An improved approximation algorithm for the two-machine flow shop scheduling problem with an interstage transporter

We study the two-machine flow shop problem with an uncapacitated interstage transporter. The jobs have to be split into batches, and upon completion on the first machine, each batch has to be shipped to the second machine by a transporter. The best known heuristic for the problem is a –approximation algorithm that outputs a two-shipment schedule. We design a –approximation algorithm that finds schedules with at most three shipments, and this ratio cannot be improved, unless schedules with more shipments are created. This improvement is achieved due to a thorough analysis of schedules with two and three shipments by means of linear programming. We formulate problems of finding an optimal schedule with two or three shipments as integer linear programs and develop strongly polynomial algorithms that find solutions to their continuous relaxations with a small number of fractional variables

An improved approximation algorithm for the two-machine open shop scheduling problem with family setup times

We consider the problem of scheduling families of jobs in a two-machine open shop so as to minimize the makespan. The jobs of each family can be partitioned into batches and a family setup time on each machine is required before the first job is processed, and when a machine switches from processing a job of some family to a job of another family. For this NP-hard problem the literature contains (5/4)-approximation algorithms that cannot be improved on using the class of group technology algorithms in which each family is kept as a single batch. We demonstrate that there is no advantage in splitting a family more than once. We present an algorithm that splits one family at most once on a machine and delivers a worst-case performance ratio of 6/5.

Differential amplifier with improved gain-accuracy and linearity

A novel circuit design technique is presented which improves gain-accuracy and linearity in differential amplifiers. The technique employs negative impedance compensation and results demonstrate a significant performance improvement in precision, lowering sensitivity, and wide dynamic range. A theoretical underpinning is given together with the results of a demonstrator differential input/output amplifier with gain of 12 dB. The simulation results show that, with the novel method, both the gain-accuracy and linearity can be improved greatly. Especially, the linearity improvement in IMD can get to more than 23 dB with a required gain.

Modelling of dosator operation for improved manufacturing performance

Purpose: To develop an improved mathematical model for the prediction of dose accuracy of Dosators - based upon the geometry of the machine in conjunction with measured flow properties of the powder. Methods: A mathematical model has been created, based on a analytical method of differential slices - incorporating measured flow properties. The key flow properties of interest in this investigation were: flow function, effective angle of wall friction, wall adhesion, bulk density, stress ratio K and permeability. To simulate the real process and (very importantly) validate the model, a Dosator test-rig has been used to measure the forces acting on the Dosator during the filling stage, the force required to eject the dose and the dose weight. Results: Preliminary results were obtained from the Dosator test-rig. Figure 1 [Omitted] shows the dose weight for different depths to the bottom of the powder bed at the end of the stroke and different levels of pre-compaction of the powder bed. A strong influence over dose weight arising from the proximity between the Dosator and the bottom of the powder bed at the end of the stroke and the conditions of the powder bed has been established. Conclusions: The model will provide a useful tool to predict dosing accuracy and, thus, optimise the future design of Dosator based equipment technology – based on measured bulk properties of the powder to be handled. Another important factor (with a significant influence) on Dosator processes, is the condition of the powder bed and the clearance between the Dosator and the bottom of the powder bed.