A multi-stage stochastic programming approach in master production scheduling

Master Production Schedules (MPS) are widely used in industry, especially within Enterprise Resource Planning (ERP) software. The classical approach for generating MPS assumes infinite capacity, fixed processing times, and a single scenario for demand forecasts. In this paper, we question these assumptions and consider a problem with finite capacity, controllable processing times, and several demand scenarios instead of just one. We use a multi-stage stochastic programming approach in order to come up with the maximum expected profit given the demand scenarios. Controllable processing times enlarge the solution space so that the limited capacity of production resources are utilized more effectively. We propose an effective formulation that enables an extensive computational study. Our computational results clearly indicate that instead of relying on relatively simple heuristic methods, multi-stage stochastic programming can be used effectively to solve MPS problems, and that controllability increases the performance of multi-stage solutions

An anticipative scheduling approach with controllable processing times

In practice, machine schedules are usually subject to disruptions which have to be repaired by reactive scheduling decisions. The most popular predictive approach in project management and machine scheduling literature is to leave idle times (time buffers) in schedules in coping with disruptions, i.e. the resources will be under-utilized. Therefore, preparing initial schedules by considering possible disruption times along with rescheduling objectives is critical for the performance of rescheduling decisions. In this paper, we show that if the processing times are controllable then an anticipative approach can be used to form an initial schedule so that the limited capacity of the production resources are utilized more effectively. To illustrate the anticipative scheduling idea, we consider a non-identical parallel machining environment, where processing times can be controlled at a certain compression cost. When there is a disruption during the execution of the initial schedule, a match-up time strategy is utilized such that a repaired schedule has to catch-up initial schedule at some point in future. This requires changing machine–job assignments and processing times for the rest of the schedule which implies increased manufacturing costs. We show that making anticipative job sequencing decisions, based on failure and repair time distributions and flexibility of jobs, one can repair schedules by incurring less manufacturing cost. Our computational results show that the match-up time strategy is very sensitive to initial schedule and the proposed anticipative scheduling algorithm can be very helpful to reduce rescheduling costs

Properties of Graphene: A Theoretical Perspective

In this review, we provide an in-depth description of the physics of monolayer and bilayer graphene from a theorist's perspective. We discuss the physical properties of graphene in an external magnetic field, reflecting the chiral nature of the quasiparticles near the Dirac point with a Landau level at zero energy. We address the unique integer quantum Hall effects, the role of electron correlations, and the recent observation of the fractional quantum Hall effect in the monolayer graphene. The quantum Hall effect in bilayer graphene is fundamentally different from that of a monolayer, reflecting the unique band structure of this system. The theory of transport in the absence of an external magnetic field is discussed in detail, along with the role of disorder studied in various theoretical models. We highlight the differences and similarities between monolayer and bilayer graphene, and focus on thermodynamic properties such as the compressibility, the plasmon spectra, the weak localization correction, quantum Hall effect, and optical properties. Confinement of electrons in graphene is nontrivial due to Klein tunneling. We review various theoretical and experimental studies of quantum confined structures made from graphene. The band structure of graphene nanoribbons and the role of the sublattice symmetry, edge geometry and the size of the nanoribbon on the electronic and magnetic properties are very active areas of research, and a detailed review of these topics is presented. Also, the effects of substrate interactions, adsorbed atoms, lattice defects and doping on the band structure of finite-sized graphene systems are discussed. We also include a brief description of graphane -- gapped material obtained from graphene by attaching hydrogen atoms to each carbon atom in the lattice.Comment: 189 pages. submitted in Advances in Physic