Browsing by Subject "Identical parallel machines"

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    Maximizing the minimum completion time on parallel machines
    (Springer, 2008) Haouari, M.; Jemmali, M.
    We propose an exact branch-and-bound algorithm for the problem of maximizing the minimum machine completion time on identical parallel machines. The proposed algorithm is based on tight lower and upper bounds as well as an effective symmetry-breaking branching strategy. Computational results performed on a large set of randomly generated instances attest to the efficacy of the proposed algorithm.
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    Minimizing schedule length on identical parallel machines: an exact algorithm
    (1991) Akyel, H. Cemal
    The primary concern of this study is to investigate the combinatorial aspects of the single-stage identical parallel machine scheduling problem and to develop a computationally feasible branch and bound algorithm for its exact solution. Although there is a substantial amount of literature on this problem, most of the work in this area is on the development and performance analysis of approximation algorithms. The few optimizing algorithms proposed in the literature have major drawbacks from the computer implementation point of view. Even though the single-stage scheduling problem is known to be unary A/’P-hard, there is still a need to develop a computationally feasible optimizing algorithm that solves the problem in a reasonable time. Development of such an algorithm is necessary for solving the multi-stage parallel machine scheduling problems which are currently an almost untouched issue in the deterministic scheduling theory. In this study, a branch and bound algorithm for the single-stage identical parallel machine scheduling problem is proposed. Promising results were obtained in the empirical analysis of the performance of this algorithm. Furthermore, the procedure that is developed to determine tight bounds at a node of the enumeration tree, is an approximation algorithm that solves a special class of identical parallel machine scheduling problems of practical interest. This algorithm delivers a solution that is arbitrarily close to 4/3 times the optimum. To our knowledge this is the best result obtained for this problem so far.
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    Tight bounds for the identical parallel machine-schedulingproblem: part II
    (Wiley-Blackwell Publishing, 2008) Haouari, M.; Jemmali, M.
    A companion paper introduces new lower bounds and heuristics for the problem of minimizing makespan onidentical parallel machines. The objective of this paper is threefold. First, we describe further enhancementsof previously described lower bounds. Second, we propose a new heuristic that requires solving a sequence of0–1 knapsack problems. Finally, we show that embedding these newly derived bounds in a branch-and-boundprocedure yields a very effective exact algorithm. Moreover, this algorithm features a new symmetry-breakingbranching strategy. We present the results of computational experiments that were carried out on a large setof instances and that attest to the efficacy of the proposed algorithm. In particular, we report proven optimalsolutions for some benchmark problems that have been open for some time