Optimizing Fashion Branding Strategies: Management of Variety of Items and Length of Lifecycles in a Stochastically Fluctuating Market

Abstract

In the fashion and apparel industry, an increasing number of clothing retailers offer a greater number of products in smaller lines. This results in a continuously changing of their products in their storefronts. The present study, by utilizing optimal stopping theory, attempts to build a stochastic dynamic model to investigate how a clothing retailer should introduce and withdraw the products with respect to the stochastic consumer market. More precisely, this chapter formulates market fluctuation as a stochastic process and attempts to examine how to optimally manage the number of “seasons” in a fluctuating market. The analysis reveals that clothing retailers should increase the variety of items with short lifecycles if (1) the clothing retailer is vulnerable to other clothing retailers’ introductions of new items or (2) the market as a whole is certain. These will directly enhance consumer welfare as fashion consumers commonly treasure more trendy clothing. Since these results identify the effect of each factor, they are important when clothing retailers consider the difference between product vulnerability and market uncertainty.

Appendix

Effects of increases in η and σ on α are shown as follows.

If η increases, as Fig. A.1 shows, F does not shift while f shifts upward, and hence α ₂ decreases to α ₂′, which is equivalent to say that α increases.

Fig. A.1

Effect of increase in η

If σ increases, F does not shift while f shifts as Fig. A.2 shows, and hence α ₂ increases to α ₂′, which is equivalent to say that α decreases.

Fig. A.2

Effect of increase in σ

As a result, the next lemma follows.

Lemma:

(1) If η increases, α increases.

(2) If σ increases, α decreases.