Citation
A Probabilistic Constrained Approach for Unrelated Parallel Machine Scheduling. In proceedings of the 7th Multidisciplinary International Conference on Scheduling : Theory and Applications (MISTA 2015), 25 - 28 Aug 2015, Prague, Czech Republic, pages 16-24, 2015.
Paper
Abstract
In this paper, we investigate a probabilistic constrained variant of the well known unrelated parallel machine scheduling problem. For this purpose, we assume that each vector of job processing times is an independent and multivariate normally distributed vector with known mean and covariance matrix. This assumption allows transforming the probabilistic constraints into deterministic equivalent second order conic constraints [9]. In particular, we consider the problem of makespan minimization when completing a subset of jobs subject to machine energy consumption and job assignment constraints. We compute feasible solutions by solving directly the equivalent deterministic mixed integer second order conic (MISOC) programming problem and also by means of piecewise mixed integer linear programming (MILP) formulations we obtain from the MISOC problem. Our numerical results indicate that one of the piecewise linear formulations allows ?nding better feasible solutions for instances with up to ten machines and ?fty jobs in less average computational cost.
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Bibtex
@INPROCEEDINGS{2015-016-024-P, author = {P. Adasme and J. Leung and A. Lisser},
title = {A Probabilistic Constrained Approach for Unrelated Parallel Machine Scheduling},
booktitle = {In proceedings of the 7th Multidisciplinary International Conference on Scheduling : Theory and Applications (MISTA 2015), 25 - 28 Aug 2015, Prague, Czech Republic},
year = {2015},
editor = {Z. Hanzalek and G. Kendall and B. McCollum and P. Sucha},
pages = {16--24},
note = {Paper},
abstract = { In this paper, we investigate a probabilistic constrained variant of the well known unrelated parallel machine scheduling problem. For this purpose, we assume that each vector of job processing times is an independent and multivariate normally distributed vector with known mean and covariance matrix. This assumption allows transforming the probabilistic constraints into deterministic equivalent second order conic constraints [9]. In particular, we consider the problem of makespan minimization when completing a subset of jobs subject to machine energy consumption and job assignment constraints. We compute feasible solutions by solving directly the equivalent deterministic mixed integer second order conic (MISOC) programming problem and also by means of piecewise mixed integer linear programming (MILP) formulations we obtain from the MISOC problem. Our numerical results indicate that one of the piecewise linear formulations allows ?nding better feasible solutions for instances with up to ten machines and ?fty jobs in less average computational cost.},
owner = {Graham},
timestamp = {2017.01.16},
webpdf = {2015-016-024-P.pdf} }