TY - JOUR
T1 - Polynomial algorithm for an integer quadratic non-separable transportation problem
AU - Hochbaum, Dorit S.
AU - Shamir, Ron
AU - Shanthikumar, J. George
PY - 1992/7/6
Y1 - 1992/7/6
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0027113835&partnerID=8YFLogxK
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AN - SCOPUS:0027113835
SN - 0025-5610
VL - 55
SP - 359
EP - 371
JO - Mathematical Programming
JF - Mathematical Programming
IS - 3
ER -