An FPTAS for uniform machine scheduling to minimize makespan with linear deterioration

Authors:
Ming Liu;Feifeng Zheng;Chengbin Chu;Jiantong Zhang
Affiliations:
School of Economics & Management, Tongji University, Shanghai, P.R. China 200092;School of Management, Xi'an Jiaotong University, Xi'an, Shaanxi, P.R. China 710049;Laboratoire Génie Industriel, Ecole Centrale Paris, Châtenay-Malabry Cedex, France 92295;School of Economics & Management, Tongji University, Shanghai, P.R. China 200092
Venue:
Journal of Combinatorial Optimization
Year:
2012

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Abstract

This paper consider m uniform (parallel) machine scheduling with linear deterioration to minimize the makespan. In an uniform machine environment, all machines have different processing speeds. Linear deterioration means that job's actual processing time is a linear increasing function on its execution starting time. We propose a fully polynomial-time approximation scheme (FPTAS) to show the problem is NP-hard in the ordinary sense.