Minimizing total weighted flowtime subject to minimum makespan on two identical parallel machines

  • Authors:

  • Johnny C. Ho;Francisco J. López;Alex J. Ruiz-Torres;Tzu-Liang (Bill) Tseng

  • Affiliations:

  • Turner College of Business, Columbus State University, Columbus, USA 31907;School of Business, Macon State College, Macon, USA 31206;Departamento de Gerencia, Facultad de Administración de Empresas, Universidad de Puerto Rico-Rio Piedras, San Juan, USA 00931;Department of Mechanical and Industrial Engineering, University of Texas at El Paso, El Paso, USA 79968

  • Venue:
  • Journal of Intelligent Manufacturing
  • Year:
  • 2011

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Abstract

We study the problem of scheduling n jobs on two identical parallel processors or machines where an optimal schedule is defined as one with the shortest total weighted flowtime (i.e., the sum of the weighted completion time of all jobs), among the set of schedules with minimum makespan (i.e., the completion time of the last job finished). We present a two phase non-linear Integer Programming formulation for its solution, admittedly not to be practical or useful in most cases, but theoretically interesting since it models the problem. Thus, as an alternative, we propose an optimization algorithm, for small problems, and a heuristic, for large problems, to find optimal or near optimal solutions. Furthermore, we perform a computational study to evaluate and compare the effectiveness of the two proposed methods.