A survey of results for sequencing problems with controllable processing times
Discrete Applied Mathematics - Southampton conference on combinatorial optimization, April 1987
On the minimization of completion time variance with a bicriteria extension
Operations Research
Single-machine scheduling with trade-off between number of tardy jobs and resource allocation
Operations Research Letters
A survey of scheduling with controllable processing times
Discrete Applied Mathematics
Optimal due date assignment and resource allocation in a group technology scheduling environment
Computers and Operations Research
Scheduling a batching machine with convex resource consumption functions
Information Processing Letters
Computers and Industrial Engineering
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We introduce a new formulation of the standard completion time variance (CTV) problem with n jobs and one machine, in which the job sequence and the processing times of the jobs are all decision variables. The processing time of job i (i=1,驴 ,n) can be compressed by an amount within [li, ui], which however will incur a compression cost. The compression cost is a general convex non-decreasing function of the amount of the job processing time compressed. The objective is to minimize a weighted combination of the completion time variance and the total compression cost. We show that, under an agreeable condition on the bounds of the processing time compressions, a pseudo-polynomial algorithm can be derived to find an optimal solution for the problem. Based on the pseudo-polynomial time algorithm, two heuristic algorithms H1 and H2 are proposed for the general problem. The relative errors of both heuristic algorithms are guaranteed to be no more than 驴, where 驴 is a measure of deviation from the agreeable condition. While H1 can find an optimal solution for the agreeable problem, H2 is dominant for solving the general problem. We also derive a tight lower bound for the optimal solution of the general problem. The performance of H2 is evaluated by complete enumeration for small n, and by comparison with this tight lower bound for large n. Computational results (with n up to 80) are reported, which show that the heuristic algorithm H2 in general can efficiently yield near optimal solutions, when n is large.