Optimal pricing and inventory strategies for fashion products under time-dependent interest rate and demand

In this work we consider the dynamic pricing problem of a retailer operating in a market with a single fashion item and under time-dependent interest rate. The demand is assumed to be deterministic and dependent on the price and decay with time, i.e., the market shrinks throughout the horizon. Using an optimal-control-theoretic approach, we analytically derive the optimal pricing and inventory strategy for the retailer over a finite horizon setting. We further analyze the ramifications of the optimal pricing decision for different initial inventory levels dictated by the relationship between the supplier and the retailer; and for varying market interest rates. Optimal dynamic pricing policy is a continuous function, which is almost impossible to use in practice. This is handled using approximate piece-wise constant pricing policies. The trade-off between dynamic pricing policy and approximate policies is also investigated.