand pattern. Upon arrival, customers follow the behavior described in Fig. 2.
model is that of buyer error. This permits the execution of scenarios in which the buyer does not have an accurate estimate of the actual demand for the season. The modeled error comes in two forms: volume error and mix error. Volume error represents a difference between the actual demand volume and the buyer’s plan volume while mix error represents differences in the anticipated and actual percentages of demand by style, by color, and by size of the garments. One of the key advantages of QR retailing is that within season demand re-estimation and reordering permits the buyer to detect the presence of error and, as the season progresses, adjust the stock to better reflect true customer preferences.
CUSTOMER ENTERS STORE
A
B
BROWSING
ITEM IN MIND
WHICH ITEM?
C YES
IN STOCK?
REDUCE INV RECORD SALE
ATTRACTIVE COLOR?
NO
NO
LEAVE
To date, all of the QR re-estimation and reordering schemes studied assume that the buyer has an accurate estimate of the demand seasonality and use the estimated figures in their calculations. When this assumption is not valid the performance of the QR procedures degrades markedly. The fuzzy-control-based reorder scheme described in the next section depends far less on the accuracy of the seasonality estimates.
YES RECORD STOCK OUT ATTRACTIVE STYLE?
ALTER LEAVE CHOICE
TO A
RECORD LOST SALE
LOOK AROUND
TO B
NO
LEAVE
YES WHICH SIZE
TO C ALTER ITEM
LEAVE
LOOK AROUND
Fuzzy-Control-Based Reorder Scheme TO A
TO B
The basic idea behind the fuzzy-controlbased reorder scheme is to apply a fuzzy controller to specify the size of the current reorder for each SKU, on a week-by-week basis beginning at the end of the first week of the selling season and ending with a week nominally chosen by the buyer. As illustrated in Fig. 3, a reorder placed at the end of week t will be available in the store at the beginning of week t+L+1, where L is the length of delivery leadtime.
Fig. 2 Consumer behavior
The initial supply, a demand re-estimation procedure, and reorder scheme are specified as input to the model, as is the reorder lead time, i.e., the time between placing the reorder and its appearance on the shelf at the store. Relevant cost data are also specified as input to the model. In order to evaluate the retail performance, a number of measures are calculated, including annualized Gross Margin Return On Inventory (GMROI); the annualized number of Inventory Turns; the percentage of customers attempting to buy who left the store empty-handed (% Lost Sales); the % Service Level, defined as the percentage of customers who found their first choice item in stock, and the percentage of items received that remain on the shelf at the end of the season, referred to as % Jobbed Off.
1st reorder received
123 1st reorder issued
R1
Rt
R1
≈
t
Rt
≈
t+L+1
Last reorder received
≈
≈
N
Last reorder issued
Fig. 3 Reorder flow, where N is the season length and L is the lead time.
An important concept embodied in the
The size of the reorder placed at the end of week t
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(to be delivered at the beginning of week t+L+1) is specified on the basis of the observed demand ratio and the inventory projected to be available at the end of week t+L. The value for the demand ratio and inventory are specified as follows.
Below Expected
As Expected
1
1
0.5 t
Demand ratio =
∑ dτ
τ =1 t ^
Fig. 4 The membership function of demand ratio
∑ dτ
where
t −1
t+L
τ =t − L
τ = t +1
∑ Rτ −
1.5
Demand Ratio
τ =1
Inventory = I t +
Above Expected
Low
∑ dτ
High
Medium
1
d τ is the estimated demand in week τ according to the buyer' s plan,
0
d τ is the actual demand in week τ , I t is the inventory at the end of week t , at the end of week τ .
1
To implement a fuzzy controller three elements are required8: a collection of fuzzy control rules, an inference mechanism, and an output interface (defuzzification). The fuzzy control rules we use are summarized in Table 1; that is, if demand ratio is as expected and the inventory is medium then the reorder size is medium, if demand ratio is below expected and the inventory is low then the reorder size is large, if demand ratio is above expected and the inventory is high then the reorder size is small, and so on. The two input linguistic variables, demand ratio and inventory, and one output linguistic variable, reorder size, are defined with the corresponding term sets { below expected, as expected, above expected}, { low, medium, high}, and {small, medium, large}, respectively. To deal with the vagueness of these linguistic terms, we employ the membership functions shown in Figs 4, 5, and 6.
INVENTORY
Low Medium High
DEMAND RATIO Expected Medium Medium Small REORDER SIZE
2dt+L+1
Fig. 5 The membership function of inventory
Rτ is the size of the reorder placed
Below Expected Large Large Medium
dt+L+1 Inventory
^
Small
Large
Medium
0.5dt+L+1 dt+L+1
2dt+L+1
Reorder Size
Fig. 6 The membership function of reorder size
For computational simplicity, we choose the Mamdani’s inference logic and the mean-ofmax defuzzification method for our implementation. Concluding Remarks The first design of a fuzzy controller, no doubt, will not result in an optimal system performance. To improve the performance, tuning will be necessary. For a complete study, we shall examine different inference logic, fuzzifications, The performance and defuzzifications9. comparison with the stochastic QR reordering scheme currently implemented in the simulation model will be reported.
Above Expected Medium Small Small
References 1 Hunter, A. (1990). Quick Response in Apparel Manufacturing. Manchester: the Textile Institute. 2 Quick Response Implementation. Kurt Salmon
Table 1 Fuzzy control rules
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Associates Technical Report (1988). 3 A Study of Costs and Benefits to Retailers. Arthur Andersen Consulting Technical Report (1989). 4 Hunter, N.A., Nuttle, H.L.W & King, R.E. (1992). An Apparel Supply System for QR Retailing. Journal of the Textiles Institute, 83, pp.462-471. 5 Hunter, N.A. & King, R.E. (1996). The Impact of Size Distribution Forecast Error on Retail Performance. NCSU-IE Technical Report, Department of Industrial Engineering, North Carolina State University, Raleigh, NC. 6 Hunter, N.A., King, R.E. & Nuttle, H.L.W (1996). Evaluation of Quick Response and Traditional Retailing Procedures by Using a Stochastic Simulation Model. Journal of the Textiles Institute, 87, No. 1, pp.42-55. 7 Nuttle, H.L.W., King, R.E. & Hunter, N.A. (1991). A Stochastic Model of the ApparelRetailing Process for Seasonal Apparel. Journal of the Textiles Institute, 82, No. 2, pp.247-259. 8 Witold Pedrycz (1993). Fuzzy Control and Fuzzy Systems. John Wiley & Sons, New York. 9 Kruse, R., Gebhardt, J., Klawonn, F. (1994). Foundations of Fuzzy Systems. John Wiley & Sons, New York.
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