An integrated scheduling problem of PCB components on sequential pick-and-place machines:mathematical models and heuristic solutions

This paper formulates several mathematical models for determining the optimal sequence of component placements and assignment of component types to feeders simultaneously or the integrated scheduling problem for a type of surface mount technology placement machines, called the sequential pick-andplace (PAP) machine. A PAP machine has multiple stationary feeders storing components, a stationary working table holding a printed circuit board (PCB), and a movable placement head to pick up components from feeders and place them to a board. The objective of integrated problem is to minimize the total distance traveled by the placement head. Two integer nonlinear programming models are formulated first. Then, each of them is equivalently converted into an integer linear type. The models for the integrated problem are verified by two commercial packages. In addition, a hybrid genetic algorithm previously developed by the authors is adopted to solve the models. The algorithm not only generates the optimal solutions quickly for small-sized problems, but also outperforms the genetic algorithms developed by other researchers in terms of total traveling distance.

Development of multiphase and multiscale mathematical models for thermal spray process

High velocity oxyfuel (HVOF) thermal spraying is one of the most significant developments in the thermal spray industry since the development of the original plasma spray technique. The first investigation deals with the combustion and discrete particle models within the general purpose commercial CFD code FLUENT to solve the combustion of kerosene and couple the motion of fuel droplets with the gas flow dynamics in a Lagrangian fashion. The effects of liquid fuel droplets on the thermodynamics of the combusting gas flow are examined thoroughly showing that combustion process of kerosene is independent on the initial fuel droplet sizes. The second analysis copes with the full water cooling numerical model, which can assist on thermal performance optimisation or to determine the best method for heat removal without the cost of building physical prototypes. The numerical results indicate that the water flow rate and direction has noticeable influence on the cooling efficiency but no noticeable effect on the gas flow dynamics within the thermal spraying gun. The third investigation deals with the development and implementation of discrete phase particle models. The results indicate that most powder particles are not melted upon hitting the substrate to be coated. The oxidation model confirms that HVOF guns can produce metallic coating with low oxidation within the typical standing-off distance about 30cm. Physical properties such as porosity, microstructure, surface roughness and adhesion strength of coatings produced by droplet deposition in a thermal spray process are determined to a large extent by the dynamics of deformation and solidification of the particles impinging on the substrate. Therefore, is one of the objectives of this study to present a complete numerical model of droplet impact and solidification. The modelling results show that solidification of droplets is significantly affected by the thermal contact resistance/substrate surface roughness.

Hypoxia-inducible factor (HIF) network:insights from mathematical models

Oxygen is a crucial molecule for cellular function. When oxygen demand exceeds supply, the oxygen sensing pathway centred on the hypoxia inducible factor (HIF) is switched on and promotes adaptation to hypoxia by up-regulating genes involved in angiogenesis, erythropoiesis and glycolysis. The regulation of HIF is tightly modulated through intricate regulatory mechanisms. Notably, its protein stability is controlled by the oxygen sensing prolyl hydroxylase domain (PHD) enzymes and its transcriptional activity is controlled by the asparaginyl hydroxylase FIH (factor inhibiting HIF-1).To probe the complexity of hypoxia-induced HIF signalling, efforts in mathematical modelling of the pathway have been underway for around a decade. In this paper, we review the existing mathematical models developed to describe and explain specific behaviours of the HIF pathway and how they have contributed new insights into our understanding of the network. Topics for modelling included the switch-like response to decreased oxygen gradient, the role of micro environmental factors, the regulation by FIH and the temporal dynamics of the HIF response. We will also discuss the technical aspects, extent and limitations of these models. Recently, HIF pathway has been implicated in other disease contexts such as hypoxic inflammation and cancer through crosstalking with pathways like NF?B and mTOR. We will examine how future mathematical modelling and simulation of interlinked networks can aid in understanding HIF behaviour in complex pathophysiological situations. Ultimately this would allow the identification of new pharmacological targets in different disease settings.

