zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Single machine scheduling with start time dependent processing times: Some solvable cases. (English) Zbl 0816.90088
Summary: A new type of single machine scheduling problem, in which the processing time is a binary function of a common start time due date is defined. The jobs have processing time penalties for starting after the due date, and the objective is to minimize the sum of the weighted completion times. The general case addressed here is for jobs with common pre-duedate processing time, general post-duedate processing time penalties, and general weights. A switching algorithm is proposed for this case and we conjecture that it is optimal. A 0-1 quadratic programming formulation of this problem is presented. Solvable cases, one with two different weights, another with two different penalties and another with structured weights and penalties have been identified and polynomial time optimal algorithms have been proposed for them.

90B35Scheduling theory, deterministic
90C20Quadratic programming
90C09Boolean programming
Full Text: DOI
[1] Baker, K.: Introduction to sequencing and scheduling. (1974)
[2] Gupta, J. N. D.; Gupta, S. K.: Single facility scheduling with non-linear processing times. Computers and industrial engineering 14/4, 387-393 (1988)
[3] Gupta, S. K.; Kyparisis, J.: Single facility scheduling research. Omega 15/3, 207-227 (1987)
[4] Gupta, S. K.; Kunnathur, A. S.; Dandapani, K.: Optimal repayment policies for multiple loans. Omega 15/4, 323-330 (1987)
[5] Knuth, D. E.: The art of computer programming: sorting and searching. 3 (1973) · Zbl 0302.68010
[6] Kunnathur, A. S.; Gupta, S. K.: Minimizing the makesapn with late start penalties added to processing times in a single facility scheduling problem. European journal of operational research 47, 56-64 (1990) · Zbl 0717.90034
[7] Luenberger, D.: Introduction to linear and nonlinear programming. (1973) · Zbl 0297.90044
[8] Sen, T.; Gupta, S. K.: A state-of-art survey of static scheduling research involving due dates. Omega 12/1, 63-76 (1984)
[9] Sriskandarajah, C.; Goyal, S. K.: Scheduling of a two-machine flowshop with processing time linearly dependent on job. Journal of the operational research society 40/10, 907-921 (1989) · Zbl 0682.90049
[10] Sundararaghavan, P. S.; Kunnathur, A. S.: Single machine scheduling with due dates and processing time penalties. Proceedings of the national meeting of the decision sciences institute (1990)
[11] Vickson, R. G.: Two single machine scheduling problems involving controllable job processing times. AIIE transactions 12, 258-262 (1980)