We propose an approach for large-scale non-separable nonlinear multicommodity flow problems by solving a sequence of subproblems which can be addressed by commercial solvers. Using a combination of solution methods such as modified gradient projection, shortest path algorithm and golden section search, the approach can handle general problem instances, including those with (i) non-separable cost, (ii) objective function not available analytically as polynomial but are evaluated using black-boxes, and (iii) additional side constraints not of network flow types. Implemented as a toolbox in commercial solvers, it allows researchers and practitioners, currently conversant with linear instances, to easily manage large-scale convex instances as well. In this article, we compared the proposed algorithm with alternative approaches in the literature, covering both theory and large test cases. New test cases with non-separable convex costs and non-network flow side constraints are also presented and evaluated. The toolbox is available free for academic use upon request.
With the need of more responsive and resilient manufacturing processes for high value, customised products, Flexible Manufacturing Systems (FMS) remain a very relevant manufacturing approach. Due to their complexity, quality monitoring in these types of systems can be very difficult, particularly in those scenarios where the monitoring cannot be fully automated due to functional, safety and legal characteristics. In these scenarios, quality practitioners concentrate on monitoring the most critical processes and leaving out the inspection of those that are still meeting quality requirements but showing signs of future failure. In this paper we introduce a methodology and visualisation tool based on data analytics that allows the practitioner to anticipate out of control processes and take action. By identifying a reference model or best performing machine, and the occurring patterns in the quality data, the presented approach identifies the adjustable processes that are still in control, allowing the practitioner to decide if any changes in the machine's settings are needed (tool replacement, repositioning the axis, etc). An initial deployment of the tool at BMW Plant Hams Hall to monitor a focussed set of part types and features has shown a reduction in scrap of 97% throughout 2020 in relation to the monitored features compared to the previous year. This in the long run will reduce reaction time in following quality control procedure, reduce significant scrap costs and ultimately reduce the need for measurements and enable more output in terms of volume capacity.
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