On the minimum number of resources for a perfect schedule

  • In the single-processor scheduling problem with time restrictions there is one main processor and B resources that are used to execute the jobs. A perfect schedule has no idle times or gaps on the main processor and the makespan is therefore equal to the sum of the processing times. In general, more resources result in smaller makespans, and as it is in practical applications often more economic not to mobilize resources that will be unnecessary and expensive, we investigate in this paper the problem to find the smallest number B of resources that make a perfect schedule possible. We show that the decision version of this problem is NP-complete, derive new structural properties of perfect schedules, and we describe a Mixed Integer Linear Programming (MIP) formulation to solve the problem. A large number of computational tests show that (for our randomly chosen problem instances) only B=3 or B=4 resources are sufficient for a perfect schedule.

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Author:Rachid Benmansour, Oliver Braun
URN:urn:nbn:de:hbz:tr5-1147
DOI:https://doi.org/10.1007/s10100-022-00803-7
Parent Title (English):Central European Journal of Operations Research
Publisher:Springer Nature
Document Type:Article (specialist journals)
Language:English
Date of OPUS upload:2022/09/03
Date of first Publication:2022/05/26
Publishing University:Hochschule Trier
Release Date:2022/09/05
Tag:minimizing the number of resources; mixed integer linear programming; perfect schedule; single-processor scheduling
GND Keyword:Lineare Optimierung
Volume:2022
Page Number:14
First Page:1
Last Page:14
Departments:FB Umweltwirtschaft/-recht (UCB)
Dewey Decimal Classification:3 Sozialwissenschaften / 33 Wirtschaft
5 Naturwissenschaften und Mathematik / 51 Mathematik
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International