The approaches to scheduling problem formulation in chemical engineering can be broadly classified into two categories, namely, the standard recipe approach (SRA) and the overall optimization approach (OOA). In the SRA, first the recipes are standardized either empirically or via single-batch optimization (SBO) and then the production scheduling problem is formulated on the basis of these standardized recipes. However, the standardization of recipes removes degrees of freedom from the system, and because of this, the solutions obtained with this approach can be suboptimal, whereas in the OOA, the process dynamics are directly included in the scheduling problem formulation instead of the standardized recipes. This restores the additional degrees of freedom of the system, and therefore this approach can yield a better solution. However, direct inclusion of the process dynamics in the scheduling problem formulation results in a mixed-integer dynamic optimization (MIDO) problem, the solution of which can be a formidable task. The objective of this paper is to illustrate the advantages and disadvantages of the SRA and OOA for short-term scheduling of batch chemical processes with the help of illustrative examples. It is shown that the results crucially depend on the cost structure of the specific application as well as on the objective function employed.
This paper proposes a novel hierarchical control architecture for a class of discrete-event systems. Under the proposed control scheme. a max-plus algebra model is introduced on the upper level to provide an optimal online plan. On the lower (implementation) level, min-plus algebra is used to solve cooperation prob lems between sub-plants as well as problems caused by unexpected events. A simple rail traffic example is gIven to show the effectiveness of the idea.
In this paper, we present a method to determine globally optimal schedules for cyclically operated plants where activities have to be scheduled on limited resources. In cyclic operation, a large number of entities is processed in an identical time scheme. For strictly cyclic operation, where the time offset between entities is also identical for all entities, the objective of maximizing throughput is equivalent to the minimization of the cycle time. The resulting scheduling problem is solved by deriving a mixed integer optimization problem from a discrete event model. The model includes timing constraints as well as open sequence decisions for the activities on the resources. In an extension, hierarchical nesting of cycles is considered, which often allows for schedules with improved throughput. The method is motivated by the application to high throughput screening plants, where a specific combination of requirements has to be obeyed (e.g. revisited resources, absence of buffers, or time window constraints).
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