We consider a scheduling game on parallel related machines, in which jobs try to minimize their completion time by choosing machine be processed on. Each uses an individual priority list decide the order according are processed. prove that it is NP-hard if pure Nash equilibrium exists and characterize four classes of instances guaranteed exist. For each these classes, we give algorithm computes...

In this paper we consider a class of parallel machine scheduling problems and their associated set-partitioning formulations. We show that the tightness of the linear programming relaxation of these formulations is directly related to the performance of a class of heuristics called parameter list scheduling heuristics. This makes it possible to characterize the worst possible gap between optima...

Production scheduling deals with scheduling production jobs on a machine (single or multiple) in order to optimise a specific objective such as total weighted completion times or total weighted tardiness. The assumption that machines are always available for processing jobs is generally used in the production scheduling literature. In reality, machines often are unavailable due to preventive ma...

The mainstream architecture of a parallel machine with more than tens of processors is a distributed-memory machine. The bulk synchronous task scheduling problem (BSSP, for short) is an task scheduling problem for distributed-memory machines. This paper shows that there does not exist a ρ-approximation algorithm to solve the optimization counterpart of BSSP for any ρ < 6 5 unless P = NP .

This paper considers a fuzzy programming approach for a multi-objective single machine scheduling problem when processing times of jobs are normal random variables. The probabilistic problem is converted into an equivalent deterministic programming problem. Then the fuzzy programming technique has been applied to obtain a compromise solution. A numerical example demonstrates the feasibility of ...

We study scheduling problems on a machine of varying speed. Assuming a known speed function (given through an oracle) we ask for a cost-efficient scheduling solution. Our main result is a PTAS for minimizing the total weighted completion time on a machine of varying speed. This implies also a PTAS for the closely related problem of scheduling to minimize generalized global cost functions. The k...