Resource Scheduling with Supply Constraint and Linear Cost

  • Qiang Zhang
  • Weiwei Wu
  • Minming Li
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7402)


We consider the following resource scheduling problem to minimize the total weighted completion time. There are m resources available at each time unit, and n jobs, each requiring an arbitrary number s i of resources. Each resource can only be assigned to one job. The objective is to find a schedule that minimizes ∑ w i c i , where w i is the weight/importance of job J i and c i is the time that job J i receives all resources it requires. We show this problem is NP-hard when m is the input of the problem. We then give a simple greedy algorithm with 2-approximation ratio. Finally, we present a polynomial time algorithm with complexity O(n d + 1) to solve this problem when the number of different resources requirements that are not multiples of m is at most d.


Algorithms Machine scheduling Parallel tasks Supply allocation 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Qiang Zhang
    • 1
  • Weiwei Wu
    • 2
  • Minming Li
    • 1
  1. 1.Department of Computer ScienceCity University of Hong KongHong Kong SARChina
  2. 2.Division of Mathematical SciencesNanyang Technological UniversitySingapore

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