Computer time scheduling

Sand, G. and Engell, S. (2003) Modeling and solving real-time scheduling problems by stochastic integer programming. Comput. Chem. Eng., 28, 1087-1103. 

Despite advances in MILP solution methods, problem size is still a major issue since scheduling problems are known to be NP-hard (i.e., exponential increase of computation time with size in worst case). While effective modeling can help to overcome to some extent the issue of computational efficiency, special solution strategies such as decomposition and aggregation are needed in order to address the ever increasing sizes of real-world problems. 

By a comparison of the new evolutionary algorithm s performance with state-of-the-art solvers for a real-world scheduling problem it was found that the new algorithm shows a competitive performance. In contrast to the other algorithms the evolutionary algorithm was able to provide relatively good solutions in short computation times. 

The results presented in Table 10.2 lead to some interesting observations. Generally, all problem instances could be scheduled within reasonable computation times and thus the method is suitable for on-line scheduling. The next observation is that the overproduction generally increases when higher amounts of raw materials are given... 

A new optimisation structure (Fig.2) for the scheduling of operational activities in a real-world pipeline network (Fig.l) has been addressed in this paper. In addition, a new computational procedure was developed, the Pre-Analysis module. The real scenario could be addressed mostly due to Pre-Analysis scalability. The considered scenario is particularly complex and involves more nodes and pipes, compared to the one discussed in a previous work [5]. In order to address this scenario, a decomposition approach was used. This decomposition relied on a Resoince Allocation block, which takes into accoimt production/consumption functions and typical lot sizes to determine a set of candidate sequences of pumping. Furthermore, a Pre-Analysis block uses candidate sequences to determine temporal and volume parameters. These parameters were used in a continuous-time MILP model, which indeed determines the short-term scheduling of each batch in each node of the pipeline network. The implemented structure can be used, for instance, to identify system bottlenecks and to test new operational conditions. Computation time has remained at few CPU seconds. The proposed approach have allowed that a monthly planning of production and consumption be detailed in short-time scheduling operations within the considered pipeline network. Thus, operational insights can be derived from the obtained solutions. As an ongoing research, the Pre-Analysis would be used to determine other parameters for the MILP model. 

The algorithm, as described above, requires a huge amount of computation time, when applied to the plant in Figure 2, as the simulation algorithm is time consuming. To eliminate unnecessary start time calculations, we modify the probabilistic step in SA slightly. In most cases, the newly created production sequences in SA are worse than the current candidate for the best schedule. However, to realize this, we have to execute all the steps of the simulation algorithm, which is a waste of time. If these bad schedules can be eliminated at... 

It is difficult to say if the schedule in Figure 11 is optimal. However, it is the best available at present, as we could not improve it by manually changing the processing orders on the basis of experience. When the same problem was solved without the modification to SA, the computation time was four times as long. This clearly indicates the impact of a small modification in the SA algorithm. 

The tracking of samples and their schedule test dates is easily handled with a modern computer system scheduler. With the computerized scheduling system in place, the workload can be organized on a daily, weekly, or monthly basis. Each sample should be identified with the methods to be used. A key factor for planning is to be able to look ahead for the required period of time to identify the resources needed so that adjustments can be implemented to cover the scheduled workload. 

The calculation for neocarzinostatin took about a month with 20 of 1.6 GHz Pentium 4 CPUs scheduled by SUN GRID engine. The computation time can be easily reduced by advanced CPUs and an increased number of GRID computing nodes. In the near future, the computation time for this size of calculations will be days or hours, and can become a routine process with full automation. If the calculation becomes a routine, there will be no need to care about differences in calculation qualities of the PDB coordinates (Section 2). By distance constraint files, the structures can be easily reproduced with equal calculation qualities. For this purpose, the deposition of the constraints file in the PDB is very important. The constraints file and order parameters (if available in the Biological Magnetic Resonance Data Bank) will be able to describe a unique NMR structural potentiality with dynamics as discussed in Section 10. 

Real-time clock Every digital computer used for process control must have a real-time clock. This is the device that keeps track of the real world s time and allows the computer to schedule its functions at time intervals in coordination with the various needs of the real world. Thus it is the real-time clock that determines when the computer should take data from measuring sensors or change the values of manipulated variables. 

Both microdialysis and ultraiiltration can be automated. The microdialysis pump can be combined with a syringe selector and computer-controlled to perfuse with different solutions on a timed schedule. The samples can be collected in a computer-controlled fraction collector at preset intervals or injected directly into an HPLC analyzer. Ultrafiltration sample collection can also be automated with the use of a pump and a fraction collector. 

Maravelias C.T. and Grossmann LE. 2004. A hybrid MILP/CP decomposition approach for the continuous time scheduling of multipurpose batch plants, Comput. Chem. Eng. (in press). 

Computers can also be used to determine the schedule of daily observations. For example, work sampling programs for the DataMyte coUecter described in Section 2.2 can print rrmdom time schedules. 

For some problems so-called polynomial time algorithms are known to exist. A polynomial time algorithm implies that the number of computational steps (which is proportional to the amount of computer time) needed to find a schedule which achieves the optimum value of the objective function is a polynomial function of the parameters of the problem (e.g., the number of jobs, n and/or the number of machines, m). A polynomial time algorithm may require, for example, a number of steps that is on the order of or /f. There are problems, however, for which no polynomial time algorithm is known to exist. These problems are the so-called NP-hard problems. The most efficient algorithms for these problems are exponential in the parameters of the problems. Such algorithms may require, for example, a number of steps that is on the order of 3" or 4". 

The five priority rules mentioned in the previous section, WSPT, HDD, LPT, SST, and CP, are fairly important. They provide optimal sequences in some very simple cases and serve as heuristics for more complicated scheduling models. It is useful to know the properties of these priority rules when designing a complicated computer-based scheduling system. Different modules in such a system may use at given times one of these rules to sequence a subset of the jobs. Or a composite priority rule may be constructed by combining two or more of these simple priority rules in order to minimize a mixture of various objectives. A more in-depth discussion of these five simple priority rules follows. 

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