Resource-constrained project scheduling with generalised precedence constraints is a very general scheduling model with applications in areas such as make-to-order production planning. We describe a time-oriented branch-and-bound algorithm that uses constraint-propagation techniques which actively exploit the temporal and resource constraints of the problem in order to reduce the search space. Extensive computational experiments with systematically generated test problems show that the algorithm solves more problems to optimality than other exact solution procedures which have recently been proposed, and that the truncated version of the algorithm is also a very good heuristic.project scheduling, resource constraints, time windows, generalised precedence constraints, branch and bound, constraint propagation
SUMMARYOnly few exact solution methods are available for the open shop scheduling problem. We describe a branch-and-bound algorithm for solving this problem which performs better than other existing algorithms. The key to the e ciency of our algorithm lies in the following approach: instead of analysing and improving the search strategies for ÿnding solutions, we focus on constraint propagation based methods for reducing the search space. Extensive computational experiments on several sets of well-known benchmark problem instances are reported. For the ÿrst time, many problem instances are solved to optimality in a short amount of computation time.
In recent years, constraint propagation techniques have been shown to be highly effective for solving difficult scheduling problems. In this paper, we present an algorithm which combines constraint propagation with a problem decomposition approach in order to simplify the solution of the job shop scheduling problem. This is mainly guided by the observation that constraint propagation is more effective for 'small' problem instances. Roughly speaking, the algorithm consists of deducing operation sequences that are likely to occur in an optimal solution of the job shop scheduling problem (JSP).The algorithm for which the name edge-guessing procedure has been chosen -since with respect to the job shop scheduling problem (JSP) the deduction of machine sequences is mainly equivalent to orienting edges in a disjunctive graph -can be applied in a preprocessing step, reducing the solution space, thus speeding up the overall solution process. In spite of the heuristic nature of edge-guessing, it still leads to near-optimal solutions. If combined with a heuristic algorithm, we will demonstrate that given the same amount of computation time, the additional application of edge-guessing leads to better solutions. This has been tested on a set of well-known JSP benchmark problem instances.
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