Online Work-Break Problem and its Competitive Analysis

An original online problem with decreasing profit growth rate is proposed to optimize the work hours of employees, named the online work-break problem (WBP). In this problem, the manager has to answer for an abstract worker when he should have a break for his work efficiency declines with the durative time of work period. The efficiency of the worker is presented by a work efficiency function P(t) in the description of our problem. We present the online algorithms to solve the WBP based on linear estimation of P(t) under two levels. Both the problems with single-period and dynamic multi-periods have 2-competitive online algorithms.

[1]  Ran El-Yaniv,et al.  Competitive Optimal On-Line Leasing , 1999, Algorithmica.

[2]  S. J. Chapman.  Hours of Labour , 1909 .

[3]  Hongyi Li,et al.  Competitive strategy for on-line leasing of depreciable equipment , 2011, Math. Comput. Model..

[4]  Lyle A. McGeoch,et al.  Competitive Algorithms for Server Problems , 1990, J. Algorithms.

[5]  Yin-Feng Xu,et al.  On the on-line rent-or-buy problem in probabilistic environments , 2007, J. Glob. Optim..

[6]  Amos Fiat,et al.  Competitive Paging Algorithms , 1991, J. Algorithms.

[7]  Bruce Philp,et al.  Preferences, Power, and the Determination of Working Hours , 2005 .

[8]  Bin Liu,et al.  Competitive analysis of online leasing problem with discount quotation , 2011, The Fourth International Workshop on Advanced Computational Intelligence.

[9]  Boaz Patt-Shamir,et al.  Ski rental with two general options , 2008, Inf. Process. Lett..

[10]  Rudolf Fleischer.  On the Bahncard problem , 2001, Theor. Comput. Sci..

[11]  Yong Zhang,et al.  Risk-reward models for on-line leasing of depreciable equipment , 2012, Comput. Math. Appl..

[12]  Chris Nyland,et al.  Capitalism and the History of Work-time Thought , 1986 .

[13]  Kazuo Iwama,et al.  Average-Case Competitive Analyses for Ski-Rental Problems , 2002, Algorithmica.

[14]  Lyle A. McGeoch,et al.  Competitive algorithms for on-line problems , 1988, STOC '88.

[15]  Yin-Feng Xu,et al.  The ski-rental problem with multiple discount options , 2011, Inf. Process. Lett..

[16]  Toshihiro Fujito,et al.  On the best possible competitive ratio for the multislope ski-rental problem , 2016, J. Comb. Optim..

[17]  Stavros Mavroudeas,et al.  Duration, Intensity and Productivity of Labour and the Distinction between Absolute and Relative Surplus-value , 2011 .