Abstract
Markdown decisions in retailing are made based on the demand forecasts which may or may not be accurate in the first place. In this chapter, we propose a framework for forecasting weekly demands of retail items via linear regression models within multi-item groups that incorporate both positive and negative item associations. We then utilize dynamic pricing models to optimize markdown decisions based on the forecasts within multi-item groups. Grouping items can be considered as a form of variable selection to prevent the overfitting in prediction models. We report regression results from multi-item groupings besides results from single-item regression model on a real-world dataset provided by an apparel retailer. We then report markdown optimization results for the single items and multi-item groupings that multi-item forecasting models are built upon. The results show that the regression models provide better estimates within multi-item groups compared to the single-item model. Moreover, the overall revenues achieved in multi-item markdown optimization across all grouping schemes are higher than the total revenue yielded by single-item markdown optimization scheme.
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Appendices
Appendix
Multi-item Markdown Optimization Model
The parameters of the model are given below:
- n :
-
number of products
- \(n_l\) :
-
number of products in cluster l
- T :
-
number of weeks in the season
- \(T_l\) :
-
planning horizon (weeks) for cluster l
- \(\varepsilon \) :
-
very small price value (such as 1 cent), which will allow to differentiate between two prices
- \({\textit{IS}}_i\) :
-
initial inventory for product i (at the beginning of the season)
- \({\textit{IP}}_i\) :
-
initial price of product i (at the beginning of the season)
- \(\beta _{0}^{i}, \ldots , \beta _{n_l}^{i}\) :
-
coefficients for the products in cluster l that represent how they contribute to the sales of product i
- \(h_{it}\) :
-
unit cost of holding product i in inventory during week t
- \({\textit{sV}}_i\) :
-
salvage value/price of product i (can be fixed as parameters, if desired)
- \({\textit{lMS}}\) :
-
maximum number of markdowns throughout a season (optional, fixed by the retail managers)
- M :
-
a large number
The variables of the model are given below:
- \(p_{it}\) :
-
price of product i during week t
- \(B_{it}\) :
-
binary variable that indicates whether a markdown is applied to product i in week t (1 if markdown was applied)
- \(r_{it}\) :
-
binary variable that indicates whether the demand forecast for product i in week t is positive (1 if demand forecast is positive)
- \({\textit{wFD}}_{it}\) :
-
demand forecast for product i for week t (even though this can be a general function of \(p_{it}\) and time, constraint (1) models the special case where it is a linear function of \(p_{it}\))
- \(D_{it}\) :
-
positive demand forecast for product i for week t
- \(S_{it}\) :
-
sales of product i in week t
- \({\textit{fS}}_i\) :
-
number of units of product i left in inventory at the end of the season
- \({\textit{TS}}_i\) :
-
total sales of product i throughout the season
- \({\textit{wIS}}_{it}\) :
-
initial inventory of product i in week t
- \({\textit{wFS}}_{it}\) :
-
ending inventory of product i in week t
- \({\textit{hC}}_{it}\) :
-
total cost of inventory for product i during week t
- \({\textit{THC}}_{i}\) :
-
total cost of inventory for product i throughout the season
- \({\textit{nMS}}_{i}\) :
-
number of markdowns applied for product i
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Demiriz, A. (2018). A Data Mining-Based Framework for Multi-item Markdown Optimization. In: Thomassey, S., Zeng, X. (eds) Artificial Intelligence for Fashion Industry in the Big Data Era. Springer Series in Fashion Business. Springer, Singapore. https://doi.org/10.1007/978-981-13-0080-6_4
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DOI: https://doi.org/10.1007/978-981-13-0080-6_4
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