Job scheduling to minimize the weighted waiting time variance of jobs

Authors:
Xueping Li;Nong Ye;Tieming Liu;Yang Sun
Affiliations:
Department of Industrial and Information Engineering, University of Tennessee, Knoxville, TN 37996-0700, USA;Department of Industrial Engineering, Arizona State University, Tempe, AZ 85287-5906, USA;School of Industrial Engineering and Management, Oklahoma State University, Stillwater, OK 74078, USA;Department of Industrial Engineering, Arizona State University, Tempe, AZ 85287-5906, USA
Venue:
Computers and Industrial Engineering
Year:
2007

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Abstract

This study considers the job scheduling problem of minimizing the weighted waiting time variance (WWTV) of jobs. It is an extension of WTV minimization problems in which we schedule a batch of n jobs, for servicing on a single resource, in such a way that the variance of their waiting times is minimized. WWTV minimization finds its applications for job scheduling in manufacturing systems with earliness and tardiness (E/T) penalties, in computer and networks systems for the stabilized QoS, and in other fields where it is desirable to minimize WWTV of jobs with different weights for priorities. We formulate a WWTV problem as an integer programming problem, prove the V-shape property for agreeably weighted WWTV problems and the nondelay property for general WWTV problems, and discover the strong V-Shape tendency of the optimal job sequences for this problem. Two job scheduling algorithms, Weighted Verified Spiral (WVS) and Weighted Simplified Spiral (WSS), are developed for the WWTV problems. Numerical testing shows that WVS and WSS significantly outperform existing WWTV algorithms.