In this work, we consider RCPSP/max with durational uncertainty. We focus on computing robust Partial Order Schedules (or, in short POS) which can be executed with risk controlled feasibility and optimality, i.e., there is stochastic posteriori quality guarantee that the derived POS can be executed with all constraints honored and completion before robust makespan. To address this problem, we propose BACCHUS: a solution method on Benders Accelerated Cut Creation for Handling Uncertainty in Scheduling. In our proposed approach, we first give an MILP formulation for the deterministic RCPSP/max and partition the model into POS generation process and start time schedule determination. Then we develop Benders algorithm and propose cut generation scheme designed for effective convergence to optimality for RCPSP/max. To account for durational uncertainty, we extend the deterministic model by additional consideration of duration scenarios. In the extended MILP, the risks of constraint violation and failure to meet robust makespan are counted during POS exploration. We then approximate the uncertainty problem with computing a risk value related percentile of activity durations from the uncertainty distributions. Finally, we apply Pareto cut generation scheme and propose heuristics for infeasibility cuts to accelerate the algorithm process. Experimental results demonstrate that BACCHUS efficiently and effectively generates robust solutions for scheduling under uncertainty.

Uncertainty in activity durations is a key characteristic of many real world scheduling problems in manufacturing, logistics and project management. RCPSP/max with durational uncertainty is a general  model that can be used to represent durational uncertainty in a wide variety of scheduling problems where there exist resource constraints. However, computing schedules or execution strategies for RCPSP/max with durational uncertainty is NP-hard and hence we focus on providing approximation methods in this paper. We provide a principled approximation approach based on Sample Average Approximation (SAA) to compute proactive schedules for RCPSP/max  with durational uncertainty. We further contribute an extension to SAA for improving scalability significantly without sacrificing on solution quality. Not only is our approach able to compute schedules at comparable runtimes as existing approaches, it also provides lower α-quantile makespan (also referred to as α-robust makespan) values than the best known approach on benchmark problems from the literature.

Scheduling problems in manufacturing, logistics and project management have frequently been modeled using the framework of Resource Constrained Project Scheduling Problems with minimum and maximum time lags (RCPSP/max). Due to the importance of these problems, providing scalable solution schedules for RCPSP/max problems is a topic of extensive research. However, all existing methods for solving RCPSP/max assume that durations of activities are known with certainty, an assumption that does not hold in real world scheduling problems where unexpected external events such as manpower availability, weather changes, etc. lead to delays or advances in completion of activities. Thus, in this paper, our focus is on providing a scalable method for solving RCPSP/max problems with durational uncertainty. To that end, we introduce the robust local search method consisting of three key ideas: (a) Introducing and studying the properties of two decision rule approximations used to compute start times of activities with respect to dynamic realizations of the durational uncertainty; (b) Deriving the expression for robust makespan of an execution strategy based on decision rule approximations; and (c) A robust local search mechanism to efficiently compute activity execution strategies that are robust against durational uncertainty. Furthermore, we also provide enhancements to local search that exploit temporal dependencies between activities. Our experimental results illustrate that robust local search is able to provide robust execution strategies efficiently.