Some Results on Shop Scheduling with S-Precedence Constraints among Job Tasks

Alessandro Agnetis,Fabrizio Rossi,Stefano Smriglio

doi:10.3390/a12120250

Alessandro Agnetis, Fabrizio Rossi + Show 1 more

Open Access

https://doi.org/10.3390/a12120250

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Journal: Algorithms	Publication Date: Nov 25, 2019
Citations: 5	License type: CC BY 4.0

Affiliation: University of Siena, University of L'Aquila

Abstract

We address some special cases of job shop and flow shop scheduling problems with s-precedence constraints. Unlike the classical setting, in which precedence constraints among the tasks of a job are finish–start, here the task of a job cannot start before the task preceding it has started. We give polynomial exact algorithms for the following problems: a two-machine job shop with two jobs when recirculation is allowed (i.e., jobs can visit the same machine many times), a two-machine flow shop, and an m-machine flow shop with two jobs. We also point out some special cases whose complexity status is open.

Highlights

This paper addresses a variant of classical shop scheduling models
In classical job shop or flow shop, the task of a job cannot start before the previous task of the same job has finished, we address a situation in which each task of a job cannot start before the previous task of the same job has started
They showed that makespan minimization is NP-hard, and developed a heuristic procedure deriving tight worst-case bounds on the relative error

Summary

Introduction

In classical job shop or flow shop (as well as in the large majority of scheduling problems with precedence constraints), the task of a job cannot start before the previous task of the same job has finished, we address a situation in which each task of a job cannot start before the previous task of the same job has started. Shop problems with few jobs occur when modeling synchronization and conflicts among processes share common resources Examples of this situation include scheduling robot moves in flexible robotic cells (Agnetis et al [6]), aircraft scheduling during taxiing at an airport so that no aircraft collides (Avella et al [7]), or, in container terminals, the synchronization of crane gantry movements once transportation tasks have been assigned (Briskorn and Angeloudis [8]).

The Job Shop with Two Jobs and Two Machines

Generating Initial No-Idle Subschedules

Minimizing the Makespan

Flow Shop

Further Research