Robust timing of markdowns

Abstract

We propose an approach to the timing of markdowns in a continuous-time finite-horizon setting that does not require the precise knowledge of the underlying probabilities, instead relying on range forecasts for the arrival rates of the demand processes, and that captures the degree of the manager’s risk aversion through intuitive budget of uncertainty functions. These budget functions bound the cumulative deviation of the arrival rates from their nominal values over the lengths of time for which a product is offered at a given price. A key issue is that using lengths of time as decision variables introduces non-convexities when budget functions are concave. In the single-product case, we describe a tractable and intuitive framework to incorporate uncertainty on customers’ arrival rates, formulate the resulting robust optimization model, describe an efficient procedure to compute the optimal sale times, and provide theoretical insights. We then describe how to use the solution of the static robust optimization model to implement a dynamic markdown policy. We also extend the robust optimization approach to multiple products and suggest the idea of constraint aggregation to preserve performance for this type of problem structure.