Experiments in time:exploring the components of motor timing behaviour in dyslexia

This investigation aimed to pinpoint the elements of motor timing control that are responsible for the increased variability commonly found in children with developmental dyslexia on paced or unpaced motor timing tasks (Chapter 3). Such temporal processing abilities are thought to be important for developing the appropriate phonological representations required for the development of literacy skills. Similar temporal processing difficulties arise in other developmental disorders such as Attention Deficit Hyperactivity Disorder (ADHD). Motor timing behaviour in developmental populations was examined in the context of models of typical human timing behaviour, in particular the Wing-Kristofferson model, allowing estimation of the contribution of different timing control systems, namely timekeeper and implementation systems (Chapter 2 and Methods Chapters 4 and 5). Research examining timing in populations with dyslexia and ADHD has been inconsistent in the application of stimulus parameters and so the first investigation compared motor timing behaviour across different stimulus conditions (Chapter 6). The results question the suitability of visual timing tasks which produced greater performance variability than auditory or bimodal tasks. Following an examination of the validity of the Wing-Kristofferson model (Chapter 7) the model was applied to time series data from an auditory timing task completed by children with reading difficulties and matched control groups (Chapter 8). Expected group differences in timing performance were not found, however, associations between performance and measures of literacy and attention were present. Results also indicated that measures of attention and literacy dissociated in their relationships with components of timing, with literacy ability being correlated with timekeeper variance and attentional control with implementation variance. It is proposed that these timing deficits associated with reading difficulties are attributable to central timekeeping processes and so the contribution of error correction to timing performance was also investigated (Chapter 9). Children with lower scores on measures of literacy and attention were found to have a slower or failed correction response to phase errors in timing behaviour. Results from the series of studies suggest that the motor timing difficulty in poor reading children may stem from failures in the judgement of synchrony due to greater tolerance of uncertainty in the temporal processing system.

A decision support system for supplier selection and order allocation in stochastic, multi-stakeholder and multi-criteria environments

Integrated supplier selection and order allocation is an important decision for both designing and operating supply chains. This decision is often influenced by the concerned stakeholders, suppliers, plant operators and customers in different tiers. As firms continue to seek competitive advantage through supply chain design and operations they aim to create optimized supply chains. This calls for on one hand consideration of multiple conflicting criteria and on the other hand consideration of uncertainties of demand and supply. Although there are studies on supplier selection using advanced mathematical models to cover a stochastic approach, multiple criteria decision making techniques and multiple stakeholder requirements separately, according to authors' knowledge there is no work that integrates these three aspects in a common framework. This paper proposes an integrated method for dealing with such problems using a combined Analytic Hierarchy Process-Quality Function Deployment (AHP-QFD) and chance constrained optimization algorithm approach that selects appropriate suppliers and allocates orders optimally between them. The effectiveness of the proposed decision support system has been demonstrated through application and validation in the bioenergy industry.

Quantitative risk assessment of groundwater quality utilizing GIS technology and coupled groundwater models

