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Scheduling two chains of unit jobs on one machine: A polyhedral study
Author(s) -
Arbib Claudio,
Labbé Martine,
Servilio Mara
Publication year - 2011
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.20452
Subject(s) - scheduling (production processes) , computer science , mathematical optimization , schedule , convex hull , job shop scheduling , set (abstract data type) , regular polygon , operations research , mathematics , geometry , programming language , operating system
We investigate polyhedral properties of the following scheduling problem: given two sets of unit, indivisible jobs and revenue functions of the jobs completion times, find a one‐machine schedule maximizing the total revenue under the constraint that the schedule of each job set respects a prescribed chain‐like precedence relation. A solution to this problem is an order preserving assignment of the jobs to a set of time‐slots. We study the convex hull of the feasible assignments and provide families of facet‐defining inequalities in two cases: (i) each job must be assigned to a time‐slot and (ii) a job does not need to be assigned to any time‐slot. © 2011 Wiley Periodicals, Inc. NETWORKS, 2011