Schedule graph

Sanmartf, E., Friedler, E, Puigjaner, L., 1998. Combinatorial technique for short term scheduling of multipurpose batch plants based on schedule-graph representation. Comput. Chem. Eng., 22(Suppl.) S847-S850... 

At this point, a data path is completed. Based on the scheduled graph and the data path, a control unit is synthesized. The user may choose either a hardwired or a micro-program style. 

Bearing in mind that a node (Pj) in the search space corresponds to a discrete combination of batches of products, the feasibility test of a node basically consists in (i) finding the minimum makespan schedule graph for the specific combination of batches of products and (ii) a comparison between the minimum makespan obtained and the fixed time horizon. Clearly, the schedule graph is feasible if the minimum makespan obtained is less or equal than the time horizon length. 

Breakeven charts present a snapshot of the present situation by means of graphs which are generally drawn in the manner shown in Figs. 9-2, 9-3, and 9-4. Since the lines are straight, this implies that Cs, Cy , and Aee will remain constant over the range of variation of R, which is of interest. The values would be based on the production rate currently achieved (or scheduled), since all the data are available from... 

Thomas L. Saaty, On the Problems of Jockeying, Collusion, Scheduling, Optimization, and Graph Theoretic Queues, Office of Naval Research Notes, June, 1961. 

In the context of reachability analysis, this graph is called symbolic reachability graph of the automaton A and can be searched using shortest path search techniques as widely used in computer science. Hence, the task of finding the cost-optimal schedule is to find the shortest (or cheapest) path in a (priced) symbolic reachability graph. 

These combinatorial problems, and many others as well, have a finite number of feasible solutions, a number that increases rapidly with problem size. In a job-shop scheduling problem, the size is measured by the number of jobs. In a traveling salesman problem, it is measured by the number of arcs or nodes in the graph. For a particular problem type and size, each distinct set of problem data defines an instance of the problem. In a traveling salesman problem, the data are the travel times between cities. In a job sequencing problem the data are the processing and set-up times, the due dates, and the penalty costs. 

The mean values of and within the population are 4mg/L and 7mg/kg/day, respectively. The variation within the population is also depicted in Fig. 6, where 50% of the population has K a and Em values within the innermost circle, 75% within the second circle, and so on. With the help of this graph, the suitable dosing rate of phenytoin for an individual patient can be determined. With two plasma concentrations at two different dosing rates of phenytoin in one patient, his/her individual and values can be obtained to further optimize the dosing schedule. 

An alternative method of getting PK data is to take a small extra sample of blood (and urine) at a child s regular scheduled visit when blood is drawn for routine blood work. The time of day of this sample is predetermined by the time of the administration of the medicine. If samples are obtained from many children, a weight-age-corrected, scatter-plot graph can be constructed and a PK profile be calculated. This is the pharmacokinetic screen method. A version of this method is also utilized to gather ethnic data for labeling in adults as well as children, and is called population pharmacokinetics . 

For a comprehensive reference on special functions, see M. Abramowitz and I. A. Stegun, eds.. Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series, Vol 55, Washington, DC, 1964). A Digital Library of Mathematical Functions is in preparation by the National Institute of Standards and Technology. This is scheduled to be online at http //dlmf.nist.gov sometime in 2007. It will feature hypertext links and graphics. 

A feasible schedule corresponds to a selection of one disjunctive arc from every pair in such a way that the resulting directed graph is acyclic. This implies, then, that each selection from a clique has to be acyclic. Such a selection, thus, determines the sequence in which the operations are to be performed on that machine. The length of such a schedule is, then, determined by the longest path... 

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