Stochastic control and optimization in retail distribution: an empirical study of a Korean fashion company

Abstract

Considerable research has recently been conducted on improving the business performance of the fashion industry through supply-chain streamlining. In addition, the accuracy enhancement of sales forecasting by using statistical methods and machine learning algorithms to minimize inventory and improve profitability has been investigated. However, few studies have focused on solving the initial distribution problem to reduce logistical costs and loss of sales opportunities. This study solves the mathematical problems related to initial distributions of fashion products using stochastic control and optimization by conducting an empirical study using real data from a leading Korean fashion company. The initial distribution of a small quantity of items among numerous shops and the distribution of special sizes produced in small quantities were examined. Monte-Carlo simulations and Lebesgue's convergence theorem were considered useful for determining initial distributions of stock produced in small quantities. Furthermore, optimal initial distributions can be achieved when experience-based expert judgment is combined with mathematical modeling using stochastic control and optimization.