A survey of scheduling with controllable processing times

Optimal due date assignment and resource allocation in a group technology scheduling environment

Single machine batch scheduling with jointly compressible setup and processing times

In the paper two resource constrained single-machine group scheduling problems with time and position dependent processing times are considered. By time and position dependent processing times and group technology assumption, we mean that the processing time of a job is defined by the function of its starting time and position in the group, and the group setup times of a group is a positive strictly decreasing continuous function of the amount of consumed resource. We present polynomial solutions for the makespan minimization problem under the constraint that the total resource consumption does not exceed a given limit, and the total resource consumption minimization problem under the constraint that the makespan does not exceed a given limit, respectively.

Single machine group scheduling with time and position dependent processing times

This article addresses the job-shop problem of minimizing the schedule length (makespan) for processing n jobs on two machines with sequence-dependent setup times and removal times. The processing of each job includes at most two operations that have to be non-preemptive. Machine routes may differ from job to job. If all setup and removal times are equal to zero, this problem is polynomially solvable via Jackson's permutations, otherwise it is NP-hard even if each of n jobs consists of one operation on the same machine. We present sufficient conditions when Jackson's permutations may be used for solving the two-machine job-shop problem with sequence-dependent setup times and removal times. For the general case of this problem, the results obtained provide polynomial lower and upper bounds for the makespan which are used in a branch-and-bound algorithm. Computational experiments show that an exact solution for this problem may be obtained in a suitable time for n ≤ 280. We also develop a heuristic algorithm and present a worst case analysis.

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Sequence-Dependent Setup Times in a Two-Machine Job-Shop with Minimizing the Schedule Length

In the paper, we consider a single machine scheduling problem with set-up times and job processing times given as linear functions dependent on some continuously divisible resources The scheduling objective is to find the optimal sequence of the jobs and the allocation of limited resources, which minimize the maximum completion time (makespan) A dual problem is also considered, ie the problem, in which the objective is to find a sequence of jobs and an allocation of resources, which minimize the total resource consumption, under a given constraint on maximum completion time Based on the problems properties, we present polynomial time solution algorithms We conclude the paper by outlining some possible directions for future research

M. Lichtenstein

Papers

Some Single Machine Scheduling Problems with Resource Dependent Set-up and Processing Times