Improved Approximation Algorithms for Shop Scheduling Problems

  • Authors:
  • David B. Shmoys;Clifford Stein;Joel Wein

  • Affiliations:
  • -;-;-

  • Venue:
  • SIAM Journal on Computing
  • Year:
  • 1994

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Abstract

In the job shop scheduling problem, there are $m$ machines and $n$ jobs. A job consists of a sequence of operations, each of which must be processed on a specified machine, and the aim is to complete all jobs as quickly as possible. This problem is strongly ${\cal NP}$-hard even for very restrictive special cases. The authors give the first randomized and deterministic polynomial-time algorithms that yield polylogarithmic approximations to the optimal length schedule. These algorithms also extend to the more general case where a job is given not by a linear ordering of the machines on which it must be processed but by an arbitrary partial order. Comparable bounds can also be obtained when there are $m'$ types of machines, a specified number of machines of each type, and each operation must be processed on one of the machines of a specified type, as well as for the problem of scheduling unrelated parallel machines subject to chain precedence constraints.