|Multiproduct plants Dynamic Optimization Mixed Integer Linear/Non-Linear Programming Scheduling|
Multiproduct batch plants (MBPs), also known as specialty plants, are capable Of sequentially producing small amounts of a large number of different products. These plants are commonly used for producing very high value products such as fine chemicals, pharmaceuticals etc. The most important features that make MBPs particularly attractive are their inherent flexibility and the ability to respond quickly to the changing market demands. Owing this inherent flexibility, in MBPs several products share the same units (for e.g., reactors, purificators etc.). There are examples of MBPs where even hundreds of products are processed in the same unit. This mandates the need for proper control of these plants so as to utilize the available resources efficiently and achieve maximum profit. The optimal control problem for the MBPs can be formally stated as: given the dynamic model for each of the processes, available units (reactors, purificators etc.) along with their capacity limits, the storage policy (zero-wait, unlimited intermediate storage etc.) to be followed and available storage capacity for each of the materials, determine the optimal sequence of tasks taking place on each unit, the amount of material being processed and the duration of each task on each unit, so as to achieve the desired objective (maximization of profit, minimization of make-span etc.) while satisfying the market demands within the given time horizon. The above mentioned optimal control problem of MBPs is a highly non-trivial hybrid control problem as it involves both discrete and continuous decisions. In practice, approaches based on standard production recipes are used, where first the recipes are standardized either empirically or via single batch optimization (using the dynamic models of each of the processes) and then the control problem is formulated on the basis of these standardized recipes. However, standardization of recipes removes degrees of freedom from the system and hence the solutions obtained with this approach can be suboptimal as they are confined to pre-determined standard production recipes. Another major disadvantage of these standard recipe based approaches arises from the fact that there are no standard guidelines available for deciding what a suitable standard recipe should be. For the same process there can be several conflicting recipes and there is no way to decide which one of these recipes would be the most suitable for the overall control problem formulation. The
ideal approach'' for the optimal control of MBPs is to include the dynamic model of each of the processes directly into the control problem formulation instead of standardized production recipes. This restores the additional degrees of freedom of the system (which were otherwise removed due to the standardization of the production recipe) and hence this approach potentially yields solutions that are usually much better or at least as good as that obtained with the standard recipe based approaches. However, direct inclusion of the dynamic models, which are usually differential algebraic equations (DAEs), results in alarge'' nonlinear mixed-integer dynamic optimization (MIDO) problem. The combinatorial complexity of MBPs and lack of standard solution methods for MIDO problems render this approach computationally intractable for real world problems. This mandates the need for novel approaches which can yield better solutions than the existing standard recipe based approaches and at the same time are computationally tractable for real world problems. An improved approach for the optimal control of MBPs, which, by imposing a suitable solution structure reduces the degrees of freedom of the system while only slightly affecting the achievable performance, is proposed in this work. This approach helps to recover the solution theoretically obtainable by the ``ideal approach'' more closely than that by the standard recipe approach while keeping a lid on the complexity. The effectiveness of this approach is illustrated with the help of several application examples.