The thesis presents a two-dimensional Risk Assessment Method (RAM) where the assessment of risk to the groundwater resources incorporates both the quantification of the probability of the occurrence of contaminant source terms, as well as the assessment of the resultant impacts. The approach emphasizes the need for a greater dependency on the potential pollution sources, rather than the traditional approach where assessment is based mainly on the intrinsic geo-hydrologic parameters. The risk is calculated using Monte Carlo simulation methods whereby random pollution events were generated to the same distribution as historically occurring events or a priori potential probability distribution. Integrated mathematical models then simulate contaminant concentrations at the predefined monitoring points within the aquifer. The spatial and temporal distributions of the concentrations were calculated from repeated realisations, and the number of times when a user defined concentration magnitude was exceeded is quantified as a risk. The method was setup by integrating MODFLOW-2000, MT3DMS and a FORTRAN coded risk model, and automated, using a DOS batch processing file. GIS software was employed in producing the input files and for the presentation of the results. The functionalities of the method, as well as its sensitivities to the model grid sizes, contaminant loading rates, length of stress periods, and the historical frequencies of occurrence of pollution events were evaluated using hypothetical scenarios and a case study. Chloride-related pollution sources were compiled and used as indicative potential contaminant sources for the case study. At any active model cell, if a random generated number is less than the probability of pollution occurrence, then the risk model will generate synthetic contaminant source term as an input into the transport model. The results of the applications of the method are presented in the form of tables, graphs and spatial maps. Varying the model grid sizes indicates no significant effects on the simulated groundwater head. The simulated frequency of daily occurrence of pollution incidents is also independent of the model dimensions. However, the simulated total contaminant mass generated within the aquifer, and the associated volumetric numerical error appear to increase with the increasing grid sizes. Also, the migration of contaminant plume advances faster with the coarse grid sizes as compared to the finer grid sizes. The number of daily contaminant source terms generated and consequently the total mass of contaminant within the aquifer increases in a non linear proportion to the increasing frequency of occurrence of pollution events. The risk of pollution from a number of sources all occurring by chance together was evaluated, and quantitatively presented as risk maps. This capability to combine the risk to a groundwater feature from numerous potential sources of pollution proved to be a great asset to the method, and a large benefit over the contemporary risk and vulnerability methods.

Optimal production planning for PCB assembly

It is indisputable that printed circuit boards (PCBs) play a vital role in our daily lives. With the ever-increasing applications of PCBs, one of the crucial ways to increase a PCB manufacturer’s competitiveness in terms of operation efficiency is to minimize the production time so that the products can be introduced to the market sooner. Optimal Production Planning for PCB Assembly is the first book to focus on the optimization of the PCB assembly lines’ efficiency. This is done by: • integrating the component sequencing and the feeder arrangement problems together for both the pick-and-place machine and the chip shooter machine; • constructing mathematical models and developing an efficient and effective heuristic solution approach for the integrated problems for both types of placement machines, the line assignment problem, and the component allocation problem; and • developing a prototype of the PCB assembly planning system. The techniques proposed in Optimal Production Planning for PCB Assembly will enable process planners in the electronics manufacturing industry to improve the assembly line’s efficiency in their companies. Graduate students in operations research can familiarise themselves with the techniques and the applications of mathematical modeling after reading this advanced introduction to optimal production planning for PCB assembly.

Integrated component scheduling models for chip shooter machines

This paper focuses on minimizing printed circuit board (PCB) assembly time for a chipshootermachine, which has a movable feeder carrier holding components, a movable X–Y table carrying a PCB, and a rotary turret with multiple assembly heads. The assembly time of the machine depends on two inter-related optimization problems: the component sequencing problem and the feeder arrangement problem. Nevertheless, they were often regarded as two individual problems and solved separately. This paper proposes two complete mathematical models for the integrated problem of the machine. The models are verified by two commercial packages. Finally, a hybrid genetic algorithm previously developed by the authors is presented to solve the model. The algorithm not only generates the optimal solutions quickly for small-sized problems, but also outperforms the genetic algorithms developed by other researchers in terms of total assembly time.

