Multi-product pricing via robust optimisation

We propose an approach to model demand uncertainty in pricing problems with capacitated resources that builds upon: (i) range forecasts for various product lines and (ii) bounds on the amount of the resources that can be used by the random part of the cumulative demand. The bounds are adjusted to reflect the decision–maker's risk preferences. Although revenue management traditionally assumes that enough historical observations are available to estimate the underlying probability distributions accurately, the model of uncertainty presented in this work is particularly well suited to the level of information available in real–life settings, in particular in applications with long production lead times, short shelf life or brand new products. We derive robust counterparts to the deterministic pricing problem in the case of additive uncertainty, and analyse the impact of uncertainty and risk aversion on the decision–maker's strategy. In particular, when the price response function is linear or when uncertainty is small, we provide an explicit characterisation of the impact of the system parameters on the optimal strategy and establish the existence of a reference price for each product, which plays a key role in understanding how randomness affects the optimal prices.