635 / 2024-04-29 08:21:31

Multiproduct Inventory and Pricing with Contextual Robust Optimization

Inventory and pricing, robust optimization, prescriptive analytics, decision-dependent prediction

Traditionally, multiproduct inventory and pricing problems are approached by initially estimating parameters for a presumed ``sufficiently accurate'' demand model, followed by optimizing specific models to determine optimal inventory and pricing decisions. However, obtaining an accurate demand model is nearly impossible due to unobservable parameters (parameter uncertainty) and the unknown distribution of the error term in the stochastic demand model (residual ambiguity). Additionally, the predicted demand is endogenously linked with pricing, leading to decision-dependent predictions that often result in intractable bilinear optimization problems. This paper addresses these challenges by introducing a contextual robust optimization (CRO) model to tackle both issues. Despite the intractability of the CRO model, we propose a fortified affine recourse approximation to resolve the decision-dependent prediction issue, reformulating the problem as a semidefinite programming model. Our extensive numerical studies demonstrate the effectiveness of the CRO model, outperforming the conventional predict-then-optimize approach in terms of average profit in out-of-sample tests.