Robust Capacity Planning with General Upgrading.

This article focuses on the capacity planning problem for multiple products under a general upgrading strategy, where customers can be upgraded to higher-end products if lower-end items are out of stock, within a distributionally robust optimization (DRO) framework. The authors formulate the problem as a two-stage DRO model using moment-based ambiguity sets with mean and variance information, and show that the dual of the second-stage problem is equivalent to an economic lot-sizing problem with bounded inventory constraints. They derive a binary extended formulation for the extreme points of the dual polyhedron via a shortest path network, enabling tractable second-order cone program (SOCP) reformulations for marginal moment and Wasserstein ambiguity sets, and semidefinite program (SDP) reformulations for partial correlation ambiguity sets. Numerical experiments and a case study with real cosmetic sales data demonstrate that the DRO approach outperforms traditional methods, especially with limited training data or under demand uncertainty and nonstationarity, highlighting the managerial value of incorporating upgrading in capacity decisions.