Approximation schemes for parallel machine scheduling with non-renewable resources

In this paper the approximability of parallel machine scheduling problems with resource consuming jobs is studied. In these problems, in addition to a parallel machine environment, there are non-renewable resources, like raw materials, energy, or money, consumed by the jobs. Each resource has an initial stock, and some additional supplies at a-priori known moments in time and in known quantities. The schedules must respect the resource constraints as well. The optimization objective is either the makespan, or the maximum lateness. Polynomial time approximation schemes are provided under various assumptions, and it is shown that the makespan minimization problem is APX-complete if the number of machines is part of the input even if there are only two resources. © 2016 Elsevier B.V

A probabilistic approach to pickup and delivery problems with time window uncertainty

In this paper we study a dynamic and stochastic pickup and delivery problem proposed recently by Srour, Agatz and Oppen. We demonstrate that the cost structure of the problem permits an effective solution method without generating multiple scenarios. Instead, our method is based on a careful analysis of the transfer probability from one customer to the other. Our computational results confirm the effectiveness of our approach on the data set of Srour et al

A PTAS for a resource scheduling problem with arbitrary number of parallel machines

In this paper we study a parallel machine scheduling problem with non-renewable resource constraints. That is, besides the jobs and machines, there is a common non-renewable resource consumed by the jobs, which has an initial stock and some additional supplies over time. Unlike in most previous results, the number of machines is part of the input. We describe a polynomial time approximation scheme for minimizing the makespan

Submicron plasticity: yield stress, dislocation avalanches, and velocity distribution

The existence of a well defined yield stress, where a macroscopic piece of crystal begins to plastically flow, has been one of the basic observations of materials science. In contrast to macroscopic samples, in micro- and nanocrystals the strain accumulates in distinct, unpredictable bursts, which makes controlled plastic forming rather difficult. Here we study by simulation, in two and three dimensions, plastic deformation of submicron objects under increasing stress. We show that, while the stress-strain relation of individual samples exhibits jumps, its average and mean deviation still specify a well-defined critical stress, which we identify with the jamming-flowing transition. The statistical background of this phenomenon is analyzed through the velocity distribution of short dislocation segments, revealing a universal cubic decay and an appearance of a shoulder due to dislocation avalanches. Our results can help to understand the jamming-flowing transition exhibited by a series of various physical systems.Comment: 5 page