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

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. First, we develop mixed integer linear programming and constraint programming models for the nominal (deterministic) problem. Second, we incorporate uncertainty in the form of stochastic and robust optimization, with sample average approximation, classical robust, box uncertainty, and polyhedral-interval uncertainty set techniques. Third, we employ three decomposition techniques, branch-relax-and-check, branch-and-check, and logic-based Benders decomposition as our solution approach. We equip the algorithms with subproblem relaxation, pre-processing, valid inequalities, and symmetry breaking cuts. Finally, we conduct a simulation evaluation to draw insights from both practical and algorithmic perspectives. We compare performances of our solution approaches with optimality gaps. We also provide insights on when and which uncertainty approach performs well and when to use which