By Christian Artigues
This identify 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. within the first half, the normal 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 likewise on similar scheduling difficulties are offered. targeted equipment and heuristics are surveyed. Computational experiments, aiming at supplying an empirical perception at the hassle of the matter, are supplied. the second one a part of the booklet specializes in numerous different variations of the RCPSP and on their resolution tools. each one variation takes account of real-life features which aren't thought of within the typical model, akin to attainable interruptions of actions, construction and intake of assets, cost-based techniques and uncertainty concerns. The final half provides commercial case reviews the place the RCPSP performs a important half. functions are awarded in numerous domain names akin to meeting store and rolling ingots creation scheduling, venture administration in info expertise businesses and guideline scheduling for VLIW processor architectures.
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Additional resources for Resource-constrained Project Scheduling
Four families of structural cutting planes for the linear relaxation are also proposed in [DEM 02a]. They are derived by translating redundant constraints deduced by constraint processing. Such an approach extends prior works on the single machine problem by Balas [BAL 85] and Dyer and Wolsey [DYE 90], and on the job-shop problem by Applegate and Cook [APP 91], who proposed effective cutting plane generation procedures for the sequence-based formulations of these problems. 2. Resource ﬂow Artigues [ART 03] proposed an alternative formulation of the resource constraints for the sequence-based model.
Families of structural valid inequalities were proposed in [CHR 87, SAN 99, DEM 05] to tighten the time-indexed formulation. Among them, the clique cuts can be particularly strong and easily identiﬁed by analyzing the problem a priori. 2): if C is a set of activities that cannot overlap in time pairwise, then at most one activity in C is in process at any time t. This statement can be formulated as t yjτ ≤ 1 ∀t∈T. 18) j∈C τ =t−pj +1 This cutting plane procedure is applied in [DEM 05]. In a preprocessing phase, disjunctive subproblems are generated from greedy heuristics and used to run some constraint propagation techniques such as edge-ﬁnding.
It should be mentioned that for the RCPSP with minimal and maximal time lags, an extension of the problem considered in Chapter 11, it generally holds pa sa ⊂ SH [NEU 00a]. 6. Forbidden sets and resource ﬂow network formulations of the RCPSP From the order-based representation of dominant schedules, we can derive two alternative formulations of the RCPSP restricting the search space to the dominant set of quasi-active schedules. A forbidden set is a set F of activities that cannot be scheduled in parallel in a feasible solution because of resource limitations due to a resource Rk such that Ai ∈F bik > Bk .