Two dimensional load balancing

We consider a bi-criteria parallel machine scheduling problem in which the first objective is the minimization of the makespan of the schedule and the second objective is the minimization of the maximum machine cost. Since the problem is strongly NP-hard, we propose a fast heuristic and derive its worst-case performance bound.     

Coordination mechanisms with hybrid local policies

We study coordination mechanisms for scheduling n jobs on m parallel machines where agents representing the jobs interact to generate a schedule. Each agent acts selfishly to minimize the completion time of his/her own job, without considering the overall system performance that is measured by a central objective. The performance deterioration due to the lack of a central coordination, the so-called price of anarchy, is determined by the maximum ratio of the central objective function value of an equilibrium schedule divided by the optimal value. In the first part of the paper, we consider a mixed local policy with some machines using the SPT rule and other machines using the LPT rule. We obtain the exact price of anarchy for the problem of minimizing the makespan and some bounds for the problem of minimizing the total completion time. In the second part of the paper, we consider parallel machine scheduling subject to eligibility constraints. We devise new local policies based on the flexibilities and the processing times of the jobs. We show that the newly devised local policies outperform both the SPT and the LPT rules.     

A note on the complexity of flow-shop scheduling with deteriorating jobs

This paper is a note on “Complexity analysis of job-shop scheduling with deteriorating jobs” [G. Mosheiov, Complexity analysis of job-shop scheduling with deteriorating jobs, Discrete Applied Mathematics 117 (2002) 195-209]. A proportional deterioration rate is assumed and the objective is the minimization of the makespan. Mosheiov presents NP-hardness results for flow-shops and open-shops with three or more machines and for job-shops with two or more machines. The proof of NP-hardness for the flow-shop case is however not correct. This paper provides a correct proof.