An optimal online algorithm for single machine scheduling to minimize total general completion time

  • Authors:

  • Ming Liu;Chengbin Chu;Yinfeng Xu;Jiazhen Huo

  • Affiliations:

  • School of Economics & Management, Tongji University, Shanghai, P.R. China 200092 and School of Management, Xi'an Jiaotong University, Xi'an, P.R. China 710049;Laboratoire Génie Industriel, Ecole Centrale Paris, Châtenay-Malabry Cedex, France 92295;School of Management, Xi'an Jiaotong University, Xi'an, P.R. China 710049;School of Economics & Management, Tongji University, Shanghai, P.R. China 200092

  • Venue:
  • Journal of Combinatorial Optimization
  • Year:
  • 2012

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Abstract

We study the online problem of single machine scheduling to minimize total general completion time. General completion time is defined as $C^{\alpha}_{j}=(C_{j})^{\alpha}$ , where C j denotes the completion time of job J j and 驴驴1 is a constant integer. Total general completion time characterizes the feather in service that when a customer is served later in time, his dissatisfaction increases in a manner of power function. The objective function 驴(C j ) 驴 can also be viewed as a total weighted completion time, but the "weight" is no longer a constant number. Our purpose to minimize customers' total dissatisfaction. The problem is online in the sense that all jobs arrive over time. Each job's processing time becomes known at its arrival time. Preemption is not allowed. For this online problem, we show that a lower bound on competitive ratio is 2 驴 and prove that D-SPT (delayed shortest processing time) algorithm is optimal with a competitive ratio 2 驴 .