Modelling either-or relations in integer programming

Logical relations occur frequently in integer programming problems and are modelled by introducing binary variables in association with linear expressions. Applications requiring constraints involving precedence, exclusion, implication and other conditions give rise to the logical relations OR and IMPLIES in the models. These relations will be considered in this paper from a modelling point of view and formulations investigated for situations where the logical variables link sets of integer variables. Valid inequalities (cuts) that can be added to a model will be developed for a number of the formulations and the computational benefits of these cuts will be considered from an experimental point of view by considering the performance of sets of problem instances. New formulations and combinations of older established formulations will be considered. It will be contended that tight formulations may not always be the most successful.     

A Strategy for Solving the Plant Layout Problem

We consider the problem of laying out the facilities of which a plant is composed, in terms of specifying which facilities are to be adjacent. For each pair of facilities a benefit from siting them adjacent to each other is known. We seek to maximise the sum of benefits over all pairs of adjacent facilities.The problem is stated in terms of graph theory, and provision is made for some edges to be considered necessary and others forbidden, where each edge represents an adjacency. We describe a branch and bound algorithm for finding an optimal layout and a sequence of tests for determining whether or not the graphs constructed in the course of the algorithm are planar.     

Photogalvanic cells: Part XI. The thionine-coated electrode

Studies using ring-disc electrodes, cyclic voltammetry, optical absorption and X-ray photoelectron spectroscopy show that up to twenty monolayers of thionine can be irreversibly coated on to platinum or tin oxide electrodes. On such electrodes the electrode kinetics of the thionine-leucothionine couple are still reversible or quasi reversible. In contrast the reduction of Fe(III) is much slower on a coated electrode compared to a clean electrode. Koutecky-Levich plots show that there is a second potential-independent rate-limiting step. This blocking of the Fe(III) reduction means that the thionine coated electrode is the ideal electrode for a photogalvanic cell using the iron thionine system.     

The H2S decomposition activity of supported MoS2 catalysts prepared via PFHS method

Silica-supported MoS₂ catalysts prepared via precipitation from homogeneous solution (PFHS) exhibited high surface areas (180–190 m² g^–1 and activities which were about twice those of the unsupported specimens. An 8% Mo catalyst showed optimum activity. The superior activity of the supported specimen was attributed to the higher population of active sites occasioned by the good dispersion during PFHS. TEM examination also confirmed the existence of small MoS₂ crystallites on the silica support.