Stable solutions for dynamic project scheduling problems

The Resource Constrained Project Scheduling Problem (rcpsp) is a general scheduling problem which consists in scheduling a set of activities taking into account temporal and resource constraints (Demeulemeester and Herroelen, 2002). Preemption is not allowed. The objective considered here is the minimization of the makespan (total duration) of the project. This problem is NP-hard (Blazewicz et al., 1983). Most work about rcpsp consider static problems in which activities are known in advance and constraints are fixed. However, every schedule is subject to unexpected events (consider for example a new activity to schedule, or a resource failure – eg. machine breakdown). When such a situation arises, a new solution taking these events into account is needed generally in a short time. Furthermore, this new solution must preferably be not too far from the previous one. Several works concern dynamic scheduling problems. But generally, they deal with very specific problems like one-machine problems (Mehta et Uzsoy, 1999;, Aloulou et Portmann, 2002) or m-processors (Moukrim et al. 1999), and the number of types of events taken into account are limited. Furthermore, to our knowledge, no optimal approach has been proposed for any dynamic scheduling problems. The only approach concerning the dynamic rcpsp has been recently proposed by (Artigues et al., 2000). The authors developed a heuristic based on a flow network model to update an initial static schedule when considering the insertion of an unexpected activity. Conversely, constraint programming is increasingly used for solving scheduling problems as its flexibility is well suited for real-life scheduling problem. Moreover, solving dynamic constraint satisfaction problems (dcsp) is a vivid research topic in the constraint programming community. A dcsp (Dechter and Dechter, 1988) is a constraint satisfaction problem whose set of variables or/and constraints evolves throughout computation leading to a series of problems differing one from the other by the addition/retraction of single variable/constraint. However, no technique, as far as we know, has been proposed yet to handle dynamic scheduling problems. We introduce here a constraint-based technique to handle dynamic rcpsp instances. This technique which provides optimal solutions is able to handle a large number of different unexpected events and computes a new solution quicker than when solving the new problem from scratch. Moreover, the successive computed solutions are much more stable than solutions computed from scratch.