Generating Robust Schedules Subject to Resource and Duration Uncertainties

We consider the Resource-Constrained Project Scheduling Problem with minimal and maximal time lags under resource and duration uncertainties. To manage resource uncertainties, we build upon the work of Lambrechts et al 2007 and develop a method to analyze the effect of resource breakdowns on activity durations. We then extend the robust local search framework of Lau et al 2007 with additional considerations on the impact of unexpected resource breakdowns to the project makespan, so that partial order schedules (POS) can absorb both resource and duration uncertainties. Experiments show that our proposed model is capable of addressing the uncertainty of resources, where the most robust POS is generated to minimize the robust makespan with statistical guarantee. Compared with prevailing methods, our method is also capable of achieving more feasible solutions with better robust makespan. Introduction Research on the Resource-Constrained Project Scheduling Problem with minimal and maximal time lags (RCPSP/max) has been mostly concerned with the generation of a precedence and resource feasible schedule that minimizes the project makespan. However, in the real-world environment, the project is often unable to observe to its given baseline schedule due to external uncontrollable events such as manpower unavailability, machine breakdowns, weather changes, and hence the scheduled completion time of the project is often delayed. Under such an uncertainty setting, the objective function assumes different values under different realizations of the uncertain data. This problem is gaining popularity, as evidenced by a recent Journal of Scheduling special issue. One of the ways to cope with the problem is what is termed proactive-reactive procedures which combines a proactive baseline schedule that is hopefully robust, and a reactive procedure that fixes the schedule during Copyright © 2008, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. execution, and a good survey is in Van de Vonder et al 2007 reported in that journal issue. Yet another interesting approach is taken from a risk management perspective. Beck and Wilson 2004 considers the Job Shop Scheduling Problem where activity durations are random variables. Given a level of risk , they are interested in a solution of minimal (probabilistic) makespan which has a probability of execution of at least ; they show how to find a lower bound for this minimal makespan by solving a deterministic problem. In Lau et al 2007, techniques from robust optimization is integrated into the classical local search resulting in a computationally efficient search approach to find a partial-order schedule (POS) with the minimum robust makespan , such that given , one guarantees the probability of that the actual realized makespan of the schedule does not exceed . The limitation of the work is that only duration variability was considered, and fixed resource units are assumed to be available throughout the execution of the whole project. In this paper, we extend the above framework with additional considerations on resource uncertainty. More precisely, we are interested in the following robust RCPSP/max problem: given duration variability described by a random variable with bounded support for each activity, and resource breakdown described by exponential distributions for the time between failure as well as repair time for each resource, construct a POS that minimizes the robust makespan. The intuition behind our approach is based on the following major ingredients: (a) a new chaining procedure that obtains a POS and corresponding resource assignment based on the given resource breakdown distributions; (b) a model that translates resource breakdowns to (further) duration variability (similar to the approach taken by Lambrechts et al 2007); and (c) a local search framework extended from Lau et al 2007 that iteratively finds the POS (using the chaining algorithm in (a)) minimizing the robust makespan, which is measured in terms of the model defined in (b). 83 Proceedings of the Eighteenth International Conference on Automated Planning and Scheduling (ICAPS 2008)