id: 01151247
dt: j
an: 01151247
au: Cheng, T.C.Edwin; Janiak, Adam; Kovalyov, Mikhail Y.
ti: Bicriterion single machine scheduling with resource dependent processing
    times.
so: SIAM J. Optim. 8, No.2, 617-630 (1998).
py: 1998
pu: Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
la: EN
cc: 
ut: single machine scheduling; resource allocation; bicriterion scheduling;
    approximation
ci: 
li: doi:10.1137/S1052623495288192
ab: Summary: A bicriterion problem of scheduling jobs on a single machine is
    studied. The processing time of each job is a linear decreasing
    function of the amount of a common discrete resource allocated to the
    job. A solution is specified by a sequence of the jobs and a resource
    allocation. The quality of a solution is measured by two criteria,
    $F_{1}$ and $F_{2}$. The first criterion is the maximal or total
    (weighted) resource consumption, and the second criterion is a regular
    scheduling criterion depending on the job completion times. Both
    criteria have to be minimized. General schemes for the construction of
    the Pareto set and the Pareto set $ε$-approximation are presented.
    Computational complexities of problems to minimize $F_{1}$ subject to
    $F_2\le K$ and to minimize $F_{2}$ subject to $F_1\le K$, where $K$ is
    any number, are studied for various functions $F_{1}$ and $F_{2}$.
    Algorithms for solving these problems and for the construction of the
    Pareto set and the Pareto set $ε$-approximation for the corresponding
    bicriterion problems are presented.
rv: