Traditionally, in the fashion industry, purchasing decisions for retailers are made based on various factors such as budget, profit target, and interest rate. Since the market demand is highly volatile, risk is inherently present and it is critically important to incorporate risk consideration into the decision making framework. Motivated by the observed industrial practice, we explore via a mean-variance approach the multi-period risk minimization inventory models for fashion product purchasing. We first construct a basic multi-period risk optimization model for the fashion retailer and illustrate how its optimal solution can be determined by solving a simpler problem. Then, we analytically find that the optimal ordering quantity is increasing in the expected profit target, decreasing in the number of periods of the season, and increasing in the market interest rate. After that, we propose and solve several extended models which consider realistic and timely industrial measures such as minimum ordering quantity, carbon emission tax, and carbon quota. We analytically derive the necessary and sufficient condition(s) for the existence of the optimal solution for each model and show how the purchasing budget, the profit target, and the market interest rate affect the optimal solution. Finally, we investigate the supply chain coordination challenge and analytically illustrate how an upstream manufacturer can offer implementable supply contracts to optimize the supply chain.
