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Extending Single Tolerances to Set Tolerances
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
2018 (engelsk)Inngår i: Discrete Applied Mathematics, ISSN 0166-218X, E-ISSN 1872-6771, Vol. 247, s. 197-215Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

The theory of single upper and lower tolerances for combinatorial minimization problems was formalized in 2005 for the three types of cost functions sum, product, and maximum, and since then it has shown to be rather useful in creating heuristics and exact algorithms. However, such single tolerances are often used because the assessment of multiple cost changes is considered too complicated. This paper addresses that issue. In this paper we extend this theory from single to set tolerances for these three types of cost functions. In particular, we characterize specific values of set upper and lower tolerances as positive and infinite, and we show a criterion for the uniqueness of an optimal solution to a combinatorial minimization problem. Furthermore, we present one exact formula and several bounds for computing set upper and lower tolerances using the relation to their corresponding single tolerance counterparts. 

sted, utgiver, år, opplag, sider
Elsevier, 2018. Vol. 247, s. 197-215
Emneord [en]
Sensitivity analysis, Combinatorial optimization, Single tolerance, Set tolerance
HSV kategori
Forskningsprogram
matematik
Identifikatorer
URN: urn:nbn:se:umu:diva-145877DOI: 10.1016/j.dam.2018.03.053ISI: 000444362700022OAI: oai:DiVA.org:umu-145877DiVA, id: diva2:1191768
Forskningsfinansiär
The Kempe Foundations, SMK-1354Tilgjengelig fra: 2018-03-20 Laget: 2018-03-20 Sist oppdatert: 2018-10-04bibliografisk kontrollert

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