By Christian Artigues
This name provides a wide number of versions and algorithms devoted to the resource-constrained venture scheduling challenge (RCPSP), which goals at scheduling at minimum period a collection of actions topic to priority constraints and constrained source availabilities.
In the 1st half, the traditional version of RCPSP is gifted and analyzed as a combinatorial optimization challenge. Constraint programming and integer linear programming formulations are given. Relaxations in accordance with those formulations and in addition on comparable scheduling difficulties are awarded. certain equipment and heuristics are surveyed. Computational experiments, aiming at offering an empirical perception at the trouble of the matter, are provided.
The moment a part of the e-book makes a speciality of a number of different versions of the RCPSP and on their resolution equipment. every one version takes account of real-life features which aren't thought of within the regular model, comparable to attainable interruptions of actions, construction and intake of assets, cost-based methods and uncertainty considerations.
The final half offers business case reports the place the RCPSP performs a critical half. purposes are awarded in a number of domain names akin to meeting store and rolling ingots creation scheduling, undertaking administration in details expertise businesses and guide scheduling for VLIW processor architectures.
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Additional info for Resource-Constrained Project Scheduling: Models, Algorithms, Extensions and Applications
Despite these drawbacks, Demassey et al. [DEM 02a] have obtained tight lower bounds on the KSD benchmark instances from this linear relaxation. 5) and to generate all the minimal forbidden sets of cardinality 2 or 3. 6) of the mathematical programming formulation are then relaxed. In addition, many deductions made during the propagation mechanism are used in order to tighten the linear relaxation a priori. In fact, the two RCPSP models, of constraint programming and of linear programming, are very close: they both are based on natural date variables and distance between tasks variables.
We brieﬂy present one of the most efﬁcient methods: edge-ﬁnding. Now, we consider the decision variant of the single machine problem as deﬁned earlier. So, we have time-windows [ESi , LCi ] (release date /deadline) in which activities have to be processed. Edge-ﬁnding and time-bound adjustments [CAR 89] consist of deducing that some activities from a given set Ω must, can or cannot be executed ﬁrst (or last) in Ω. , strengthened release dates and deadlines. These methods of edge-ﬁnding and time-bound adjustments are closely related to recent works using constraint programming.
Moreover, activity Ai needs f (bi ) units of the redundant resource. These functions are linked to the dual feasible solution introduced in [JOH 74] for the bin-packing problem and used in [FEK 98], and [MAR 90]. Let us consider a basic lower bound for the duration of a cumulative scheduling problem, that is, the ratio of the workload divided by the available resource capacity ( Ai ∈A pi · bi /B). Thus, the basic bound on this redundant resource is now equal to f (bi ) B · pi . This new bound can be larger than the one computed on the initial resource, which conﬁrms the interest of Redundant Resources.
Resource-Constrained Project Scheduling: Models, Algorithms, Extensions and Applications by Christian Artigues