Single-machine scheduling with time-and-resource-dependent processing times

Single-machine group scheduling with both learning effects and deteriorating jobs

We consider single-machine scheduling problem in which the processing time of a job is a function of its position in a sequence, its starting time, and its resource allocation. The objective is to find the optimal sequence of jobs and the optimal resource allocation separately. We concentrate on two goals separately, namely, minimizing a cost function containing makespan, total completion time, total absolute differences in completion times, and total resource cost; minimizing a cost function containing makespan, total waiting time, total absolute differences in waiting times, and total resource cost. The problem is modeled as an assignment problem, and thus can be solved in polynomial time. Some extensions of the problem are also shown.

Scheduling jobs with processing times dependent on position, starting time, and allotted resource

In this paper, we consider single machine scheduling problems with controllable processing time (resource allocation), truncated job-dependent learning and deterioration effects. The goal is to find the optimal sequence of jobs and the optimal resource allocation separately for minimizing a cost function containing makespan (total completion time, total absolute differences in completion times) and/or total resource cost. For two different processing time functions, i.e., a linear and a convex function of the amount of a common continuously divisible resource allocated to the job, we solve them in polynomial time respectively.

Scheduling jobs with controllable processing time, truncated job-dependent learning and deterioration effects

Single-machine scheduling time-dependent jobs with resource-dependent ready times

The paper deals with a single machine scheduling problem for the maximum completion time (makespan) minimization subject to the constraint on the total amount of available resources. The job processing times are given by non-decreasing linear functions simultaneously dependent on the starting moment of their execution and on the amount of allocated resources. We prove the ordinary NP-completeness of the considered problem by reducing to it the ordinary NP-complete Partition Problem. We give also some properties of the optimal resource allocation. The optimal solutions for some special cases of the latter problem are also presented.

A. Bachman

Papers

Scheduling Deteriorating Jobs Dependent on Resources for the Makespan Minimization