Mechanisms of convective drying in thick beds of solids

The literature on heat and mass transfer mechanisms in the convective drying of thick beds of solids has been critically reviewed. Related mathematical models of heat transfer are also considered. Experimental and theoretical studies were made of the temperature distribution within beds, and of drying rates, with various materials undergoing convective drying. The experimental work covered thick beds of hygroscopic and non-hygroscopic materials (glass beads of different diameters, polystyrene pellets, activated alumina and wood powder) at air temperatures of 54°C to 84°C. Tests were carried out in a laboratory drying apparatus comprising a wind tunnel through which the air, of controlled temperature and humidity, was passed over a sample suspended from a balance. Thermocouples were inserted at different depths within the sample bed. The temperature distribution profiles for both hygroscopic and non-hygroscopic beds exhibited a clear difference between the temperatures at the surface and bottom during the constant rate period. An effective method was introduced for predicting the critical moisture content. During the falling rate the profiles showed the existence of a receding evaporation plane; this divided the system into a hotter dry zone in the upper section and a wet zone near the bottom. A graphical procedure was established to predict accurately the position of the receding evaporation front at any time. A new mathematical model, based on the receding evaporation front phenomenon, was proposed to predict temperature distributions throughout a bed during drying. Good agreement was obtained when the model was validated by comparing its predictions with experimental data. The model was also able to predict the duration of each drying stage. In experiments using sample trays of different diameters, the drying rate was found to increase with a decrease in the effective length of the bed surface. During the constant rate period with trays of a small effective length, i.e. less than 0.08 m, an 'inversion' in temperature distribution occurred in the bed; the bottom temperature increased and became greater than that of the surface. Experimental measurements were verified in several ways to ensure this phenomenon was real. Theoretical explanations are given for both the effective length and temperature inversion phenomena.

The separation of secondary oil-water dispersions in particulate beds

The literature relating to haze formation, methods of separation, coalescence mechanisms, and models by which droplets <100 μm are collected, coalesced and transferred, have been reviewed with particular reference to particulate bed coalescers. The separation of secondary oil-water dispersions was studied experimentally using packed beds of monosized glass ballotini particles. The variables investigated were superficial velocity, bed depth, particle size, and the phase ratio and drop size distribution of inlet secondary dispersion. A modified pump loop was used to generate secondary dispersions of toluene or Clairsol 350 in water with phase ratios between 0.5-6.0 v/v%.Inlet drop size distributions were determined using a Malvern Particle Size Analyser;effluent, coalesced droplets were sized by photography. Single phase flow pressure drop data were correlated by means of a Carman-Kozeny type equation. Correlations were obtained relating single and two phase pressure drops, as (ΔP2/μc)/ΔP1/μd) = kp Ua Lb dcc dpd Cine A flow equation was derived to correlate the two phase pressure drop data as, ΔP2/(ρcU2) = 8.64*107 [dc/D]-0.27 [L/D]0.71 [dp/D]-0.17 [NRe]1.5 [e1]-0.14 [Cin]0.26  In a comparison between functions to characterise the inlet drop size distributions a modification of the Weibull function provided the best fit of experimental data. The general mean drop diameter was correlated by: q_p q_p p_q /β      Γ ((q-3/β) +1) d qp = d fr  .α        Γ ((P-3/β +1 The measured and predicted mean inlet drop diameters agreed within ±15%. Secondary dispersion separation depends largely upon drop capture within a bed. A theoretical analysis of drop capture mechanisms in this work indicated that indirect interception and London-van der Waal's mechanisms predominate. Mathematical models of dispersed phase concentration m the bed were developed by considering drop motion to be analogous to molecular diffusion.The number of possible channels in a bed was predicted from a model in which the pores comprised randomly-interconnected passage-ways between adjacent packing elements and axial flow occured in cylinders on an equilateral triangular pitch. An expression was derived for length of service channels in a queuing system leading to the prediction of filter coefficients. The insight provided into the mechanisms of drop collection and travel, and the correlations of operating parameters, should assist design of industrial particulate bed coalescers.

