Modeling of High Throughput Screening Systems
In this paper we propose a max-plus algebra modeling, which guarantees non-negative order models for any predetermined optimal schedule of high throughput screening systems. Often for such systems, some events in previous batches are expected to happen af
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Abstract In this paper we propose a max-plus algebra modeling, which guarantees non-negative order models for any predetermined optimal schedule of high throughput screening systems. Often for such systems, some events in previous batches are expected to happen after certain events in later batches. Therefore there are negative order system matrices in the corresponding models. With a straightforward re-indexing process, the proposed modeling avoids searching and calculating of transformation matrix and thus derives non-negative order models directly and quickly. Keywords High throughput screening systems • Max-plus algebra • Modeling
1 Introduction High throughput screening (HTS) systems [1] are used in fields of biology, chemistry and especially in pharmaceutical industries to automatically identify biochemical and/or chemical compounds. In a very short time, HTS processes are able to automatically screen thousands of substances. In such processes, hundreds of substances are aggregated within one batch. A large number of batches have to pass through resources (e.g., incubators, pipettes) to finish all activities or work steps. In order to compare many different batches of an assay, it is often required that each batch follows an identical time scheme. In other words, HTS systems are operated in a strictly cyclic way. Although cyclic operation is sometimes also
D. Li (*) • X. Li • H. Wan • B. Xu • J. Wang School of Electrical and Electronic Engineering, Shanghai Institute of Technology, Shanghai, China e-mail: [email protected] W. Wang (ed.), Mechatronics and Automatic Control Systems, Lecture Notes in Electrical Engineering 237, DOI 10.1007/978-3-319-01273-5_50, © Springer International Publishing Switzerland 2014
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applied to other discrete event system (DES) applications such as manufacturing or chemical engineering, the HTS scheduling problem and its control still differ from problems of those systems [2]. For example, there may be upper and/or lower time bounds for batch time scheme. Especially, in HTS systems, resources may be shared by several batches and may be revisited several times by the same batch. Moreover, there are no buffers between the resources. Mayer, Raisch and colleagues proposed a method to determine the globally optimal schedules for such systems [1, 2]. With max-plus algebra, it is then possible to model the predetermined optimal schedule to perform further system analysis and control. Often for such optimal schedules of HTS systems, some events in previous batches are expected to occur after certain events of later batches. This results in negative order system matrices in the corresponding models. By introducing the γ transformation [3, 4], the existing negative order system matrices could be eliminated with the help of some certain transformation matrix t. However, in this paper, instead of searching for the corresponding transformation matrix t, we especially discuss a straightforward re-indexing process to model predetermined schedules for HTS systems. For a p
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