Lot sizing with piecewise concave production costs

Cataloged from PDF version of article.We study the lot-sizing problem with piecewise concave production costs and concave holding costs. This problem is a generalization of the lot-sizing problem with quantity discounts, minimum order quantities, capacities, overloading, subcontracting or a combination of these. We develop a dynamic programming algorithm to solve this problem and answer an open question in the literature: we show that the problem is polynomially solvable when the breakpoints of the production cost function are time invariant and the number of breakpoints is fixed. For the special cases with capacities and subcontracting, the time complexity of our algorithm is as good as the complexity of algorithms available in the literature. We report the results of a computational experiment where the dynamic programming is able to solve instances that are hard for a mixed-integer programming solver. We enhance the mixed-integer programming formulation with valid inequalities based on mixing sets and use a cut-and-branch algorithm to compute better bounds. We propose a state space reduction–based heuristic algorithm for large instances and show that the solutions are of good quality by comparing them with the bounds obtained from the cut-and-branch

Stochastic lot sizing problem with controllable processing times

Cataloged from PDF version of article.In this study, we consider the stochastic capacitated lot sizing problem with controllable processing times where processing times can be reduced in return for extra compression cost. We assume that the compression cost function is a convex function as it may reflect increasing marginal costs of larger reductions and may be more appropriate when the resource life, energy consumption or carbon emission are taken into consideration. We consider this problem under static uncertainty strategy and α service level constraints. We first introduce a nonlinear mixed integer programming formulation of the problem, and use the recent advances in second order cone programming to strengthen it and then solve by a commercial solver. Our computational experiments show that taking the processing times as constant may lead to more costly production plans, and the value of controllable processing times becomes more evident for a stochastic environment with a limited capacity. Moreover, we observe that controllable processing times increase the solution flexibility and provide a better solution in most of the problem instances, although the largest improvements are obtained when setup costs are high and the system has medium sized capacities

Adsorption of carbon adatoms to graphene and its nanoribbons

Cataloged from PDF version of article.This paper investigates the adsorption of carbon adatoms on graphene and its nanoribbons using first-principles plane wave calculations within density functional theory. The stability at high carbon adatom coverage, migration, and cluster formation of carbon atoms are analyzed. Carbon adatoms give rise to important changes in electronic and magnetic properties even at low coverage. While bare graphene is nonmagnetic semimetal, it is metallized and acquires magnetic moment upon coverage of carbon adatoms. Calculated magnetic moments vary depending on the coverage of adatoms even for large adatom-adatom distances. Electronic and magnetic properties of hydrogen passivated armchair and zigzag nanoribbons show strong dependence on the adsorption site. We also predict a new type of carbon impurity defect in graphene, which has a small formation energy. Interactions between distant carbon adatoms imply a long ranged interaction

Pure cycles in flexible robotic cells

Cataloged from PDF version of article.In this study, an m-machine flexible robotic manufacturing cell consisting of CNC machines is considered. The flexibility of the machines leads to a new class of robot move cycles called the pure cycles. We first model the problem of determining the best pure cycle in an m-machine cell as a special travelling salesman problem in which the distance matrix consists of decision variables as well as parameters.We focus on two specific cycles among the huge class of pure cycles.We prove that, in most of the regions, either one of these two cycles is optimal. For the remaining regions we derive worst case performances of these cycles.We also prove that the set of pure cycles dominates the flowshop-type robot move cycles considered in the literature. As a design problem, we consider the number of machines in a cell as a decision variable. We determine the optimal number of machines that minimizes the cycle time for given cell parameters such as the processing times, robot travel times and the loading/unloading times of the machines. 2007 Elsevier Ltd. All rights reserved

High-capacity hydrogen storage by metallized graphene

First-principles plane wave calculations predict that Li can be adsorbed on graphene forming a uniform and stable coverage on both sides. A significant part of the electronic charge of the Li-$2s$ orbital is donated to graphene and is accommodated by its distorted $\pi^*$-bands. As a result, semimetallic graphene and semiconducting graphene ribbons change into good metals. It is even more remarkable that Li covered graphene can serve as a high-capacity hydrogen storage medium with each adsorbed Li absorbing up to four H$_2$ molecules amounting to a gravimetric density of 12.8 wt%.Comment: 4 pages, 2 figure

Scheduling in a three-machine robotic flexible manufacturing cell

Cataloged from PDF version of article.In this study, we consider a flexible manufacturing cell (FMC) processing identical parts on which the loading and unloading of machines are made by a robot. The machines used in FMCs are predominantly CNC machines and these machines are flexible enough for performing several operations provided that the required tools are stored in their tool magazines. Traditional research in this area considers a flowshop type system. The current study relaxes this flowshop assumption which unnecessarily limits the number of alternatives. In traditional robotic cell scheduling literature, the processing time of each part on each machine is a known parameter. However, in this study the processing times of the parts on the machines are decision variables. Therefore, we investigated the productivity gain attained by the additional flexibility introduced by the FMCs. We propose new lower bounds for the 1-unit and 2-unit robot move cycles (for which we present a completely new procedure to derive the activity sequences of 2-unit cycles in a three-machine robotic cell) under the new problem domain for the flowshop type robot move cycles. We also propose a new robot move cycle which is a direct consequence of process and operational flexibility of CNC machines.We prove that this proposed cycle dominates all 2-unit robot move cycles and present the regions where the proposed cycle dominates all 1-unit cycles.We also present a worst case performance bound of using this proposed cycle. 2005 Elsevier Ltd. All rights reserved

Scheduling in robotic cells: Process flexibility and cell layout

The focus of this study is the identical parts robotic cell scheduling problem with m machines under the assumption of process and operational flexibility. A direct consequence of this assumption is a new robot move cycle that has been overlooked in the existing literature. We prove that this new cycle dominates all classical robot move cycles considered in the literature for m = 2. We also prove that changing the layout from an in-line robotic cell to a robot-centered cell reduces the cycle time of the proposed cycle even further, whereas the cycle times of all other cycles remain the same. For the m-machine case, we find the regions where the proposed cycle dominates the classical robot move cycles, and for the remaining regions present its worst case performance with respect to classical robot move cycles. Considering the number of machines as a decision variable, we also find the optimal number of machines that minimizes the cycle time of the proposed cycle