Multi-function controllers for a hydraulic pump

This project has been undertaken for Hamworthy Hydraulics Limited. Its objective was to design and develop a controller package for a variable displacement, hydraulic pump for use mainly on mobile earth moving machinery. A survey was undertaken of control options used in practice and from this a design specification was formulated, the successful implementation of which would give Hamworthy an advantage over its competitors. Two different modes for the controller were envisaged. One consisted of using conventional hydro-mechanics and the other was based upon a microprocessor. To meet short term customer prototype requirements the first section of work was the realisation of the hydro-mechanical system. Mathematical models were made to evaluate controller stability and hence aid their design. The final package met the requirements of the specification and a single version could operate all sizes of variable displacement pumps in the Hamworthy range. The choice of controller options and combinations totalled twenty-four. The hydro-mechanical controller was complex and it was realised that a micro-processor system would allow all options to be implemented with just one design of hardware, thus greatly simplifying production. The final section of this project was to determine whether such a design was feasible. This entailed finding cheap, reliable transducers, using mathematical models to predict electro-hydraulic interface stability, testing such interfaces and finally incorporating a micro-processor in an interactive control loop. The study revealed that such a system was technically possible but it would cost 60% more than its hydro-mechanical counterpart. It was therefore concluded that, in the short term, for the markets considered, the hydro-mechanical design was the better solution. Regarding the micro-processor system the final conclusion was that, because the relative costs of the two systems are decreasing, the electro-hydraulic controller will gradually become more attractive and therefore Hamworthy should continue with its development.

GIS linked environmental process models

In recent years there has been a great effort to combine the technologies and techniques of GIS and process models. This project examines the issues of linking a standard current generation 2½d GIS with several existing model codes. The focus for the project has been the Shropshire Groundwater Scheme, which is being developed to augment flow in the River Severn during drought periods by pumping water from the Shropshire Aquifer. Previous authors have demonstrated that under certain circumstances pumping could reduce the soil moisture available for crops. This project follows earlier work at Aston in which the effects of drawdown were delineated and quantified through the development of a software package that implemented a technique which brought together the significant spatially varying parameters. This technique is repeated here, but using a standard GIS called GRASS. The GIS proved adequate for the task and the added functionality provided by the general purpose GIS - the data capture, manipulation and visualisation facilities - were of great benefit. The bulk of the project is concerned with examining the issues of the linkage of GIS and environmental process models. To this end a groundwater model (Modflow) and a soil moisture model (SWMS2D) were linked to the GIS and a crop model was implemented within the GIS. A loose-linked approach was adopted and secondary and surrogate data were used wherever possible. The implications of which relate to; justification of a loose-linked versus a closely integrated approach; how, technically, to achieve the linkage; how to reconcile the different data models used by the GIS and the process models; control of the movement of data between models of environmental subsystems, to model the total system; the advantages and disadvantages of using a current generation GIS as a medium for linking environmental process models; generation of input data, including the use of geostatistic, stochastic simulation, remote sensing, regression equations and mapped data; issues of accuracy, uncertainty and simply providing adequate data for the complex models; how such a modelling system fits into an organisational framework.

The application of expert systems techniques in the design of durable concrete

This thesis describes work done exploring the application of expert system techniques to the domain of designing durable concrete. The nature of concrete durability design is described and some problems from the domain are discussed. Some related work on expert systems in concrete durability are described. Various implementation languages are considered - PROLOG and OPS5, and rejected in favour of a shell - CRYSTAL3 (later CRYSTAL4). Criteria for useful expert system shells in the domain are discussed. CRYSTAL4 is evaluated in the light of these criteria. Modules in various sub-domains (mix-design, sulphate attack, steel-corrosion and alkali aggregate reaction) are developed and organised under a BLACKBOARD system (called DEX). Extensions to the CRYSTAL4 modules are considered for different knowledge representations. These include LOTUS123 spreadsheets implementing models incorporating some of the mathematical knowledge in the domain. Design databases are used to represent tabular design knowledge. Hypertext representations of the original building standards texts are proposed as a tool for providing a well structured and extensive justification/help facility. A standardised approach to module development is proposed using hypertext development as a structured basis for expert systems development. Some areas of deficient domain knowledge are highlighted particularly in the use of data from mathematical models and in gaps and inconsistencies in the original knowledge source Digests.