ABSTRACT
In the practical production, after the completion of a job on a machine, it may be transported between the different machines. And, the transportation time may affect product quality in certain industries, such as steelmaking. However, the transportation times are commonly neglected in the literature. In this paper, the transportation time and processing time are taken as the independent time into the flexible job shop scheduling problem. The mathematical model of the flexible job shop scheduling problem with transportation time is established to minimize the maximum completion time. The FJSP problem is NP-hard. Then, an improved genetic algorithm is used to solve the problem. In the decoding process, an operation left shift insertion method according to the problem characteristics is proposed to decode the chromosomes in order to get the active scheduling solutions. The actual instance is solved by the proposed algorithm used the Matlab software. The computational results show that the proposed mathematical model and algorithm are valid and feasible, which could effectively guide the actual production practice.
Subject(s)
Models, Theoretical , Personnel Staffing and Scheduling , Transportation , Algorithms , Humans , Industry , Machine Learning , SoftwareABSTRACT
Reflection and transmission due to the incident wave in one-dimensional bead chains when there are impurities have been studied. The impurities can be any kind of material, any size, and their numbers are arbitrary. The dependence of the transmission and the reflection on the numbers and the material parameters of the impurities are given. The analytical results are given by using the inverse scattering method. Substantial reflection is observed if there is only one steel bead. However, the reflection is negligible if there are two steel beads. The reflection monotonously increases as the numbers of the steel beads increase. The reflection remains a constant when the numbers of the steel beads are so many that the length composed by the steel beads is larger than the width of the solitary wave. It can be used to detect the impurities in the beads' chain by measuring the reflection of a pulse.
ABSTRACT
A novel acid-promoted rearrangement is disclosed. In the previously unknown transformation, an allyl group migrated to an in situ formed carbocation stabilized by an electron-rich aryl or heteroaryl group, resulting in a stereoselective intramolecular Grob fragmentation. The outcome of the rearrangement observed with an array of substrates can be satisfactorily rationalized using a working hypothesis with the aid of a six-membered transition state similar to those proposed for the anionic oxy-Cope or oxonia-Cope rearrangements, but involving only one instead of two double bonds.
