A polynomial algorithm for an integer quadratic non-separable transportation problem

Dorit S. Hochbaum*, Ron Shamir, J. George Shanthikumar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We study the problem of minimizing the total weighted tardiness when scheduling unti-length jobs on a single machine, in the presence of large sets of identical jobs. Previously known algorithms, which do not exploit the set structure, are at best pseudo-polynomial, and may be prohibitively inefficient when the set sizes are large. We give a polynomial algorithm for the problem, whose number of operations is independent of the set sizes. The problem is reformulated as an integer program with a quadratic, non-separable objective and transportation constraints. Employing methods of real analysis, we prove a tight proximity result between the integer solution to that problem and a fractional solution of a related problem. The related problem is shown to be polynomially solvable, and a rounding algorithm applied to its solution gives the optimal integer solution to the original problem.

Original languageEnglish
Pages (from-to)359-371
Number of pages13
JournalMathematical Programming
Issue number1-3
StatePublished - Apr 1992


  • Integer programming
  • proximity
  • quadratic non-separable programming
  • scheduling
  • transportation


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