Parallel Makespan Calculation for Flow Shop Scheduling Problem with Minimal and Maximal Idle Time

Jarosław Rudy

doi:10.3390/app11178204

Abstract

In this paper, a flow shop scheduling problem with minimal and maximal machine idle time with the goal of minimizing makespan is considered. The mathematical model of the problem is presented. A generalization of the prefix sum, called the job shift scan, for computing required shifts for overlapping jobs is proposed. A work-efficient algorithm for computing the job shift scan in parallel for the PRAM model with n processors is proposed and its time complexity of O(logn) is proven. Then, an algorithm for computing the makespan in time O(mlogn) in parallel using the prefix sum and job shift scan is proposed. Computer experiments on GPU were conducted using the CUDA platform. The results indicate multi-thread GPU vs. single-thread GPU speedups of up to 350 and 1000 for job shift scan and makespan calculation algorithms, respectively. Multi-thread GPU vs. single-thread CPU speedups up to 4.5 and 14.7, respectively, were observed as well. The experiments on the Taillard-based problem instances using a simulated annealing solving method and employing the parallel makespan calculation show that the method is able to perform many more iterations in the given time limit and obtain better results than the non-parallel version.

Highlights

For several decades, scheduling and job scheduling have received constant attention from both researchers and practitioners from across the world. Such a level of interest is justified by the broad applications of scheduling which go from production planning and manufacturing [1,2], construction [3], cloud computing [4,5], transportation [6], education [7], healthcare [8] to CPUs [9], Internet of Things [10] and sensor networks [11]
The aim of the paper was to propose a novel parallel computing technique for the faster computation of the goal function for flow shop scheduling problem (FSSP)-MMI and to develop a solving method that is: (1) capable of solving large-size FSSP-MMI problems in reasonable time; and (2) working fast enough for small- and medium-sized FSSP-MMI problems to be applicable as a local-search subroutine in larger algorithms
Aside from the speedups and improved quality, the results indicated the importance of SSE vectorization

Summary

Introduction

For several decades, scheduling and job scheduling have received constant attention from both researchers and practitioners from across the world Such a level of interest is justified by the broad applications of scheduling which go from production planning and manufacturing [1,2], construction [3], cloud computing [4,5], transportation [6], education [7], healthcare [8] to CPUs [9], Internet of Things [10] and sensor networks [11]. In order to better model real-life situations, more specific problem variants with additional constraints are considered. Such constraints may include, for example, transport times [12], setups [13], limited buffers [14] or idle times [15]. Due to ever-growing markets and the emergence of Big Data, larger and larger problems are being considered [16,17], which is especially true for cloud scheduling [18,19]

Objectives

Methods

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Conclusion