Dynamic pricing in retail with diffusion process demand

When randomness in demand affects the sales of a product, retailers use dynamic pricing strategies to maximize their profits. In this article, we formulate the pricing problem as a continuous-time stochastic optimal control problem and find the optimal policy by solving the associated Hamilton-Jacobi-Bellman (HJB) equation. We propose a new approach to modelling the randomness in the dynamics of sales based on diffusion processes. The model assumes a continuum approximation to the stock levels of the retailer which should scale much better to large-inventory problems than the existing Poisson process models in the revenue management literature. The diffusion process approach also enables modelling of the demand volatility, whereas Poisson process models do not. We present closed-form solutions to the HJB equation when there is no randomness in the system. It turns out that the deterministic pricing policy is near-optimal for systems with demand uncertainty. Numerical errors in calculating the optimal pricing policy may, in fact, result in a lower profit on average than with the heuristic pricing policy.Comment: 18 pages, 14 figures, 1 tabl

Dealing with the Dimensionality Curse in Dynamic Pricing Competition: Using Frequent Repricing to Compensate Imperfect Market Anticipations

Most sales applications are characterized by competition and limited demand information. For successful pricing strategies, frequent price adjustments as well as anticipation of market dynamics are crucial. Both effects are challenging as competitive markets are complex and computations of optimized pricing adjustments can be time-consuming. We analyze stochastic dynamic pricing models under oligopoly competition for the sale of perishable goods. To circumvent the curse of dimensionality, we propose a heuristic approach to efficiently compute price adjustments. To demonstrate our strategy's applicability even if the number of competitors is large and their strategies are unknown, we consider different competitive settings in which competitors frequently and strategically adjust their prices. For all settings, we verify that our heuristic strategy yields promising results. We compare the performance of our heuristic against upper bounds, which are obtained by optimal strategies that take advantage of perfect price anticipations. We find that price adjustment frequencies can have a larger impact on expected profits than price anticipations. Finally, our approach has been applied on Amazon for the sale of used books. We have used a seller's historical market data to calibrate our model. Sales results show that our data-driven strategy outperforms the rule-based strategy of an experienced seller by a profit increase of more than 20%