Integrated Order Acceptance and Resource Decisions Under Uncertainty: Robust and Stochastic Approaches

Abstract

We study the order acceptance and resource planning problem which has applications in many industries such as healthcare, logistics, and manufacturing. We extend the recent literature by considering two new features: the number of resources is a decision and processing times are uncertain. We first develop mixed integer linear programming and constraint programming models for the nominal (deterministic) problem. Second, we incorporate uncertainty in the form of both stochastic and robust optimization us- ing sample average approximation, classical robust, box uncertainty, and polyhedral-interval uncertainty set techniques. Third, to solve these models, we use three decomposition techniques, branch-relax- and-check, branch-and-check, and logic-based Benders decomposition. We equip the algorithms with subproblem relaxation, pre-processing, valid inequalities, and symmetry breaking cuts. Finally, we conduct a comprehensive simulation evaluation to draw insights from both practical and algorithmic perspectives. We compare performances of algorithms with their optimality gaps. We also provide in- sights on which uncertainty approach performs well and when to use which.

Keywords: Order acceptance, mixed-integer programming, constraint programming, robust optimization, uncertainty sets, sample average approximation model, Benders decomposition.