Application of Submodular Optimization to Single Machine Scheduling with Controllable Processing Times Subject to Release Dates and Deadlines

Akiyoshi Shioura,Vitaly A Strusevich,Natalia V Shakhlevich

doi:10.1287/ijoc.2015.0660

Akiyoshi Shioura, Vitaly A Strusevich + Show 1 more

Open Access

https://doi.org/10.1287/ijoc.2015.0660

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Abstract

In this paper, we study a scheduling problem on a single machine, provided that the jobs have individual release dates and deadlines, and the processing times are controllable. The objective is to find a feasible schedule that minimizes the total cost of reducing the processing times. We reformulate the problem in terms of maximizing a linear function over a submodular polyhedron intersected with a box. For the latter problem of submodular optimization, we develop a recursive decomposition algorithm and apply it to solving the single machine scheduling problem to achieve the best possible running time.

Highlights

We consider a scheduling problem on a single machine, provided that the processing times of the jobs are controllable and each job has a release date and a deadline
We study the general version of the single machine model in which the jobs are available at arbitrary, nonequal release times and should be completed by their individual deadlines, which can be different for different jobs
In the latter problem it is required to verify whether there exists a feasible schedule meeting the deadline and release time constraints

Summary

Introduction

We consider a scheduling problem on a single machine, provided that the processing times of the jobs are controllable and each job has a release date and a deadline. The objective is to determine the actual durations of jobs from given intervals and to find a feasible preemptive schedule such that the total cost of compressing the processing times is minimized. The main outcome of our study implies that this problem with controllable processing times is no harder in terms of its computational complexity than its counterpart with fixed processing times. In the latter problem it is required to verify whether there exists a feasible schedule meeting the deadline and release time constraints

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