Scheduling: Agreement graph vs resource constraints

W. Ramdane Cherif , Younes Rahmani , Wahiba Ramdane , Mikhail Kovalyov , Ameur Soukhal , Mohamed Bendraouche (1, 2) , Mourad Boudhar (2) , Ammar Oulamara (3)

1 Faculté des Sciences [Blida]
2 USTHB - Université des Sciences et de la Technologie Houari Boumediene = University of Sciences and Technology Houari Boumediene [Alger]
3 OPTIMIST - OPTImisation Methods for Integrated SysTems

We investigate two scheduling problems. The first is scheduling with agreements (SWA) that consists in scheduling a set of jobs non-preemptively on identical machines in a minimum time, subject to constraints that only some specific jobs can be scheduled concurrently. These constraints are represented by an agreement graph. We extend the NP-hardness of SWA with three distinct values of processing times to only two values and this definitely closes the complexity status of SWA on two machines with two fixed processing times. The second problem is the so-called resource-constrained scheduling. We prove that SWA is polynomially equivalent to a special case of the resource-constrained scheduling and deduce new complexity results of the latter.

Mots clés: Scheduling; Resource constraints; Agreement graph; Identical machines; Complexity theory

Domaines: Recherche opérationnelle [math.OC]

W. Ramdane Cherif, Younes Rahmani, Wahiba Ramdane, Mikhail Kovalyov, Ameur Soukhal, et al.. Scheduling: Agreement graph vs resource constraints. European Journal of Operational Research, 2015, 240 (2), pp.355-360. ⟨10.1016/j.ejor.2014.07.003⟩. ⟨hal-03047195⟩