Robust homecare service capacity planning

Abstract

We study a home healthcare planning problem under the demand uncertainty, where the service type (authorization) and capacity are the first-stage decision and the homecare resource allocation is the second-stage decision which adapts to the demand realizations. We model the problem using an adaptive robust optimization technique where we construct a budget uncertainty set of demand using the well-known Mahalanobis Distance. We analyze the impact of the authorization, capacity decisions as well as the budget (robustness level) of the Mahalanobis uncertainty set onto the worst-case revenue. To solve the model, we develop a Benders decomposition algorithm that solves a pair of a mixed-integer second-order cone program (MISOCP) and a mixed integer linear program (MILP) in each iteration, both can be handled by off-the-shelf MIP solvers, with finite-step convergence. We also develop an affine approximation approach that directly solves one instance of MISOCP. Finally, sufficient numerical studies demonstrate the effectiveness of our model and the solution approaches.