Number Of Unrelated Machines Research Articles

Maximizing the number of jobs scheduled at their baseline starting times in case of machine failures

We investigate the problem of keeping the maximum number of starting times of a baseline schedule if some machines happen to be out of order when the baseline schedule is to be implemented. If the machines are identical, we show that the problem is polynomially solved when no deadline is imposed on the reactive schedule and is strongly NP-hard otherwise. If the number of unrelated machines is fixed and if no deadline is imposed on the reactive schedule, a polynomial algorithm, based on a state graph, has been developed. We conclude with an open complexity question and some further research directions for this class of problems.

Modeling realistic hybrid flexible flowshop scheduling problems

This paper aims to contribute to the recent research efforts to bridge the gap between the theory and the practice of scheduling by modelizing a realistic manufacturing environment and analyzing the effect of the inclusion of several characteristics in the problem formulation. There are several constraints and characteristics that affect the scheduling operations at companies. While these constraints are many times tackled in the literature, they are seldom considered together inside the same problem formulation. We propose a formulation along with a mixed integer modelization and some heuristics for the problem of scheduling n jobs on m stages where at each stage we have a known number of unrelated machines. The jobs might skip stages and, therefore, we have what we call a hybrid flexible flowshop problem. We also consider per machine sequence-dependent setup times which can be anticipatory and non-anticipatory along with machine lags, release dates for machines, machine eligibility and precedence relationships among jobs. Manufacturing environments like this appear in sectors like food processing, ceramic tile manufacturing and several others. The optimization criterion considered is the minimization of the makespan. The MIP model and the heuristics proposed are tested against a comprehensive benchmark and the results evaluated by advanced statistical tools that make use of decision trees and experimental designs. The results allow us to identify the constraints that increase the difficulty.